in-9-26-write-each-expression-as-the-product-of-two-binomials-x27-xx7

Question

In $9-26,$ write each expression as the product of two binomials.
$$
x^{2}+7 x+x+7
$$

Bahar Tehranipoor · Accepted Answer

So for this question, we want to write this expression as the product of two. By normal&#x27;s. This is a kind of an interesting one, because you would think, OK, you have X Triple seven X plus X. We could just make that extra call eight extra seven factor that way. But what they&#x27;re trying to get you to do is to use that trick where you take two terms in the two terms, finds the, um, a normal factor for both of those and then factor like that. So we&#x27;re gonna do is basically just do what they want us to do here. So we&#x27;re gonna take our X squared me highlight. We have X squared and extra mes as our first pair and then our second barrel the seven Excell seven. Let&#x27;s start with our expert plus X. If you break that down, in fact, or that we&#x27;re going to get just X Times X plus one is pretty easy to see that one now for our seven x Class seven. It&#x27;s pretty easy to see this one to. You&#x27;re just going to get seven times X plus one. As you can see, there&#x27;s that common X plus one here and very easily. You can write that answer, and it would be a plus here to write that answer as taking first experts one, then taking the coefficient so X in plus seven, and that would be your answer.

M S · Answer

So we have X squared plus Father X plus six. Then we want back through this. So the first thing we do is we look at our coefficient in this case, one in our last time, which is six. And multiply them together and they would look at our middle term, which is positive block. So we want our number sold part of six. We want them to add to five. So we list of factors of six. So one in six and two and three and we asked ourselves which one of these which pair can adds a positive body. So technically, both pairs and some variations can adds a five. But we need them both to be positive, ruining them boats to be negative. And because this five is positive, we need them both to be positive. So this is now out of the question. So now we know that our pair is two in three. So now we want to expand this middle term here, so exclude stayed the same. And now we&#x27;re expanding our five x So we&#x27;ll have plus two x plus three x because super stories, Father X. So that&#x27;s what we do. We expand their and then just plus six. He&#x27;s never won a group that vice two times in the last two terms and went back there out. The greatest comment Mon Ami. So whenever we factor out variables, we always talked about the lows exponents. So in this case, we&#x27;re in a factor out next to the first, which is just X and X times. What gives Us x squared. And it&#x27;s X and X times. What gives us two X? And that&#x27;s two. They do the same thing to our second wind. The girl&#x27;s coming back to between three and six. Well, the factors of three are one in three. Enough actors of six are 123 and six. So just did a ghost coming Factors three. So I&#x27;m gonna pack two out of three here, and we&#x27;re left with X plus two on the inside. So because this time is the same here and here we have X Plus two and whatever&#x27;s left. So explosives three

Bahar Tehranipoor · Answer

in this exercise. You want to write this expression as the product of two by no meals. So we can either use a trick that we went before or you can start to get good at recognizing how to factor questions like this and write them as products. So what I do when I see something like this is I think of first this constant term, so six, we could write as six times one, and we can write it as two times three. So using you&#x27;re gonna have to use one of these products to help write your expression. So we also know that this constant is positive, but the coefficient in front of excess negative. So that means when we write, our product is going to be something like X minus, something X minus something because that&#x27;s the only way we&#x27;re going to get a positive constant but a negative coefficient in front of X. So we have to have that. So it&#x27;s either going to be negative six times a good one or negative two times negative street. So we confer. This one&#x27;s really easy to just try both, But what we can think is if we have six of one in our head. Quickly. We know that&#x27;s going to give us a negative six accident. Negative one x, which will give us a negative seven x So that&#x27;s what we want. So it has to be two and three. So we put those in. We get X squared minus two X minus three x, which does give us that negative five x plus six.

M S · Answer

So you want to express this function that the product to buy No meals. So buy something. You wanna factor this? So we take the coefficient of the first term and multiply it by the last term, we get negative six and everyone look at our middle turn and say that that&#x27;s Paul&#x27;s a new five. So you know that we want the number so multiplied, indignant six and we want in the ads. So now we lift the factors of negative six. So that&#x27;s one in six in two and three now it now, because it is negative here that one of these factors has to be negative in the payer. So it has to be like negative one or negative six when it can&#x27;t be both because I will give us a positive suits. So it&#x27;s a pine. Which one of these will give us which one of these culmination give us spot positive. But so I&#x27;m just gonna test something. So we have a negative one and positive six. That gives us positive five. So we know that this is our pair here. So now we rewrite it. So have X squared and then we break apart There&#x27;s five X term here still would have minus next, plus six six and then minus six. Thought it was right down this little term to five x here and now it factor further. We&#x27;re gonna group the 1st 2 terms and in group the lasting terms. And I wanted to pull out the greatest common factor supper in the first term. Well, having a regular numbers. So we need to look at our variables and pull out the Lois degree. So just below X, the first on just that. So we say, What time&#x27;s excuses expired? Next? Just X and X times. What gives us needing a fix and that&#x27;s making this one. You can always test by redistributing back. Will we pull it out? So now we&#x27;re gonna pull out a plus sixth in our negative one in our next one. So plus six and six times, look is the six pecs and that&#x27;s X and six times what? Kansas native six. And that&#x27;s a negative one. So because he&#x27;s too artist thing, we know that X minus one is a factor and they would pull down what&#x27;s left so explicit, sick, and now we&#x27;ve expressed it

M S · Answer

So we want to write this expression as the product of two by novels. So basically, we want a factor. So that means we look at the coefficient of the first time and multiply by the last term. And one times 20 gives us 20. And then we look at our little term and we see that it&#x27;s not so you wanted to multiply to 20 in ads and nine. So now I need a list of backers of 20 someone in 20 two into four in five. So now we need to look at which of these combinations will give us positive night. So we know that they&#x27;ll both be positive because our nine term our number nine is positive. So both of these times have to be positive and the only combination that works is this for in this spot because four plus five is No, it&#x27;s not. So now we&#x27;re going to re write this expression using our broken down terms, So I&#x27;m gonna do plus four x splice biotics. Good. All we did was separate this Nynex here and some foreplay spot, and then we bring them in the place 20 and I were gonna group the 1st 2 terms, and in group this last two terms, they would pull out the greatest common factor or the greatest killer. Mommy, You. So in the first actor, we pull out the variable with the lowest degree in this case, just regular X cause x of the first. So you plotted next and we&#x27;re left with explosive or only inside. And you can always check yourself are redistributing this ex bag into it to make sure that you bastard out correctly and from the 2nd 1 with a pull out of five. So plus five and we&#x27;re left with X plus four on the inside. So you know you&#x27;re on the right path when you have the same term here in the same term here. So have explosives for and then whatever we&#x27;re left with in this case too explicit five. And we have expressed it as the factor, too

Bahar Tehranipoor · Answer

in this exercise. We want to write this expression as the party of two by no meals. So I think what these questions they get super simple when you get really quick at recognizing how to solve them. So I&#x27;m gonna take you pretty slowly through the steps of how I would approach this, and it will become really quick in your head, almost intuitive. So with extra bias X minus six. First thing I would do is look at this constant term. So we have a six, which means that we could either right as a product of three times two for six times one. So it&#x27;s six. It&#x27;s really simple because you could only do three times to six times one. Of course, in the future there will be a lot harder ones. We&#x27;re going to consider a lot of cases. But even then, as you get better at doing these, it gets quite intuitive. Which one you should pick. So the next thing you notice after so step one being looked at the constant and basically factory Step two would be Look at these signs. So we have a negative here. Gonna just erase that Sounds a little equals. Yeah. So we have a negative here and we have to consider now, because we have a negative in villa term. It means that when we have a process something right, Donald the X minus something X plus something because that will be the only way that you&#x27;re going to get a negative constant now, in the case where maybe the factors were really different from each other. So you had a small negative and a greater positive factor adding to their together with so give you a positive factor. But in this case, six a small enough to say if we have a, um, negative terminate positive term, we just be really careful looking at it, which was negative. It was positive to make sure that when you then add them together to get your term, it&#x27;s going to be making another. The next thing you&#x27;re going to notice is the, uh, sign of the coefficient that&#x27;s going to be in front of back to the marker. They go, so we&#x27;ll be in front of X. We have a negative coefficient of eggs, a negative constant. So let&#x27;s consider our cases. It&#x27;s just look at six of one First, let&#x27;s say we had six and one. Of course that&#x27;s not going to be X will have X squared plus six x minus. One is going to give us a positive. Like I said, Well, you have a huge difference between the terms. That is usually what ends up happening. You&#x27;re gonna get a positive or a negative like you want. Now how about three and two is probably going to have to be three and 2 61 doesn&#x27;t work. So if we do three and two, let&#x27;s go back to Green real quick. So if we d&#x27;oh, let&#x27;s say we do three here and to hear now, this won&#x27;t be either, because we have X squared. Plus three X minus two exit will give us a positive X. So you should be careful here because it&#x27;s almost the right answer. But it&#x27;s not. So we&#x27;re going to do is we&#x27;re actually just going to switch the sign because now, if we switched the signs and we have a plus to an a minus here we will get X Times x X work minus three plus two X That gives us a negative X and minus six and then that is your answer. So you just gotta be really careful with signs, and it&#x27;ll become quite intuitive.

Problem

In $9-26,$ write each expression as the product o…

Problem 15 Medium Difficulty

In $9-26,$ write each expression as the product of two binomials.
$$
x^{2}+7 x+x+7
$$

Answer

$(x+7)(x+1)$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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Absolute Value - Example 1

Absolute Value - Example 2

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$(x+7)(x+1)$

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Algebra 2 and Trigonometry