Complete each factoring x^2+8 x+15 =(x+5) ()

Name: Problem 7, Chapter 5: Algebra for College Students
Uploaded: 2022-02-08T19:02:15-08:00
Duration: 4 min 31 s
Channel: Asif Khan
Description: Complete each factoring x^2+8 x+15 =(x+5) ()

Key Concepts

Quadratic Expression

A quadratic expression is a second-degree polynomial typically written in the form ax² + bx + c. Understanding quadratics is fundamental to algebra because they often model parabolic relationships, and factoring them into two binomials is a key method for solving quadratic equations and simplifying expressions.

Product-Sum Method

This method involves finding two numbers that multiply to the constant term (c) of a quadratic and add to the coefficient of the linear term (b). It is a common strategy for factoring quadratic expressions when the leading coefficient is 1, as it allows the expression to be rewritten as a product of two binomials.

Transcript

00:01 Hi, today in this video we will learn the concept of factoring a trinomial and we are given a trinomial that is x squared plus 8x plus 15 equals to one of its factor is given that is x plus 5 and we have to find one of its another factor that is unknown.

00:25 Now is the given trinomial is of the form simply x squared plus 8x plus 15 and that's equals to actually 0 because this is a quadratic equation and and simply in general form it's written is a x squared plus b x plus c equals to 0.

00:51 Where we have a you can see that is 1 here b is 8 and c is 15 and this a that is one is also called learning coefficient and whenever we have a quality equation with the value of a that is the learning coefficient equals to one all we need to find the factors for c and in our case our c is you can see 15 so first we have to find the factors of 15 and factors are those numbers which you will multiply together you will get this 15 in our case so list of factors first make the list of of factors simply and whenever we will make the list of factors you can see that is 1 times 15 will be equals to 15 and you can see 3 times 5 we can get 15 these are the possible pairs and the another task which we have to do is we have to sum these factors sum of factors some of factors you can see here when we will sum 1 plus 5 15 that will give us 16 and when we will add 3 plus 5 they will give us 8 and now among these two pair of factors we have to select date pair which will give us on their product on their product they will give us this 15 as both of they are given but they on their addition they should give this middle from that is you can see b simply and here in our case that should be 8 and you we can see that that is simply in this second pair which satisfies this condition.

02:34 So on their product they give us 15 on their addition they give us 8.

02:39 So we will select these two pairs.

02:43 And simply when we will found these two pairs, when we will identify these two pairs, we have to just write them in a factored expression form...

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