Problem

Fill in each blank to explain how to factor $x^{2…

01:09

Problem 11 Medium Difficulty

Consider a trinomial of the form $x^{2}+b x+c$
a. If $c$ is positive, what can be said about the two integers that should be chosen for the factorization?
b. If $c$ is negative, what can be said about the two integers that should be chosen for the factorization?

Answer

a. They are both positive or both negative.
b. One will be positive, the other negative.

Related Courses

Algebra

Elementary and Intermediate Algebra

Chapter 6

Factoring and Quadratic Equations

Section 2

Factoring Trinomials of the Form $x^{2}+b x+c 443$

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Video Transcript

um, we're from this problem. We're considering a try. No meal of the form X squared plus bx plus c. Um, so the first part A is saying if c is positive, what can be said about the two images that should be chosen for the factory ization. So remember, I can factor x squared plus bx plus e. I can factor. This is X plus, Um, let's call this so expose something Times X plus another something. Okay, so the major's always figure out what these two numbers are. So, um, so the two images that we're gonna choose for the factory ization are going to go on these two spots. So now I've see is positive what must be true, Um, about the numbers that go here. Well, um, these two numbers here have to be positive. So these two numbers must be positive because thes two numbers here, they need to multiply these two numbers they need to multiply to see, And if C is positive, the only way that it could be positive is if these two numbers are positive. However, we could also have thes two numbers also being negative or so. These two numbers must both be positive or both. B negative. Um, negative. So if I multiplied to positive numbers together, I will get a positive number. I multiplied to negative numbers together. How also been a negative number. So when we needed you just two positives or two negative numbers. Part B is saying, um, if C is negative, what has to be true about the factory ization? So again, I have X plus something Times X plus another something and still there Talking about these two numbers here now, except to see is negative. So again, I'm gonna multiply these two numbers together here and whatever these two numbers must multiply to see if C is negative. How can we get what? What must be true about these two numbers So that sea is negative? Well, one must be positive and one negative, because a negative number times a positive number, will give me a negative number. So I see is negative. So we get that by multiplying a negative times a positive

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