Question

Factor x^2 – 7x + 10

Answer 1

what 2 numbers multiply to get -10 and add to get -7
-2 and -5

(x-2)(x-5)
this only works if the number in front of the x^2 term is 1

Answer 2

Step-by-step explanation: The trinomial shown here is in a special form that can be factored as the product of two binomials.

The way you do that is by setting up 2 sets of

parenthses that will contain your 2 binomials.

The first term in each binomial will be a factor of x².

Since x² factors x · x, we will use an x as the first term in each binomial.

To fill the second position in each binomial,

we will use factors of 10 that give us a sum of -7.

So how do we get factors of a positive

number that add to a negative number?

Well 10 for instance can be thought of as 10 · 1

but it can also be thought of as -10 · -1.

Another option would then be -5 · -2.

Since -5 + -2 is -7, we will use those.

So our answer is (x - 5)(x - 2).