Question

Kristoff needs to fill in the blanks below to factor x2 - 12x + 20. Which of the following is

NOT true about the missing values?

Answer 1

c. The numbers must have a sum of 12.

Explanation:

Given a polynomial
`x^2+cx+d`, in its factored form,
`(x+a)(x+b)`, the following must be true:

`a + b = c`

`a \cdot b = d`

In the given polynomial, we can assign the following values:

`c = -12`

`d=20`

Using these values, we can go through the answer choices:

Remember: we are finding the statement that is NOT true.

a) "the numbers must have a product of 20"

If we look at the equation
`ab = d`, we can see that this statement is correct; therefore, we should not check it.

b) "the numbers must both be negative"

This is not necessarily true, as a positive plus a negative can still result in a negative; however, in this case, it is true (if we factor, we get a = -2, b = -10).

c) "the numbers must have a sum of 12"

This is false, since c = -12. The numbers (a and b) must add to negative 12, not positive 12; therefore c) is the correct answer.