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

NOT true about the missing values?

Kristoff needs to fill in the blanks below to factor x2 - 12x + 20. Which of the following-example-1
User Sam French
by
8.6k points

1 Answer

6 votes

Answer:

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.

User Eychu
by
8.4k points
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