Question

Sorry this a lot.

According to the synthetic division below, which of the following statements are true?
-4| 3 7 -20
-12 20
______________
3 -5 0

Check all that apply.


A. (x - 4) is a factor of 3x^2 + 7x - 20.
B. (x + 4) is a factor of 3x^2 + 7x - 20.
C. The number -4 is a root of F(x) = 3x^2 + 7x - 20.
D. The number 4 is a root of F(x) = 3x^2 + 7x - 20.
E. (3x^2 + 7x - 20) (x - 4) = (3x - 5)
F. (3x^2 + 7x - 20) (x + 4) = (3x - 5)

Answer 1

In synthetic division, when we divide the polynomial 3x^2 + 7x - 20 by x - 4, we get a quotient of 3x - 5. This allows us to determine which statements are true.

Step-by-step explanation:

The synthetic division shown above is dividing the polynomial 3x^2 + 7x - 20 by x - 4. The result of the division is 3x - 5. From this, we can determine the following:

• (x - 4) is a factor of 3x^2 + 7x - 20, so statement A is true.
• (x + 4) is not a factor of the polynomial, so statement B is false.
• The number -4 is a root of the polynomial, so statement C is true.
• The number 4 is not a root of the polynomial, so statement D is false.
• The expression (3x^2 + 7x - 20) (x - 4) simplifies to (3x - 5), so statement E is true.
• The expression (3x^2 + 7x - 20) (x + 4) does not simplify to (3x - 5), so statement F is false.

Answer 2

The correct answers are,

The number -4 is a root of F(x) = 3^x2 + 7x - 20.

(x + 4) is a factor of 3x^2 + 7x - 20.

(3x^2 + 7x - 20) (x + 4) = (3x - 5)