Question

Consider the polynomial function f(x) = 3r³ - 4x² - 17x+6. Use synthetic division to show that -2 is a zero of f(x). Show your work in the space at the right. If -2 is a zero of f(x), then what is one of the factors of f(x) 2

then
Now that you know one of the factors of f(x), use the result of your synthetic division and your knowledge of factoring to completely factor f(x). Show your work in the space at the right and enter the factored form of f(x) below.​

Answer 1

To show that -2 is a zero of the polynomial function f(x) = 3x³ - 4x² - 17x + 6, you can use synthetic division. The remainder derived from the synthetic division provides proof that -2 is a zero.

To show that -2 is a zero of the polynomial function f(x) = 3x³ - 4x² - 17x + 6, we can use synthetic division.

The coefficients of the polynomial are 3, -4, -17, and 6.

We divide the polynomial by (x + 2), where 2 is the value we want to test as a zero.

Using synthetic division, we set up the division:

-2 | 3 -4 -17 6

Performing the synthetic division, we get:

3 -4 -17 6

-2 -2 8 18

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3 -6 -9 24

The last number in the synthetic division is the remainder.

Since the remainder is 0, it means that -2 is a zero of f(x).