Question

Use synthetic division to determine whether the x- 6 is a factor of 4x3^3-26x^2+ 8x + 24.

Answer 1

Given the polynomial:

$4x^3-26x^2+8x+24$

Let's use synthetic division to detetrmine whether (x - 6) is a factor of the polynomial.

Set x - 6 to zero and solve for x.

x - 6 = 0

Add 6 to both sides:

x - 6 + 6 = 0 + 6

x = 6

Let's divide the coefficients in the polynomial by 6.

We have the synthetic division below:

The last value in the result line is the remainder.

After dividing the polynomial, we can see there is no remainder.

Since there is no remainder, we can say x-6 is a factor of the given polynomial.

ANSWER:

Yes, it is a factor