Question

The polynomial p(x)=3x^3-5x^2-4x+4p(x)=3x 3 −5x 2 −4x+4p, left parenthesis, x, right parenthesis, equals, 3, x, cubed, minus, 5, x, squared, minus, 4, x, plus, 4 has a known factor of (x-2)(x−2)left parenthesis, x, minus, 2, right parenthesis. Rewrite p(x)p(x)p, left parenthesis, x, right parenthesis as a product of linear factors.

Answer 1

Answer:

(3x-2)(x-2)(x+1)

Step-by-step explanation:

Here, given a factor of 3x^3 -5x^2 -4x + 4, we want to fully express the polynomial as a product of its linear factor

To find the other factors, we shall divide the polynomial by the given factor

That will be;

3x^3-5x^2-4x + 4/(x-2)

we use long polynomial division here

Please check attachment for the division

The division yields 3x^2 + x - 2

what is left is to factorize the expression above

That will be;

3x^2 + 3x -2x - 2

= 3x(x + 1) -2(x + 1)

So we have (3x-2)(x + 1)

So the complete factorization will be;

3x^3-5x^2-4x + 4 = (x-2)(3x-2)(x+1)