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The polynomial p(x) = 5x^3 – 9x^2 - 6x + 8 has a known factor of (x + 1).
Rewrite p(x) as a product of linear factors.

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Answer:

[tex](x+1)(5x-4)(x-2)[/tex]

Step-by-step explanation:

We know that (x+1) is a factor, so we can use synthetic division to factor it out of [tex]5x^3-9x^2-6x+8[/tex].

Once factored, we get [tex](x+1)(5x^2-14x+8)[/tex]

Now all we need to do is factor[tex](5x^2-14x+8)[/tex]

[tex](5x^2-14x+8)=(5x-4)(x-2)[/tex]

This gives us the answer [tex](x+1)(5x-4)(x-2)[/tex].

p(x) as a product of its linear factors is:

[tex]p(x) = (x+1)(x-2)(5x-4)[/tex]

The given polynomial is:

[tex]p(x) = 5x^3-9x^2-6x+8[/tex]

The divisor = x + 1

The division expression can be written as:

[tex]\frac{5x^3 - 9x^2 -6x + 8 }{x+1} \\\\= 5x^2-14x+8[/tex]

Factorize [tex]5x^2-14x+8[/tex]

[tex]5x^2-14x+8\\\\5x^2-10x-4x+8\\\\5x(x-2)-4(x-2)\\\\(5x-4)(x-2)[/tex]

Therefore, p(x) as a product of its linear factors is written as:

[tex]p(x) = (x+1)(x-2)(5x-4)[/tex]

Learn more here: https://brainly.com/question/18818577

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