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The polynomial p ( x ) = x 3 + 3 x 2 − 4 p(x)=x 3 +3x 2 −4p, left parenthesis, x, right parenthesis, equals, x, cubed, plus, 3, x, squared, minus, 4 has a known factor of ( x − 1 ) (x−1)left parenthesis, x, minus, 1, right parenthesis. Rewrite p ( x ) p(x)p, left parenthesis, x, right parenthesis as a product of linear factors. p ( x ) =

Respuesta :

Answer:

p(x)= (x-1)(x+2)^2

Step-by-step explanation:

The linear factors of the given polynomial is P(x) = x³ + 3x²-4 = (x-1)(x+2)(x+2).

What are the linear factors of a polynomial?

When a polynomial of higher degree is expressed as the product of two or more factors of lower degree, then they are called linear factors of that polynomial.

Here, the given polynomial is P(x) = x³ + 3x²-4.

Therefore, P(x)

= x³ + 3x²-4

= x²(x - 1) + 4x(x-1) +4(x-1)

= (x-1)(x² + 4x + 4)

= (x-1)(x+2)²

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

Therefore, P(x) = x³ + 3x²-4 = (x-1)(x+2)(x+2).

Learn more about linear factors of a polynomial here: https://brainly.com/question/26354419

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