Question

The polynomial p(x)=x^3+3x^2-4 has a known factor of (x-1). Rewrite p(x) as a product of linear factors

Answer 1

Answer:

$p(x) = x^{3} + 3x^{2} -4 = (x-1)(x+2)(x+2)$

Step-by-step explanation:

The given polynomial $p(x) = x^{3} + 3x^{2} -4$

Now, given that (x-1) is a factor of the above equation.

Now, divide the given polynomial with the factor (x-1)

By Long division, we get

Quotient =  $4x^{2} + 4x + 4$ and Remainder = 0

So, by the Remainder theorem

$p(x) = x^{3} + 3x^{2} -4 = (4x^{2} + 4x + 4) \times (x-1)$

Now, Simplifying the quotient further, we get

$4x^{2} + 4x + 4$  =  $4x^{2} + 2x + 2x+ 4$

=  $x(x+2)+ 2(x+2)$  

or,  $4x^{2} + 4x + 4$ = (x+2)(x+2)

Hence, the given polynomial $p(x) = x^{3} + 3x^{2} -4$ can be written as a product of linear factors.

$p(x) = x^{3} + 3x^{2} -4 = (x-1)(x+2)(x+2)$

Answer 2

Answer:

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

Step-by-step explanation: