Question

Determine the product, h(x), of the linear and quadratic factors.

Answer 1

Answer:

$h(x)=x^3-17x-4$

Step-by-step explanation:

Given $f(x)=x^2 - 4x -1\ and\ g(x)=x+4$

$h(x)=f(x)\times g(x)$

$(x^2-4x-1)(x+4)\ \ \\Distribute\ parenthesis\\=x^2x+x^2\times \:4+\left(-4x\right)x+\left(-4x\right)\times \:4+\left(-1\right)x+\left(-1\right)\times \:4$

Apply minus-plus rules

$+(-a)=-a$

$=x^2x+4x^2-4x(x)-4\times\:4x-1\times\:x-1\times\:4$

$\\Simplify\\=x^3+4x^2-4x^2-16x-x-4\\=x^3-16x-x-4\\=x^3-17x-4$

$h(x)=x^3-17x-4$