Question

The polynomial p(x)=x^3-19x-30p(x)=x 3 −19x−30p, (, x, ), equals, x, cubed, minus, 19, x, minus, 30 has a known factor of (x+2)(x+2)(, x, plus, 2, ). Rewrite p(x)p(x)p, (, x, )as a product of linear factors.

Answer 1

∴P(x) = (x-5)(x+3)(x+2)

Explanation:

A cubic polynomial has three zeros.

Given polynomial,

P(x)= x³-19x-30 has a know factor of (x+2).

To find the other zeros we first divide the polynomial by (x+2)

x+2)x³-19x-30 (x²-2x-15

x³ +2x²

- -

_______________

-2x²-19x-30

-2x²-4x

+ +

_______________

-15x-30

-15x-30

________

×

We know that,

Polynomial= quotient×division +reminder

∴ x³-19x-30=(x²-2x-15)(x+2)

=(x²-5x+3x-15)(x+2)

={x(x-5)+3(x-5)}(x+2)

=(x-5)(x+3)(x+2)

∴P(x) = (x-5)(x+3)(x+2)