factor the polynomial f(x) = x^4 - 4x^3 + 16x - 16 given that 2 and -2 are zeros factored form: f(x)=

Question

secondly identify all real zeros

x=

Answer 1

All rational zeros can be identified by the quotient of all factors of the constant and all factors of the leading coefficient.

Since you are told that 2 and -2 are both zeros this means that (x - 2) and (x + 2) are factors! One approach would be to divide f(x) by the product of those binomials using long division.

When f(x) is divided by the product of the binomials (x² - 4) the result is: x² - 4x + 4

The resulting trinomial factors to (x - 2)^2. Now don't forget the 2 factors we were given!

(x - 2)² (x - 2) (x + 2); or (x - 2)³ (x + 2)

This means that 2, and -2 are the only real zeros!

Answer 2

Hi Shayleigh S.,

A piece of cake. Since 2 and -2 are roots, there must be factors of the form (x+2) and (x-2) in the factoring of the polynomial. So make the product of those 2 terms: (x²-4) . Divide the polynomial by that, and you will have a quadratic term as the quotient. You know what to do from there, right?

--Cheers, --Mr. d.