Factoring polynomials with a power of 4?

Question

We haven't gone over this in school, so I'm not sure how I would completely factor this polynomial:

q(x) = x^4 - 6x^3 + 4x^2 + 3x + 10

I don't really need a definite answer, just step by step explanations of what I need to do.

Thanks.

hii · Accepted Answer

.
q(x) = x⁴ - 6x³ + 4x² + 3x + 10

q(2) = 16 - 48 + 16 + 6 + 10 = 0..............(x - 2) is fator

q(5) = 625 - 750 + 100 + 15 + 10 = 0 ........ (x - 5) is fator

(x - 2)(x - 5) = x² - 7x + 10

.........................
.......................1... 1... .1
.................―――――――――――――――
...1..-7..10 ｜...1...-6.....4....3....10
........................1...-7....10
.....................――――――――――――――
....................... 1....-6.. ..3
....................... 1....-7...10
....................――――――――――――
....................... .... .1...-7... 10
............................. 1...-7... 10
...........................――――――――
.................................. .........0

q(x) = (x - 2)(x - 5)(x² + x + 1)

ted s · Answer

Use the Rational Root Theorem , try ± 1 , 2, 5 , 10 for possible rational roots ...2 & 5 work...

thus [ x - 2 ] [ x - 5 ] { quadratic } = q(x)

alex · Answer

q(2)=q(5)=0---> (x-2) , (x-5) are factors
and you can do

Anonymous · Answer

yes

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Factoring polynomials with a power of 4?

4 Answers