Factor 5x^4-10x^3-3x^2+6x

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faiz3507 | High School Teacher | (Level 2) Adjunct Educator

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to factor 5x^4-10x^3-3x^2+6x,

let us write all the terms as a product of factors,

5.x.x.x.x - 5.2.x.x.x - 3.x.x + 3.2.x

we can take 5x^3 common(Greatest common factor) from first two terms and -3x common(GCF) from last two terms,

we get ,

5x^3(x-2) -3x(x-2),

we see that (x-2) is common(GCF) to both the terms, so take (x-2) common

(x-2)(5x^3 - 3x)

also we see that x is common(GCF) in the second factor (5x^3 - 3x),

this can be written as x(5x^2-3)

so the factors are (x-2)x(5x^2-3) = x(x-2)(5x^2-3)

thus the factors are x(x-2)(5x^2-3)