Using a given zero to write a polynomial as a product of linear factors.

Algebra
Tutor: None Selected Time limit: 1 Day

For the polynomial below, 3 is a zero.

f(x)= 3x^3 - 10x^2 + x + 6

Express f(x) as a product of linear factors.

Use fractions or square roots, not decimals.

Oct 17th, 2015

Thank you for the opportunity to help you with your question!

since 3 is a zero,

x-3 = 0

so, f(x)= 3x^3 - 10x^2 + x + 6
= 3x^2(x-3) - x(x-3) -2 (x-3)
= (3x^2 - x -2)(x-3)
=(3x^2 -3x +2x -2)(x-3)
=[3x(x-1)+2(x-1)](x-3)
=(3x+2)(x-1)(x-3)  (Answer)

Let me know incase you need any further help ! Thanks :)
Oct 17th, 2015

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