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, the -2 is a zero.

f(x)= x^3 - 2x^2 - 6x + 4

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

Use fractions or radicals in answers not decimals.

Oct 17th, 2015

f(x) = x^3 - 2x^2 - 6x + 4

x^3 - 2x^2 - 6x + 4 = 0

as - 2 is the root, so one factor is (x - (-2)) = (x + 2)

now dividing the expression by (x + 2), we get

Now we factorize 

= x^2 - 4x + 2

= - (-4) ± √(-4)^2 - 4(1)(2) / 2(1)

= 4 ± √16 - 8 / 2

= 4 ± √8 / 2

= 4 ± 2√2 / 2

= 2 ± √2

So the other two roots are

2 + √2 & 2 - √2

So roots as linear factors are

(x + 2)(x - (2 + √2))(x - (2 - √2))

Oct 17th, 2015

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