# Mates y TIC - Maths and ICT

## Factoring polynomials

Posted by ricardogm on November 22nd, 2018

Hi

Now you have several tools to factorize polynomials (common factor, Ruffini, second degree formula).

For example, a second degree polynomial can be factorized using the formula, and writing it this way:

a x2 + bx + c =a · (x − s1) · (x − s2

being s1, s2, the solutions or roots of the polynomial.

An important word to use here is root. We say that x=a is a root or zero of the polynomial P(x) if P(a)=0. That means that this same x=a is a solution of the equation P(x)=0

With that in mind, you can use the method we saw for biquadratic equations as well. Use it to find the solutions (=roots) and then you can write the factorization this way:

ax4 + bx2 + c =a·(x-s1)(x-s2)(x-s3)(x-s4)

being s1, s2, s3, s4 the solutions or roots of the polynomial,

Now some exercises to work out in your notebook. Use Symbolab to check them.

#### Factor and Calculate the Roots of the Following Polynomials

a) x3 + x2

b) 2x4 + 4x2

c) x2 − 4

d) x4 − 16

e)  9 + 6x + x2

f)

g) x4 − 10x2 + 9

h) x4 − 2x2 − 3

i) 2x4 + x3 − 8x2 − x + 6

Now solve these equations. You should use the same tools, the only difference is the solution you have to give me.

a) 2x3 − 7x2 + 8x − 3

b) x3 − x2 − 4

c) x3 + 3x2 − 4 x − 12

d) 6x3 + 7x2 − 9x + 2

e) 3x5 − 18x3 + 27x =

f) 2x3 − 50x =

g) 2x5 − 32x =

h) 2x2 + x − 28 =

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