Mates y TIC - Maths and ICT

Actividades de Matemáticas con TIC - Math Activities with ICT - - - (matesytic@gmail.com) Ricardo García Mesa

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) trinomio

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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