Question

Directions: Find the prime factors of the polynomials





1.



a. 2a2 - 2b2

b. 6x2 - 6y2

c. 4x2 - 4

d. ax2 - ay2

e. cm2 - cn2



2.

f. st2 - s

g. 2x2 - 18

h. 2x2 - 32

i. 3x2 - 27y2

j. 18m2 - 8



3.

k. 12a2 - 27b2

l. 63c2 - 7

m. x3 - 4x

n. y3 - 25y

o. z3 - z



4.

p. 4c3 - 49c

q. 9db2 - d

r. 4a3 - ab2

s. 4a2 - 36

t. x4 - 1


5.

u. 3x2+ 6x

v. 4r2 - 4r - 48

w. x3 - 7x2 + 10x

x. 4x2 -6 x - 48

y. 16x2 - x2 v 4

Please help I don't understand how to do this pleasssseeeeee help I need to hand it in by tomorrow

Answer 1

Usually people don't talk about "prime factors" of polynomials, but a complete factorization should do the job. Here are a few:

a. 2a^2 - 2b^2
= 2(a^2-b^2)
= 2(a-b)(a+b)

b. 6x^2 - 6y^2
= 6(x^2-y^2)
= 2*3(x-y)(x+y)

c. 4x^2 - 4
= 4(x^2-1)
= 2*2(x-1)(x+1)

d. ax^2 - ay^2
= a(x^2-y^2)
= a(x-y)(x+y)

e. cm^2 - cn^2
= c(m^2-n^2)
= c(m-n)(m+n)

w. x^3 - 7x^2 + 10x
= x(x^2-7x+10)
= x(x-2)(x-5)

Now you try some. It looks like this is mainly a set of exercises on the difference of squares.