# FACTORING POLYNOMIALS EXAMPLES

## About "Factoring Polynomials Examples"

Factoring Polynomials Examples :

Here we are going to see some example problems on factoring polynomials.

## Factoring Polynomials Examples - Examples

Question 1 :

Factorise the following expressions:

(i) 2a2 + 4a2 b + 8a2 c

Solution :

=  2a2 + 4a2 b + 8a2 c

By factoring 2a from the three terms, we get

=  2a (a + 2ab + 4ac)

(ii)  ab - ac - mb + mc

Solution :

=  ab - ac - mb + mc

=  a(b - c) - m(b - c)

=  (a - m) (b - c)

Question 2 :

Factorise the following:

(i) x2 + 4x + 4

Solution :

=  x2 + 4x + 4

=  x2 + 2 ⋅ ⋅ 2 + 22

=  (x + 2)2

(ii)  3a2 - 24ab + 48b2

Solution :

=  3a2 - 24ab + 48b2

=  3 (a2 - 8ab + 16b2)

=  3 [a2 - 2a(4b) + (4b)2]

=  3 (a - 4b)2

(iii)  x5 - 16x

Solution :

=  x5 - 16x

=  x(x4 - 16)

=  x [(x2)2 - 42]

=  x(x2 + 4)(x2 - 4)

=  x(x2 + 4)(x + 2)(x - 2)

(iv)  m2 + 1/m2 - 23

Solution :

m2 + 1/m2 - 23  =  m2 + 1/m2 - 25 + 2

=  (m2 + 1/m2  + 2) - 25

=  (m + (1/m))- 52

=  (m + (1/m) + 5) (m + (1/m) - 5)

(v)  6 - 216 x2

Solution :

=  6 - 216 x2

=  6(1 - 36x2)

=  6[1 - (6x)2]

=  6(1 + 6x)(1 - 6x)

(vi)  a2 + 1/a2 - 18

Solution :

a2 + 1/a2 - 18  =  a2 + 1/a2 - 16 - 2

=  (a2 + 1/a2 - 2) - 16

=  (a - (1/a))- 42

=  (a + (1/a) + 4) (a + (1/a) - 4)

Question 3 :

Factorise the following:

(i)  4x2 +  9y2 + 25z2 + 12xy + 30yz + 20xz

Solution :

=  4x2 +  9y2 + 25z2 + 12xy + 30yz + 20xz

=  (2x)2+(3y)2+(5z)2+2(2x)(3y)+2(3y) (5z)+2(5z)(2x)

=  (2x + 3y + 5z)2

(ii)  25x2 + 4y2 + 9z2 - 20xy + 12yz - 30zx

Solution :

=  25x2 + 4y2 + 9z2 - 20xy + 12yz - 30zx

=  (5x)2+(-2y)2+(-3z)2+2(5x)(-2y)+2(-2y)(3z)+2(-3z)(5x)

=  (5x - 2y - 3z)2 After having gone through the stuff given above, we hope that the students would have understood, "Factoring Polynomials Examples"

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