Solutions to Factoring Polynomials by Common Factor - Grade 11 Math Questions With Detailed Solutions

Solutions on how factor polynomials by common factor are presented.

Use common factors to factor completely the following polynomials.

a) - 3 x + 9

b) 28 x + 2 x 2

c) 11 x y + 55 x 2 y

d) 20 x y + 35 x 2 y - 15 x y 2

e) 5 y (x + 1) + 10 y 2(x + 1) - 15 x y (x + 1)



Solution

a) Find any common factors in the two terms of - 3 x + 9 by expressing both terms 3 x and 9 in the given binomial as prime factorization.

- 3 x + 9 = - 3 x - 3 3

The greatest common factor is 3 and is factored out. Hence

- 3x + 9 = 3 (- x + 3) = - 3 (x - 3)


b) Write the prime factorization of each of the terms in the given polynomial 28 x + 2 x 2.

28 x + 2 x 2 = 2 2 7 x + 2 x x

The greatest common factor is 2 x and is factored out. Hence

28 x + 2 x 2 = 2 x (14 + x)


c) Write the prime factorization of each of the terms in the given polynomial 11 x y + 55 x 2 y.

11 x y + 55 x 2 y = 11 x y + 5 11 x x y

The greatest common factor is 11 x y and is factored out. Hence

11 x y + 55 x 2 y = 11 x y(1 + 5 x)


d) Write the prime factorization of each of the terms in the given polynomial 20 x y + 35 x 2 y - 15 x y 2.

20 x y + 35 x 2 y - 15 x y 2 = 2 2 5 x y + 5 7 x x y - 3 5 x y y

The greatest common factor is 5 x y and is factored out. Hence

20 x y + 35 x 2 y - 15 x y 2 = 5 x y( 4 + 7 x - 3 y)


e) We start by factoring out the common factor (x + 1) in the given polynomial.

5 y (x + 1) + 10 y 2(x + 1) - 15 x y (x + 1) = (x + 1)(5y + 10y2 - 15 x y)

We now factor the polynomial 5y + 10y2 - 15 x y using the GCF to all three terms.

5 y + 10y2 - 15 x y = 5 y + 2 5 y y - 3 5 y x = 5 y (1 + 2 y - 3 x)

The given polynomial may be factored as follows.

5 y (x + 1) + 10 y 2(x + 1) - 15 x y (x + 1) = 5 y(x + 1)(1 + 2y - 3 x)


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Updated: 20 January 2017 (A Dendane)