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EXAMPLE 1. Find a common monomial factor. Factor the polynomial completely. a. x 3 + 2 x 2 – 15 x. = x ( x 2 + 2 x – 15). Factor common monomial. = x ( x + 5)( x – 3 ). Factor trinomial. = 2 y 3 ( y 2 – 9). b. 2 y 5 – 18 y 3. Factor common monomial.

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EXAMPLE 1

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EXAMPLE 1

Find a common monomial factor

Factor the polynomial completely.

a. x3 + 2x2 – 15x

= x(x2 + 2x – 15)

Factor common

monomial.

= x(x + 5)(x – 3)

Factor trinomial.

= 2y3(y2 – 9)

b. 2y5 – 18y3

Factor common

monomial.

= 2y3(y + 3)(y – 3)

Difference of two

squares

= 4z2(z2 – 4z + 4)

c. 4z4 – 16z3 + 16z2

Factor common

monomial.

= 4z2(z – 2)2

Perfect square trinomial


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= 2z2 (2z)3 – 53

EXAMPLE 2

Factor the sum or difference of two cubes

Factor the polynomial completely.

= x3 + 43

a. x3 + 64

Sum of two cubes

= (x + 4)(x2 – 4x + 16)

= 2z2(8z3 – 125)

b. 16z5 – 250z2

Factor common monomial.

Difference of two cubes

= 2z2(2z – 5)(4z2 + 10z + 25)


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for Examples 1 and 2

GUIDED PRACTICE

Factor the polynomial completely.

1.x3 – 7x2 + 10x

ANSWER

x( x – 5 )( x – 2 )

2. 3y5 – 75y3

ANSWER

3y3(y – 5)(y + 5 )

3. 16b5 + 686b2

2b2(2b + 7)(4b2 –14b + 49)

ANSWER

4. w3 – 27

ANSWER

(w – 3)(w2 + 3w + 9)


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