Problems 1-2 : Factor each quadratic trinomial by guess and check.

Problem 1 :

x2 + 19x + 60

Problem 2 :

4x2 + 16x + 15

Problems 2-8 : Factor each quadratic trinomial.

Problem 3 :

2x2 + 11x + 12

Problem 4 :

5x2 - 14x + 8

Problem 5 :

4y2 + 7y - 2

Problem 6 :

4x2 + 19x - 5

Problem 7 :

2x2 - 7x - 15

Problem 8 :

-2x2 - 15x - 7 x2 + 19x + 60

Write two sets of parentheses.

( _ + _ )( _ + _ )

The first term is x2, so the variable terms have a coefficient of 1.

( x + _ )(x +  _ )

The constant term in the trinomial is 60.

Try factors of 60 for the constant terms in the binomials.

(x + 1)(x + 60)  =  x2 + 61x + 60

(x + 2)(x + 30)  =  x2 + 32x + 60

(x + 3)(x + 30)  =  x2 + 33x + 60

(x + 4)(x + 15)  =  x2 + 19x + 60

The factors of x2 + 19x + 60 are (x + 4) and (x + 15).

4x2 + 16x + 15

Write two sets of parentheses.

( _ + _ )( _ + _ )

The first term is 4x2, so at least one variable term has a coefficient other than 1.

( _ x + _ )( _ x + _ )

The coefficient of the x2-term is 4. The constant term in the trinomial is 15.

Try factors of 4 for the coefficients and factors of 15 for the constant terms.

(1x + 15)(4x + 1)  =  4x2 + 61x + 15

(1x + 5)(4x + 3)  =  4x2 + 23x + 15

(1x + 3)(4x + 5)  =  4x2 + 17x + 15

(1x + 1)(4x + 15)  =  4x2 + 19x + 15

(2x + 15)(2x + 1)  =  4x2 + 32x + 15

(2x + 5)(2x + 3)  =  4x2 + 16x + 15

The factors of 4x2 + 16x + 15 are (2x + 5) and (2x + 3).

2x2 + 11x + 12

a = 2 and c = 12; Outer + Inner = 11.

( _ x + _ )( _ x + _ ) The factors of 2x2 + 11x + 12 are (x + 4) and (2x + 3).

5x2 - 14x + 8

a = 5 and c = 8; Outer + Inner = -14.

_ x + _ )( _ x + _ ) The factors of 5x2 - 14x + 8 are (x - 2) and (5x - 4).

4y2 + 7y - 2

a = 4 and c = -2; Outer + Inner = 7.

_ y + _ )( _ y + _ ) The factors of 4y2 + 7y - 2 are (y + 2) and (4y - 1).

4x2 + 19x - 5

a = 4 and c = -5; Outer + Inner = 19.

_ x + _ )( _ x + _ ) The factors of 4x2 + 19x - 5 are (x + 5) and (4x - 1).

2x2 - 7x - 15

a = 2 and c = -15; Outer + Inner = -7.

_ x + _ )( _ x + _ ) The factors of 2x2 - 7x - 15 are (x - 5) and (2x + 3).

-2x2 - 15x - 7

Factor out -1.

=  -1(2x2 + 15x + 7)

a = 2 and c = 7; Outer + Inner = 15.

_ x + _ )( _ x + _ ) So,

-2x2 - 15x - 7  =  -1(x + 7)(2x + 1)

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