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
1. Answer :
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).
2. Answer :
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).
3. Answer :
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).
4. Answer :
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).
5. Answer :
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).
6. Answer :
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).
7. Answer :
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).
8. Answer :
-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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