When we factor a trinomial with a leading coefficient of 1, we reverse the FOIL process. Write two sets of parentheses and start with the first spots: if we see x^{2}, we know that is produced by x • x. We then find the last positions from two integers whose sum is b and whose product is c.
Test Objectives:•Demonstrate a general understanding of factoring a trinomial
•Demonstrate the ability to find two integers whose sum is b and whose product is c
•Demonstrate the ability to factor a trinomial into the product of two binomials
Factoring Trinomials with a Leading Coefficient of 1 Test:
#1:
Instructions: Factor each.
a) v^{2} + 11v + 30
b) x^{2} - 3x - 4
#2:
Instructions: Factor each.
a) x^{2} - 4x - 28
b) x^{2} + 15x + 44
#3:
Instructions: Factor each.
a) 2x^{2} + 16x + 24
b) 3m^{2} - 18m - 81
#4:
Instructions: Factor each.
a) 2x^{2} + 14xy - 36y^{2}
#5:
Instructions: Factor each.
a) 6x^{2} + 36xy + 30y^{2}
Written Solutions:
Solution:
a) (v + 5)(v + 6)
b) (x - 4)(x + 1)
Solution:
a) prime
b) (x + 4)(x + 11)
Solution:
a) 2(x + 6)(x + 2)
b) 3(m + 3)(m - 9)
Solution:
a) 2(x + 9y)(x - 2y)
Solution:
a) 6(x + 5y)(x + y)