When we factor a trinomial into the product of two binomials, we are essentially reversing the FOIL process. The easier scenario occurs when the leading coefficient is one. In this case, the first position for each binomial is given. The second position for each binomial is obtained by finding two integers whose sum is b (coefficient for the variable raised to the first power) and whose product is c (constant term).
Test Objectives:•Demonstrate the ability to factor out the GCF or -(GCF) from a group of terms
•Demonstrate the ability to factor a trinomial into the product of two binomials
•Demonstrate the ability to factor a trinomial when two variables are involved
Factoring Trinomials (Leading Coefficient of 1) Test:
#1:
Instructions: Factor each trinomial into the product of two binomials.
a) x^{2} - 15x + 50
b) k^{2} - 6k - 16
#2:
Instructions: Factor each trinomial into the product of two binomials.
a) x^{2} + 6x - 7
b) b^{2} + 6b + 8
#3:
Instructions: Factor each trinomial into the product of two binomials.
a) r^{2} + 6r - 12
b) 6x^{2} + 54x + 84
#4:
Instructions: Factor each trinomial into the product of two binomials.
a) 4m^{2} - 12mn - 216n^{2}
b) 5x^{2} - 20xy - 60y^{2}
#5:
Instructions: Factor each trinomial into the product of two binomials.
a) 6x^{2} - 90xy + 324y^{2}
b) 2m^{2} - 16mn + 24n^{2}
Written Solutions:
Solution:
a) (x - 5)(x - 10)
b) (k - 8)(k + 2)
Solution:
a) (x - 1)(x + 7)
b) (b + 4)(b + 2)
Solution:
a) prime
b) 6(x + 7)(x + 2)
Solution:
a) 4(m - 9n)(m + 6n)
b) 5(x + 2y)(x - 6y)
Solution:
a) 6(x - 9y)(x - 6y)
b) 2(m - 2n)(m - 6n)