7.2E: Exercises
( \newcommand{\kernel}{\mathrm{null}\,}\)
Practice Makes Perfect
Factor Trinomials of the Form x2+bx+c
In the following exercises, factor each trinomial of the form x2+bx+c
x2+4x+3
- Answer
-
(x+1)(x+3)
y2+8y+7
m2+12m+11
- Answer
-
(m+1)(m+11)
b2+14b+13
a2+9a+20
- Answer
-
(a+4)(a+5)
m2+7m+12
p2+11p+30
- Answer
-
(p+5)(p+6)
w2+10w+21
n2+19n+48
- Answer
-
(n+3)(n+16)
b2+14b+48
a2+25a+100
- Answer
-
(a+5)(a+20)
u2+101u+100
x2−8x+12
- Answer
-
(x−2)(x−6)
q2−13q+36
y2−18y+45
- Answer
-
(y−3)(y−15)
m2−13m+30
x2−8x+7
- Answer
-
(x−1)(x−7)
y2−5y+6
p2+5p−6
- Answer
-
(p−1)(p+6)
n2+6n−7
y2−6y−7
- Answer
-
(y+1)(y−7)
v2−2v−3
x2−x−12
- Answer
-
(x−4)(x+3)
r2−2r−8
a2−3a−28
- Answer
-
(a−7)(a+4)
b2−13b−30
w2−5w−36
- Answer
-
(w−9)(w+4)
t2−3t−54
x2+x+5
- Answer
-
prime
x2−3x−9
8−6x+x2
- Answer
-
(x−4)(x−2)
7x+x2+6
x2−12−11x
- Answer
-
(x−12)(x+1)
−11−10x+x2
Factor Trinomials of the Form x2+bxy+cy2
In the following exercises, factor each trinomial of the form x2+bxy+cy2
p2+3pq+2q2
- Answer
-
(p+q)(p+2q)
m2+6mn+5n2
r2+15rs+36s2
- Answer
-
(r+3s)(r+12s)
u2+10uv+24v2
m2−12mn+20n2
- Answer
-
(m−2n)(m−10n)
p2−16pq+63q2
x2−2xy−80y2
- Answer
-
(x+8y)(x−10y)
p2−8pq−65q2
m2−64mn−65n2
- Answer
-
(m+n)(m−65n)
p2−2pq−35q2
a2+5ab−24b2
- Answer
-
(a+8b)(a−3b)
r2+3rs−28s2
x2−3xy−14y2
- Answer
-
prime
u2−8uv−24v2
m2−5mn+30n2
- Answer
-
prime
c2−7cd+18d2
Mixed Practice
In the following exercises, factor each expression.
u2−12u+36
- Answer
-
(u−6)(u−6)
w2+4w−32
x2−14x−32
- Answer
-
(x+2)(x−16)
y2+41y+40
r2−20rs+64s2
- Answer
-
(r−4s)(r−16s)
x2−16xy+64y2
k2+34k+120
- Answer
-
(k+4)(k+30)
m2+29m+120
y2+10y+15
- Answer
-
prime
z2−3z+28
m2+mn−56n2
- Answer
-
(m+8n)(m−7n)
q2−29qr−96r2
u2−17uv+30v2
- Answer
-
(u−15v)(u−2v)
m2−31mn+30n2
c2−8cd+26d2
- Answer
-
prime
r2+11rs+36s2
Everyday Math
Consecutive integers Deirdre is thinking of two consecutive integers whose product is 56. The trinomial x2+x−56 describes how these numbers are related. Factor the trinomial.
- Answer
-
(x+8)(x−7)
Consecutive integers Deshawn is thinking of two consecutive integers whose product is 182. The trinomial x2+x−182 describes how these numbers are related. Factor the trinomial describes how these numbers are related. Factor the trinomial.
Writing Exercises
Many trinomials of the form x2+bx+c factor into the product of two binomials (x+m)(x+n). Explain how you find the values of m and n.
- Answer
-
Answers may vary
How do you determine whether to use plus or minus signs in the binomial factors of a trinomial of the form x2+bx+c where b and c may be positive or negative numbers?
Will factored x2−x−20 as (x+5)(x−4). Bill factored it as (x+4)(x−5). Phil factored it as (x−5)(x−4). Who is correct? Explain why the other two are wrong.
- Answer
-
Answers may vary
Look at Example, where we factored y2+17y+60. We made a table listing all pairs of factors of 60 and their sums. Do you find this kind of table helpful? Why or why not?
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. After reviewing this checklist, what will you do to become confident for all goals?