Factors of Algebraic Expressions: Worksheets, Online Test and Calculators

Factors of algebraic expressions worksheets, solved worksheet problems or exercises with step-by-step work, formative assessment as online test, calculator and more learning resources to learn, practice, assess and master the basic math skills of algebra.

Factors of Algebraic Expressions
Name Grade School
Date Questions20 Score

1
2y2+16y+24
2
x2-17x+42
3
x2-6x+8
4
y2-7y+10
5
x2-5x+6
6
5y2+25y+30
7
z2-9z+14
8
x2-9x+20
9
y2-8y+15
10
y2-10y+16
11
x2-15x+50
12
x2-7x+10
13
2z2+12z+18
14
y2-16y+55
15
x2-11x+30
16
y2-12y+20
17
z2-11z+24
18
x2-4x-21
19
3m2+15m+18
20
x2-4x-12

Solved Worksheet Problems
Show All Workout
1
2y2+16y+24
2 (y+2) (y+6)
Solution
2y2+16y +24 = 0
2(y2+8y +12) = y2+8y +12
.`. Factors of 12 = 2 x 6 and 2 + 6 = 8
=> y2+2y+6y+12
=> y(y+2) + 6(y+2)
=> 2 (y+2) (y+6)
2
x2-17x+42
(x-3) (x-14)
Solution
x2-17x +42 = 0
.`. Factors of 42 = 3 x 14 and 3 + 14 = 17
=> x2-3x-14x+42
=> x(x-3) - 14(x-3)
=> (x-3) (x-14)
3
x2-6x+8
(x-2) (x-4)
Solution
x2-6x +8 = 0
.`. Factors of 8 = 2 x 4 and 2 + 4 = 6
=> x2-2x-4x+8
=> x(x-2) - 4(x-2)
=> (x-2) (x-4)
4
y2-7y+10
(y-2) (y-5)
Solution
y2-7y +10 = 0
.`. Factors of 10 = 2 x 5 and 2 + 5 = 7
=> y2-2y-5y+10
=> y(y-2) - 5(y-2)
=> (y-2) (y-5)
5
x2-5x+6
(x-2) (x-3)
Solution
x2-5x +6 = 0
.`. Factors of 6 = 2 x 3 and 2 + 3 = 5
=> x2-2x-3x+6
=> x(x-2) - 3(x-2)
=> (x-2) (x-3)
6
5y2+25y+30
5 (y+2) (y+3)
Solution
5y2+25y +30 = 0
5(y2+5y +6) = y2+5y +6
.`. Factors of 6 = 2 x 3 and 2 + 3 = 5
=> y2+2y+3y+6
=> y(y+2) + 3(y+2)
=> 5 (y+2) (y+3)
7
z2-9z+14
(z-2) (z-7)
Solution
z2-9z +14 = 0
.`. Factors of 14 = 2 x 7 and 2 + 7 = 9
=> z2-2z-7z+14
=> z(z-2) - 7(z-2)
=> (z-2) (z-7)
8
x2-9x+20
(x-4) (x-5)
Solution
x2-9x +20 = 0
.`. Factors of 20 = 4 x 5 and 4 + 5 = 9
=> x2-4x-5x+20
=> x(x-4) - 5(x-4)
=> (x-4) (x-5)
9
y2-8y+15
(y-3) (y-5)
Solution
y2-8y +15 = 0
.`. Factors of 15 = 3 x 5 and 3 + 5 = 8
=> y2-3y-5y+15
=> y(y-3) - 5(y-3)
=> (y-3) (y-5)
10
y2-10y+16
(y-2) (y-8)
Solution
y2-10y +16 = 0
.`. Factors of 16 = 2 x 8 and 2 + 8 = 10
=> y2-2y-8y+16
=> y(y-2) - 8(y-2)
=> (y-2) (y-8)
11
x2-15x+50
(x-5) (x-10)
Solution
x2-15x +50 = 0
.`. Factors of 50 = 5 x 10 and 5 + 10 = 15
=> x2-5x-10x+50
=> x(x-5) - 10(x-5)
=> (x-5) (x-10)
12
x2-7x+10
(x-2) (x-5)
Solution
x2-7x +10 = 0
.`. Factors of 10 = 2 x 5 and 2 + 5 = 7
=> x2-2x-5x+10
=> x(x-2) - 5(x-2)
=> (x-2) (x-5)
13
2z2+12z+18
2 (z+3) (z+3)
Solution
2z2+12z +18 = 0
2(z2+6z +9) = z2+6z +9
.`. Factors of 9 = 3 x 3 and 3 + 3 = 6
=> z2+3z+3z+9
=> z(z+3) + 3(z+3)
=> 2 (z+3) (z+3)
14
y2-16y+55
(y-5) (y-11)
Solution
y2-16y +55 = 0
.`. Factors of 55 = 5 x 11 and 5 + 11 = 16
=> y2-5y-11y+55
=> y(y-5) - 11(y-5)
=> (y-5) (y-11)
15
x2-11x+30
(x-5) (x-6)
Solution
x2-11x +30 = 0
.`. Factors of 30 = 5 x 6 and 5 + 6 = 11
=> x2-5x-6x+30
=> x(x-5) - 6(x-5)
=> (x-5) (x-6)
16
y2-12y+20
(y-2) (y-10)
Solution
y2-12y +20 = 0
.`. Factors of 20 = 2 x 10 and 2 + 10 = 12
=> y2-2y-10y+20
=> y(y-2) - 10(y-2)
=> (y-2) (y-10)
17
z2-11z+24
(z-3) (z-8)
Solution
z2-11z +24 = 0
.`. Factors of 24 = 3 x 8 and 3 + 8 = 11
=> z2-3z-8z+24
=> z(z-3) - 8(z-3)
=> (z-3) (z-8)
18
x2-4x-21
(x+3) (x-7)
Solution
x2-4x -21 = 0
.`. Factors of -21 = 3 x -7 and -7 + 3 = -4
=> x2+3x-7x-21
=> x(x+3) - 7(x+3)
=> (x+3) (x-7)
19
3m2+15m+18
3 (m+2) (m+3)
Solution
3m2+15m +18 = 0
3(m2+5m +6) = m2+5m +6
.`. Factors of 6 = 2 x 3 and 2 + 3 = 5
=> m2+2m+3m+6
=> m(m+2) + 3(m+2)
=> 3 (m+2) (m+3)
20
x2-4x-12
(x+2) (x-6)
Solution
x2-4x -12 = 0
.`. Factors of -12 = 2 x -6 and -6 + 2 = -4
=> x2+2x-6x-12
=> x(x+2) - 6(x+2)
=> (x+2) (x-6)

Worksheet: Factors of Algebraic Expressions

Factors of algebraic expressions worksheet is the largest collection of practice problems and solved exercises which can be served as homework, classwork or assignment problems for the students to learn, practice, assess, iterate and master the skills of how to solve such algebra problems in basic mathematics.

Online Test
00:00
Start my Challenge
Find the Factors : 4z2+52z +120
Find the Factors : x2-9x +20
Find the Factors : y2-3y -10
Find the Factors : p2-15p +44
Find the Factors : p2-15p +50
Find the Factors : 5p2+125p +230
Find the Factors : y2+11y +28
Find the Factors : y2+15y +26
Find the Factors : 4y2+100y +184
Find the Factors : x2+9x +14

Online Test: Factors of Algebraic Expressions

This online test to find the factors of algebraic expressions is a formative assessment which can be used as homework, classwork or assignment problems to assess and improve the learner's math skills on algebra.