High School Practice Problems
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Khan Academy Algebra Practice
Mendham High School
Ixl Algebra 2
Application of Factoring Quiz
Solve by factoring.
1. Factor x
2
+ 5x + 6 = 0.
x = 3 and x = -1/5
x = -2 and x = -3
x = 2/3 and x = -1/7
x = 2/5 and x = -1
2. Factor the expression 3x
2
+ 12x + 9 completely.
3(x + 3)(x + 1)
5(x + 4)(x + 2)
7(x + 3)(x + 1.5)
(2x + 3)(x)
3. Solve the quadratic equation by factoring: 6x
2
- 13x + 6 = 0.
x = 1/2 and x = 4
x = 5/4 and x = -1/2
x = 1/2 amd x = -1/2
x = 3/2 and x = 2/3
4. Factor the following expression: 3x
2
- 5y
2
(√3x + √5y)(√3x - √5y)
(√2x + √1y)(√7x - √5y)
(√x + √y)(√3x - √4y)
(√1.5x + √5y)(√5x - √6y)
5. Find the roots of the quadratic equation by factoring: 2x
2
- 7x + 3 = 0.
x = 1 and x = 3
x = 3 and x = -1/3
x = 1/2 and x = 3
x = 1/4 and x = 3
6. Factor the following expression completely: 8x
3
- y
3
.
(x² - 2)(3x⁴ + 6x² + 9)
(2x² - 5)(7x⁴ + 6x² + 10)
(2x² - 3)(3x⁴ + 5x² + 9)
(2x - y)(4x² + 2xy + y²)
7. Solve the quadratic equation by factoring: 6x
4
- 7x
2
+ 2 = 0.
x = ±√(1/3) and x = ±√(2/5)
x = ±√(1/2) and x = ±√(2/3)
x = ±√(1/6) and x = ±√(3/7)
x = ±√(2/3) and x = ±√(2/5)
8. Solve the quadratic equation by factoring: 2x
2
- 7x = 3.
x = 3 and x = -1/2
x = 2 and x = -6
x = 1/2 and x = 5
x = 2 and x = 3/5
9. Solve the equation by factoring: x
3
+ x
2
+ x + 1 = 0. Only find the real root(s).
x = 6
x = 3
x = -4.5
x = 1
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