Here you will find a concise collection of factoring practice problems. Visit this page directly at hunkim.com/factor
Factor fully:
- 3x-9
Solution3(x-3) - 15x^4y-20x^3y^5
Solution5x^3y(3x-4y^4) - \frac{x^2}{2}-2x
Solution\frac{x}{2}(x-4) - x^2-25
Solution(x+5)(x-5) - x^2+1
SolutionCannot be factored - 4a^2-9x^4b^2
Solution(2a+3x^2b)(2a-3x^2b) - \frac{4}{49}a^4 b^2-\frac{1}{100}
Solution\left ( \frac{2}{7} a^2b+\frac{1}{10} \right) \left( \frac{2}{7} a^2b-\frac{1}{10}\right) - 2a^2-18
Solution2(a+3)(a-3) - x^2+x-12
Solution(x-3)(x+4) - 2x^2+12x+18
Solution2(x+3)^2 - \frac{x^2}{2}+x-4
Solution=\frac{1}{2}(x^2+2x-8)
=\frac{1}{2}(x+4)(x-2) - 2x^2+x-6
Solution(2x-3)(x+2) - 200x^2+500x-1200
Solution=100(2x^2+5x-12)
=100(2x-3)(x+4) - 10x^2+29x-21
Solution(5x-3)(2x+7) - x^4-81
Solution=(x^2+9)(x^2-9)
=(x^2+9)(x+3)(x-3) - (x+1)x^2-(x+1)9
Solution=(x+1)(x^2-9)
=(x+1)(x+3)(x-3) - 2(3x+2)^2+9(3x+2)-5
SolutionLet a=(3x+2)
Factor 2a^2+9a-5
=[2a-1][a+5]
=[2(3x+2)-1][(3x+2)+5]
=[6x+4-1][(3x+2)+5]
=[6x+3][3x+7]
=3[3x+1][3x+7] - a^2(2x-3)+b^6(3-2x)
Solution=a^2(2x-3)-b^6(2x-3)
=(2x-3)(a^2-b^6)
=(2x-3)(a+b^3)(a-b^3) - Factor by grouping: x^3+7x^2+2x+14
Solution=x^2(x+7)+2(x+7)
=(x+7)(x^2+2) - Challenge:
- What is the area of the shaded region below in fully factored form?
Solution4\pi(x+1) - Factor 2(\sin \theta)^2-5 \sin \theta -3
Solution(2 \sin \theta+1)(\sin \theta -3) - Factor e^{2x}-25 (e\approx 2.718 is a special constant)
Solution(e^x+5)(e^x-5) - x^2+kx+8. Find the possible values of k such that this trinomial can be factored
Solutionk=\pm 9, \pm 6 - Expand then factor:
- (x+y)(x^2-xy+y^2)
Solutionx^3+y^3 - (x-y)(x^2+xy+y^2)
Solutionx^3-y^3
- (x+y)(x^2-xy+y^2)
- Factor 8a^6+b^3
Solution(2x^2+b)(4a^4-2a^2b+b^2) - Factor x^3-3x^2+4
Solution(x-2)^2(x+1) - Factor 2x^4+8x^3-4x^2-24x+18
Solution2(x+3)^2(x-1)^2
- What is the area of the shaded region below in fully factored form?
