ExercisesExercises

Completely factor each expression.

1.

$4x^2-10xy+16x^2y^2$

Solution

$4x^2-10xy+16x^2y^2=2x(2x-5y+8xy^2)$

2.

$-12a^2b^3c^4+18ab^3c^5-60ab^2c^4$

Solution

$-12a^2b^3c^4+18ab^3c^5-60ab^2c^4=-6ab^2c^4(2ab-3bc+10)$

3.

$45x^7y^{11}+75x^6y^{12}+15x^6y^9$

Solution

$45x^7y^{11}-75x^6y^{12}+15x^6y^9=15x^6y^9(3xy^2-5y^3+1)$

4.

$x^2-10x-24$

Solution

$x^2-10x-24=(x-12)(x+2)$

5.

$x^2+11x+30$

Solution

$x^2+11x+30=(x+6)(x+5)$

6.

$y^2-12y+36$

Solution

$y^2-12y+36=(y-6)(y-6)$

7.

$w^2+12w+24$

Solution

$w^2+12w+24$ is prime.

8.

$w^2+21w+80$

Solution

$w^2+21w+80=(w+15)(w+6)$

9.

$x^2y+4x-3xy^2-12y$

Solution

$x^2y+4x-3xy^2-12y=(xy+4)(x-3y)$

10.

$12x^2+8x-21x-14$

Solution

$12x^2+8x-21x-14=(3x+2)(4x-7)$

11.

$4a^2b-8ab^2+a-2b$

Solution

$4a^2b-8ab^2+a-2b=(a-2b)(4ab+1)$

12.

$4x^2-17x-15$

Solution

$4x^2-17x-15=(4x+3)(x-5)$

13.

$6x^2+17x+5$

Solution

$6x^2+17x+5=(2x+5)(3x+1)$

14.

$2x^2+5x-4$

Solution

$2x^2+5x-4$ is prime.

15.

$3x^2-10x-8$

Solution

$3x^2-10x-8=(x-4)(3x+2)$

16.

$16x^2-8x+1$

Solution

$16x^2-8x+1=(4x-1)(4x-1)$

17.

$x^3+8$

Solution

$x^3+8=(x+2)(x^2-2x+4)$

18.

$w^2-64$

Solution

$w^2-64=(w-8)(w+8)$

19.

$y^2+49$

Solution

$y^2+49$ is prime.

20.

$1-27x^3$

Solution

$1-27x^3=(1-3x)(1+3x+9x^2)$

21.

$100-9y^{10}$

Solution

$100-9y^{10}=(10-3y^5)(10+3y^5)$

22.

$w^2-3w-88$

Solution

$w^2-3w-88=(w-11)(w+8)$

23.

$3x^2-54x+240$

Solution

$3x^2-54x+240=3(x-10)(x-8)$

24.

$3x^2-11x-20$

Solution

$3x^2-11x-20=(3x+4)(x-5)$

25.

$3x^3-81y^{15}$

Solution

$3x^3-81y^{15}=3(x-3y^5)(x^2+3xy^5+9y^{10})$

26.

$4x^2-16y^{12}$

Solution

$4x^2-16y^{12}=4(x-2y^6)(x+2y^6)$

27.

$4x^2+16y^{12}$

Solution

$4x^2+16y^{12}=4(x^2+4y^{12})$

28.

$20x^2-3xy-2y^2$

Solution

$20x^2-3xy-2y^2=(4x+y)(5x-2y)$

29.

$1+125w^9$

Solution

$1+125w^9=(1+5w^3)(1-5w^3+25w^6)$

30.

$xy^4+6x^2y^3-40x^3y^2$

Solution

$xy^4+6x^2y^3-40x^3y^2=xy^2(y-4x)(y+10x)$