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Section 3.8 Additional Practice Factoring

Exercises Exercises

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

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