Section 4.8 Additional Practice Factoring
¶Exercises Exercises
Completely factor each expression.
1.
\(4x^2-10xy+16x^2y^2\)
\(4x^2-10xy+16x^2y^2=2x(2x-5y+8xy^2)\)
2.
\(-12a^2b^3c^4+18ab^3c^5-60ab^2c^4\)
\(-12a^2b^3c^4+18ab^3c^5-60ab^2c^4=-6ab^2c^4(2ab-3bc+10)\)
3.
\(45x^7y^{11}+75x^6y^{12}+15x^6y^9\)
\(45x^7y^{11}-75x^6y^{12}+15x^6y^9=15x^6y^9(3xy^2-5y^3+1)\)
4.
\(x^2-10x-24\)
\(x^2-10x-24=(x-12)(x+2)\)
5.
\(x^2+11x+30\)
\(x^2+11x+30=(x+6)(x+5)\)
6.
\(y^2-12y+36\)
\(y^2-12y+36=(y-6)(y-6)\)
7.
\(w^2+12w+24\)
\(w^2+12w+24\) is prime.
8.
\(w^2+21w+80\)
\(w^2+21w+80=(w+15)(w+6)\)
9.
\(x^2y+4x-3xy^2-12y\)
\(x^2y+4x-3xy^2-12y=(xy+4)(x-3y)\)
10.
\(12x^2+8x-21x-14\)
\(12x^2+8x-21x-14=(3x+2)(4x-7)\)
11.
\(4a^2b-8ab^2+a-2b\)
\(4a^2b-8ab^2+a-2b=(a-2b)(4ab+1)\)
12.
\(4x^2-17x-15\)
\(4x^2-17x-15=(4x+3)(x-5)\)
13.
\(6x^2+17x+5\)
\(6x^2+17x+5=(2x+5)(3x+1)\)
14.
\(2x^2+5x-4\)
\(2x^2+5x-4\) is prime.
15.
\(3x^2-10x-8\)
\(3x^2-10x-8=(x-4)(3x+2)\)
16.
\(16x^2-8x+1\)
\(16x^2-8x+1=(4x-1)(4x-1)\)
17.
\(x^3+8\)
\(x^3+8=(x+2)(x^2-2x+4)\)
18.
\(w^2-64\)
\(w^2-64=(w-8)(w+8)\)
19.
\(y^2+49\)
\(y^2+49\) is prime.
20.
\(1-27x^3\)
\(1-27x^3=(1-3x)(1+3x+9x^2)\)
21.
\(100-9y^{10}\)
\(100-9y^{10}=(10-3y^5)(10+3y^5)\)
22.
\(w^2-3w-88\)
\(w^2-3w-88=(w-11)(w+8)\)
23.
\(3x^2-54x+240\)
\(3x^2-54x+240=3(x-10)(x-8)\)
24.
\(3x^2-11x-20\)
\(3x^2-11x-20=(3x+4)(x-5)\)
25.
\(3x^3-81y^{15}\)
\(3x^3-81y^{15}=3(x-3y^5)(x^2+3xy^5+9y^{10})\)
26.
\(4x^2-16y^{12}\)
\(4x^2-16y^{12}=4(x-2y^6)(x+2y^6)\)
27.
\(4x^2+16y^{12}\)
\(4x^2+16y^{12}=4(x^2+4y^{12})\)
28.
\(20x^2-3xy-2y^2\)
\(20x^2-3xy-2y^2=(4x+y)(5x-2y)\)
29.
\(1+125w^9\)
\(1+125w^9=(1+5w^3)(1-5w^3+25w^6)\)
30.
\(xy^4+6x^2y^3-40x^3y^2\)
\(xy^4+6x^2y^3-40x^3y^2=xy^2(y-4x)(y+10x)\)