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