Chapter 6

Factor completely. $$ 2 x 5 y 2-12 x 4 y 3 $$

Determine the missing factor. $$ 12 x 3-24 x 2+4 x=4 x(\quad ? \quad) $$

One integer is five times another. If the product of the two integers is \(80,\) then find the integers.

Determine whether the given set of values are solutions to the quadratic equation. $$ \\{-3,5\\} ; x_{2}-2 x-15=0 $$

Factor. $$ 3 x 2-14 x-5 $$

Give the prime factorization of each number and determine the GCF. $$ \text { 18, } 24 $$

Are the following factored correctly? Check by multiplying. $$ x 2+5 x-6=(x+2)(x+3) $$

Factor completely. $$ x_{2}-9 $$

Factor completely. $$ 18 x 5 y 3-6 x 4 y 5 $$

Determine the missing factor. $$ 10 y 4-35 y 3-5 y 2=5 y 2(\quad ? \quad) $$

One integer is four times another. If the product of the two integers is \(36,\) then find the integers.

Factor. $$ 5 x 2+7 x+2 $$

Give the prime factorization of each number and determine the GCF. $$ 45,75 $$

Are the following factored correctly? Check by multiplying.] $$ x 2+6 x+16=(x+8)(x-2) $$

Factor completely. $$ 5 x 2+20 x-25 $$

Determine the missing factor. $$ -18 a 5+9 a 4-27 a 3=-9 a 3(\quad ? \quad) $$

An integer is one more than four times another. If the product of the two integers is 39 , then find the integers.

Give the prime factorization of each number and determine the GCF. $$ 72,60 $$

Are the following factored correctly? Check by multiplying. $$ y 2+2 y-8=(y+4)(y-2) $$

An integer is 3 more than another. If the product of the two integers is \(130,\) then find the integers.

Factor completely. $$ 4 x 2+10 x-6 $$

Determine the missing factor. $$ -21 x 2 y+7 x y 2-49 x y=-7 x y(\quad ? \quad) $$

Determine whether the given set of values are solutions to the quadratic equation. $$ \\{-3 / 4,3 / 4\\} ; x_{2}-916=0 $$

Give the prime factorization of each number and determine the GCF. $$ 168,175 $$

Are the following factored correctly? Check by multiplying. $$ y 2-10 y+21=(y-3)(y-7) $$

An integer is 2 less than twice another. If the product of the two integers is \(220,\) then find the integers.

Factor completely. $$ 24 x 3-30 x 2-9 x $$

Factor out the GCF. $$ 22 x 2+11 x $$

Determine whether the given set of values are solutions to the quadratic equation. $$ \\{-3,2\\} ; x 2-x-6=0 $$

Factor. $$ 2 x 2+9 x-5 $$

Give the prime factorization of each number and determine the GCF. $$ 144,245 $$

An integer is 3 more than twice another. If the product of the two integers is \(90,\) then find the integers.

Factor completely. $$ x 2-18 x+72 $$

Factor out the GCF. $$ 15 y 4-5 y 3 $$

Determine whether the given set of values are solutions to the quadratic equation. $$ \\{-5,1\\} ; x 2-4 x-5=0 $$

Factor. $$ 7 x 2+20 x-3 $$

Give the prime factorization of each number and determine the GCF. $$ 15,50,60 $$

One integer is 2 units more than another. If the product of the two integers is equal to five times the larger, then find the two integers.

Factor completely. $$ 6 x 3+27 x 2-9 x $$

Solve. $$ (x-3)(x+2)=0 $$

Give the prime factorization of each number and determine the GCF. $$ 14,63,70 $$

A positive integer is 1 less than twice another. If the product of the two integers is equal to fifteen times the smaller, then find the two integers.

Factor out the GCF. $$ 12 a 5+20 a 3-4 a $$

Solve. $$ (x+5)(x+1)=0 $$

Factor. $$ 3 x 2+x-2 $$

Give the prime factorization of each number and determine the GCF. $$ 12,48,125 $$

Are the following factored correctly? Check by multiplying. $$ x 2+5 x+14=(x-2)(x+7) $$

A positive integer is 3 more than twice a smaller positive integer. If the product of the two integers is equal to six times the larger, then find the integers.

Factor completely. $$ 5 x 3-30 x 2-15 x+90 $$

Factor out the GCF. $$ 9 x 3 y 2-18 x 2 y 2+27 x y 2 $$