Section 1
Common Factors
Name the greatest common factor of $4,12,$ and 16.
Name the greatest common factor of $x^{3}, x^{5},$ and $x^{6}$.
For the expression $x(2 x-1),$ name a. the monomial factor and b. the binomial factor.
Name the common binomial factor in the expression $5 b(c-6)+8(c-6).$
Rewrite the expression $2 x^{3}-x^{2}+6 x-3$ by grouping the first two terms and the last two terms.
Explain why the statement is true.a. The terms of the binomial $3 x-6$ have a common factor.b. The expression $3 x^{2}+15$ is not in factored form.c. $5 y-7$ is a factor of $y(5 y-7)$
Factor.$$5 a+5$$
Factor.$$7 b-7$$
Factor.$$16-8 a^{2}$$
Factor.$$12+12 y^{2}$$
Factor.$$8 x+12$$
Factor.$$16 a-24$$
Factor.$$7 x^{2}-3 x$$
Factor.$$12 y^{2}-5 y$$
Factor.$$3 a^{2}+5 a^{5}$$
Factor.$$6 b^{3}-5 b^{2}$$
Factor.$$2 x^{4}-4 x$$
Factor.$$3 y^{4}-9 y$$
Factor.$$10 x^{4}-12 x^{2}$$
Factor.$$12 a^{5}-32 a^{2}$$
Factor.$$8 a^{8}-4 a^{5}$$
Factor.$$16 y^{4}-8 y^{7}$$
Factor.$$x^{2} y^{2}-x y$$
Factor.$$a^{2} b^{2}+a b$$
Factor.$$3 x^{2} y^{4}-6 x y$$
Factor.$$12 a^{2} b^{5}-9 a b$$
Factor.$$3 x^{3}+6 x^{2}+9 x$$
Factor.$$5 y^{3}-20 y^{2}+5 y$$
Factor.$$2 x^{4}-4 x^{3}+6 x^{2}$$
Factor.$$3 y^{4}-9 y^{3}-6 y^{2}$$
Factor.$$2 x^{3}+6 x^{2}-14 x$$
Factor.$$3 y^{3}-9 y^{2}+24 y$$
Factor.$$2 y^{5}-3 y^{4}+7 y^{3}$$
Factor.$$6 a^{5}-3 a^{3}-2 a^{2}$$
Factor.$$x^{3} y-3 x^{2} y^{2}+7 x y^{3}$$
Factor.$$2 a^{2} b-5 a^{2} b^{2}+7 a b^{2}$$
Factor.$$5 y^{3}+10 y^{2}-25 y$$
Factor.$$4 b^{5}+6 b^{3}-12 b$$
Factor.$$3 a^{2} b^{2}-9 a b^{2}+15 b^{2}$$
Factor.$$8 x^{2} y^{2}-4 x^{2} y+x^{2}$$
What is the GCF of the terms of the polynomial $x^{a}+x^{b}+x^{c}$ given that $a, b,$ and $c$ are all positive integers, and $a>b>c ?$
Use the three expressions at the right.a. Which expressions are equivalent to $x^{2}-5 x+6 ?$b. Which expression can be factored by grouping?(i) $x^{2}-15 x+10 x+6$(ii) $x^{2}-x-4 x+6$(iii) $x^{2}-2 x-3 x+6$
Factor.$$x(b+4)+3(b+4)$$
Factor.$$y(a+z)+7(a+z)$$
Factor.$$a(y-x)-b(y-x)$$
Factor.$$3 r(a-b)+s(a-b)$$
Factor.$$x(x-2)+y(2-x)$$
Factor.$$t(m-7)+7(7-m)$$
Factor.$$8 c(2 m-3 n)+(3 n-2 m)$$
Factor.$$2 y(4 a+b)-(b+4 a)$$
Factor.$$x^{2}+2 x+2 x y+4 y$$
Factor.$$x^{2}-3 x+4 a x-12 a$$
Factor.$$p^{2}-2 p-3 r p+6 r$$
Factor.$$t^{2}+4 t-s t-4 s$$
Factor.$$a b+6 b-4 a-24$$
Factor.$$x y-5 y-2 x+10$$
Factor.$$2 z^{2}-z+2 y z-y$$
Factor.$$2 y^{2}-10 y+7 x y-35 x$$
Factor.$$2 x^{2}-5 x-6 x y+15 y$$
Factor.$$4 a^{2}+5 a b-10 b-8 a$$
Factor.$$3 y^{2}-6 y-a y+2 a$$
Factor.$$2 r a+a^{2}-2 r-a$$
Factor.$$3 x y-y^{2}-y+3 x$$
Factor.$$2 a b-3 b^{2}-3 b+2 a$$
Factor.$$3 s t+t^{2}-2 t-6 s$$
Factor.$$4 x^{2}+3 x y-12y-16x$$
Fill in the blank to make a true statement.$a-3=$_____$(3-a)$
Fill in the blank to make a true statement.$$2-(x-y)=2+(\text{____})$$
Fill in the blank to make a true statement.$$4 x+(3 a-b)=4 x-(\text{____})$$
Write an expression in factored form for the shaded portion in each of the following diagrams. Use the equation for the area of a rectangle $(A=L W)$ and the equation for the area of a circle $\left(A=\pi r^{2}\right).$(FIGURE CANT COPY)