### Review Exercises

## 7.1 Greatest Common Factor and Factor by Grouping

**Find the Greatest Common Factor of Two or More Expressions**

In the following exercises, find the greatest common factor.

$450,420$

$60,294,630$

**Factor the Greatest Common Factor from a Polynomial**

In the following exercises, factor the greatest common factor from each polynomial.

$35y+84$

$24p{t}^{4}+16{t}^{7}$

**Factor by Grouping**

In the following exercises, factor by grouping.

${x}^{2}y-x{y}^{2}+2x-2y$

$4{x}^{2}-16x+3x-12$

$5x-5y-y+x$

## 7.2 Factor Trinomials of the form ${x}^{2}+bx+c$

**Factor Trinomials of the Form ${x}^{2}+bx+c$**

In the following exercises, factor each trinomial of the form ${x}^{2}+bx+c$.

${a}^{2}+14a+33$

${r}^{2}-11r+28$

${m}^{2}+3m-54$

${x}^{2}-3x-10$

**Factor Trinomials of the Form ${x}^{2}+bxy+c{y}^{2}$**

In the following examples, factor each trinomial of the form ${x}^{2}+bxy+c{y}^{2}$.

${u}^{2}+14uv+48{v}^{2}$

${p}^{2}-5pq-36{q}^{2}$

## 7.3 Factoring Trinomials of the form $a{x}^{2}+bx+c$

**Recognize a Preliminary Strategy to Factor Polynomials Completely**

In the following exercises, identify the best method to use to factor each polynomial.

$12{r}^{2}+32r+5$

$4m-mn-3n+12$

**Factor Trinomials of the Form $a{x}^{2}+bx+c$ with a GCF**

In the following exercises, factor completely.

$8{a}^{2}+32a+24$

$5{y}^{4}+25{y}^{2}-70y$

**Factor Trinomials Using the “ac” Method**

In the following exercises, factor.

$3{y}^{2}+17y+10$

$8{u}^{2}-14u+3$

$15{x}^{2}+6x-2$

$20{n}^{2}-7n-3$

**Factor Trinomials with a GCF Using the “ac” Method**

In the following exercises, factor.

$4{x}^{2}+4x-8$

$18{a}^{2}-57a-21$

## 7.4 Factoring Special Products

**Factor Perfect Square Trinomials**

In the following exercises, factor.

$16{y}^{2}+72y+81$

$64{r}^{2}-176rs+121{s}^{2}$

$75{u}^{2}+180u+108$

$5{k}^{3}-70{k}^{2}+245k$

**Factor Differences of Squares**

In the following exercises, factor.

$49{a}^{2}-144$

$64{x}^{2}-{y}^{2}$

$1-16{s}^{2}$

$100{k}^{2}-81$

$18{y}^{2}-98$

$169{n}^{3}-n$

**Factor Sums and Differences of Cubes**

In the following exercises, factor.

${b}^{3}-216$

$81{x}^{3}+3$

## 7.5 General Strategy for Factoring Polynomials

**Recognize and Use the Appropriate Method to Factor a Polynomial Completely**

In the following exercises, factor completely.

$24{a}^{4}-9{a}^{3}$

$6{a}^{2}-25a-9$

$5{u}^{4}-45{u}^{2}$

$64{j}^{2}+225$

${b}^{3}-64$

$2{b}^{2}-2bc+5cb-5{c}^{2}$

## 7.6 Quadratic Equations

**Use the Zero Product Property**

In the following exercises, solve.

$(b-3)(b+10)=0$

$7n(3n+8)(n-5)=0$

**Solve Quadratic Equations by Factoring**

In the following exercises, solve.

${y}^{2}-y-72=0$

${q}^{3}+3{q}^{2}+2q=0$

$4{n}^{2}=36$

**Solve Applications Modeled by Quadratic Equations**

In the following exercises, solve.

The area of a rectangular shaped patio $400$ square feet. The length of the patio is $9$ feet more than its width. Find the length and width.