Chapter 6

Solve.$$ (x+3)(x+8)=x $$

Factor each completely. $$ 16 r^{2}+1 $$

Find the length of the shorter leg of a right triangle if the longer leg is 12 feet more than the shorter leg and the hypotenuse is 12 feet less than twice the shorter leg.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 54 a^{2}-9 a-30 $$

Factor out the GCF from each polynomial. $$ 32 x y-18 x^{2} $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ r^{2}-16 r+48 $$

Factor each trinomial completely. See Examples 1 through 5 . \(18 x^{2}-9 x-14\)

Solve. $$ x(3 x-1)=14 $$

Factor each completely. $$ 49 y^{2}+9 $$

Find the length of the shorter leg of a right triangle if the longer leg is 10 miles more than the shorter leg and the hypotenuse is 10 miles less than twice the shorter leg.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 30 a^{2}+38 a-20 $$

Factor out the GCF from each polynomial. $$ 10 x y-15 x^{2} $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ r^{2}-10 r+21 $$

Factor each trinomial completely. See Examples 1 through 5 . \(42 a^{2}-43 a+6\)

Solve. $$ x(4 x-11)=3 $$

Factor each completely. $$ x^{3} y-121 x y^{3} $$

An object is dropped from 39 feet below the tip of the pinnacle atop one of the 1483 -foot-tall Petronas Twin Towers in Kuala Lumpur, Malaysia. (Source: Council on Tall Buildings and Urban Habitat) The height \(h\) of the object after \(t\) seconds is given by the equation \(h=-16 t^{2}+1444 .\) Find how many seconds pass before the object reaches the ground.

Factor out the GCF from each polynomial. $$ 4 x-8 y+4 $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ x^{2}+x y-2 y^{2} $$

Factor each trinomial completely. See Examples 1 through 5 . \(2 m^{2}+17 m+10\)

Solve. $$ 3 x^{2}+19 x-72=0 $$

Factor each completely. $$ 25 x y^{2}-4 x $$

An object is dropped from the top of 311 South Wacker Drive, a 961 -foot-tall office building in Chicago. (Source: Council on Tall Buildings and Urban Habitat) The height \(h\) of the object after \(t\) seconds is given by the equation \(h=-16 t^{2}+961 .\) Find how many seconds pass before the object reaches the ground.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 10 a^{3}+17 a^{2}+3 a $$

Factor out the GCF from each polynomial. $$ 7 x+21 y-7 $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ x^{2}-x y-6 y^{2} $$

Factor each trinomial completely. See Examples 1 through 5 . \(3 n^{2}+20 n+5\)

Solve. $$ 36 x^{2}+x-21=0 $$

Factor each completely. $$ (y+2)^{2}-49 $$

At the end of 2 years, \(P\) dollars invested at an interest rate \(r\) compounded annually increases to an amount, \(A\) dollars, given by $$ A=P(1+r)^{2} $$ Find the interest rate if \(\$ 100\) increased to \(\$ 144\) in 2 years. Write your answer as a percent.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 12 x^{3}-27 x^{2}-27 x $$

Factor out the GCF from each polynomial. $$ 6 x^{3}-9 x^{2}+12 x $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ 3 x^{2}+9 x-30 $$

Solve each equation. $$ 4 x^{3}-x=0 $$

Factor each completely. $$ (x-1)^{2}-z^{2} $$

At the end of 2 years, \(P\) dollars invested at an interest rate \(r\) compounded annually increases to an amount, \(A\) dollars, given by $$ A=P(1+r)^{2} $$ Find the interest rate if \(\$ 2000\) increased to \(\$ 2420\) in 2 years. Write your answer as a percent.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 30 x^{3}-155 x^{2}+25 x $$

Factor out the GCF from each polynomial. $$ 12 x^{3}+16 x^{2}-8 x $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ 4 x^{2}-4 x-48 $$

Solve each equation. $$ 4 y^{3}-36 y=0 $$

Factor each completely. $$ 64 x^{2}-100 $$

Find the dimensions of a rectangle whose width is 7 miles less than its length and whose area is 120 square miles.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 3 x^{2} y+4 x y^{2}+y^{3} $$

Factor out the GCF from each polynomial. $$ a^{7} b^{6}-a^{3} b^{2}+a^{2} b^{5}-a^{2} b^{2} $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ 3 x^{2}-60 x+108 $$

Factor each trinomial completely. See Examples 1 through 7. \(12 x^{3}+11 x^{2}+2 x\)

Solve each equation. $$ 4(x-7)=6 $$

Factor each completely. $$ 4 x^{2}-36 $$

Find the dimensions of a rectangle whose width is 2 inches less than half its length and whose area is 160 square inches.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 6 r^{2} t+7 r t^{2}+t^{3} $$