Chapter 6

Factor out the GCF from each polynomial. $$ x^{9} y^{6}+x^{3} y^{5}-x^{4} y^{3}+x^{3} y^{3} $$

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. $$ 2 x^{2}-24 x+70 $$

Factor each trinomial completely. See Examples 1 through 7. \(8 a^{3}+14 a^{2}+3 a\)

Solve each equation. $$ 5(3-4 x)=9 $$

Factor each completely. $$ 18 x^{2} y-2 y $$

If the cost, \(C,\) for manufacturing \(x\) units of a certain product is given by \(C=x^{2}-15 x+50,\) find the number of units manufactured at a cost of \(\$ 9500\).

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 20 z^{2}+7 z+1 $$

Factor out the GCF from each polynomial. $$ 5 x^{3} y-15 x^{2} y+10 x y $$

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. $$ x^{2}-18 x-144 $$

Factor each trinomial completely. See Examples 1 through 7. \(21 b^{2}-48 b-45\)

$$ 5(3-4 x)=9 $$$$ (4 x-3)\left(16 x^{2}-24 x+9\right)=0 $$

Factor each completely. $$ 12 x y^{2}-108 x $$

If a switchboard handles \(n\) telephones, the number \(C\) of telephone connections it can make simultaneously is given by the equation \(C=\frac{n(n-1)}{2} .\) Find how many telephones are handled by a switchboard making 120 telephone connections simultaneously.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 36 z^{2}+6 z+1 $$

Factor out the GCF from each polynomial. $$ 14 x^{3} y+7 x^{2} y-7 x y $$

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. $$ x^{2}+x-42 $$

Factor each trinomial completely. See Examples 1 through 7. \(12 x^{2}-14 x-10\)

Solve each equation. $$ (2 x+5)\left(4 x^{2}+20 x+25\right)=0 $$

Factor each completely. $$ 9 x^{2}-49 $$

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 24 a^{2}-6 a b-30 b^{2} $$

Factor out the GCF from each polynomial. $$ 8 x^{5}+16 x^{4}-20 x^{3}+12 $$

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. $$ r^{2}-3 r+6 $$

Factor each trinomial completely. See Examples 1 through 7. \(12 x^{2}-14 x-10\)

Solve each equation. $$ 4 y^{2}-1=0 $$

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

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 30 a^{2}+5 a b-25 b^{2} $$

Factor out the GCF from each polynomial. $$ 9 y^{6}-27 y^{4}+18 y^{2}+6 $$

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. $$ x^{2}+4 x-10 $$

Solve each equation. $$ 4 y^{2}-81=0 $$

Factor each completely. $$ x^{4}-81 $$

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 15 p^{4}+31 p^{3} q+2 p^{2} q^{2} $$

Factor out the GCF from each polynomial. $$ \frac{1}{3} x^{4}+\frac{2}{3} x^{3}-\frac{4}{3} x^{5}+\frac{1}{3} x $$

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. $$ x^{2}-8 x+15 $$

Factor each trinomial completely. See Examples 1 through 7. \(6 x^{2} y^{2}-2 x y^{2}-60 y^{2}\)

Solve each equation. $$ (2 x+3)\left(2 x^{2}-5 x-3\right)=0 $$

Factor each completely. $$ x^{4}-256 $$

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 20 s^{4}+61 s^{3} t+3 s^{2} t^{2} $$

Factor out the GCF from each polynomial. $$ \frac{2}{5} y^{7}-\frac{4}{5} y^{5}+\frac{3}{5} y^{2}-\frac{2}{5} y $$

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. $$ x^{2}-9 x+14 $$

Factor each trinomial completely. See Examples 1 through 7. \(8 x^{2} y+34 x y-84 y\)

Solve each equation. $$ (2 x-9)\left(x^{2}+5 x-36\right)=0 $$

Factor each completely. $$ (x+2 y)^{2}-9 $$

The following double line graph shows a comparison of the number of annual visitors (in millions) to Glacier National Park and Gettysburg National Military Park for the years shown. Use this graph to answer. In your own words, explain the meaning of the point of intersection in the graph.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 35+12 x+x^{2} $$

Factor out the GCF from each polynomial. $$ y\left(x^{2}+2\right)+3\left(x^{2}+2\right) $$

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. $$ 6 x^{3}+54 x^{2}+120 x $$

Factor each trinomial completely. See Examples 1 through 7. \(4 x^{2}-8 x-21\)

Solve each equation. $$ x^{2}-15=-2 x $$

Factor each completely. $$ (3 x+y)^{2}-25 $$

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 33+14 x+x^{2} $$