Chapter 10

Find the product. $$ (4 n-3)^{2} $$

Find the x-intercepts and the vertex of the graph of the function. Then sketch the graph of the function. \(y=(x-4)(x+2)\)

$$ (4 b-1)(b-6) $$

COMMON FACTOR Factor the expression. $$ 5 c^{2}+20 c+20 $$

Use a horizontal format to add or subtract. $$ \left(z^{3}+z^{2}+1\right)-z^{2} $$

Factor the expression completely. \(c^{4}+c^{3}-12 c-12\)

Solve the equation by factoring. Then use a graphing calculator to check your answer. $$ x^{2}+3 x-18=0 $$

Find the product. $$ (a+2 b)(a-2 b) $$

Find the x-intercepts and the vertex of the graph of the function. Then sketch the graph of the function. \(y=(x+5)(x+3)\)

$$ (x-9)(2 x+15) $$

Solve the equation by factoring. $$ 2 x^{2}-9 x-35=0 $$

COMMON FACTOR Factor the expression. $$ 6 b^{2}-54 $$

Use a horizontal format to add or subtract. $$ 12-\left(y^{3}+10 y+16\right) $$

Factor the expression completely. \(x^{3}-3 x^{2}+x-3\)

In Exercises 42 and 43, a triangular sign has a base that is 2 feet less than twice its height. A local zoning ordinance restricts the surface area of street signs to be no more than 20 square feet. Write an inequality involving the height that represents the largest triangular sign allowed.

Find the product. $$ (4 x+5)^{2} $$

Find the x-intercepts and the vertex of the graph of the function. Then sketch the graph of the function. \(y=(x-3)(x+3)\)

$$ (3 a-1)(a-9) $$

Solve the equation by factoring. $$ 7 x^{2}-10 x+3=0 $$

COMMON FACTOR Factor the expression. $$ 27 t^{2}+18 t+9 $$

Use a horizontal format to add or subtract. $$ \left(3 n^{2}+2 n-7\right)-\left(n^{3}-n-2\right) $$

Factor the expression completely. \(3 x^{3}+3000\)

In Exercises 42 and 43, a triangular sign has a base that is 2 feet less than twice its height. A local zoning ordinance restricts the surface area of street signs to be no more than 20 square feet. Find the base and height of the largest triangular sign that meets the zoning ordinance.

Find the product. $$ (3 x-4 y)(3 x+4 y) $$

Find the x-intercepts and the vertex of the graph of the function. Then sketch the graph of the function. \(y=(x-1)(x+7)\)

$$ (2 z+7)(3 z+2) $$

Solve the equation by factoring. $$ 3 x^{2}+34 x+11=0 $$

COMMON FACTOR Factor the expression. $$ 28 y^{2}-7 $$

Use a horizontal format to add or subtract. $$ \left(3 a^{3}-4 a^{2}+3\right)-\left(a^{3}+3 a^{2}-a-4\right) $$

Factor the expression completely. \(2 x^{3}-6750\)

Find the product. $$ (3 y+8)^{2} $$

Find the x-intercepts and the vertex of the graph of the function. Then sketch the graph of the function. \(y=(x-2)(x-6)\)

$$ (4 q-1)(3 q+8) $$

Solve the equation by factoring. $$ 4 x^{2}-21 x+5=0 $$

COMMON FACTOR Factor the expression. $$ 3 k^{2}-39 k+90 $$

Use a vertical format or a horizontal format to add or subtract. $$ \left(9 x^{3}+12 x\right)+\left(16 x^{3}-4 x+2\right) $$

Solve the equation. Tell which method you used. \(y^{2}+7 y+12=0\)

Find the product. $$ (9-4 t)(9+4 t) $$

Find the x-intercepts and the vertex of the graph of the function. Then sketch the graph of the function. \(y=(x+4)(x+3)\)

$$ (5 t-3)(2 t+3) $$

Solve the equation by factoring. $$ 2 x^{2}-17 x-19=0 $$

COMMON FACTOR Factor the expression. $$ 24 a^{2}-54 $$

Use a vertical format or a horizontal format to add or subtract. $$ \left(-2 t^{4}+6 t^{2}+5\right)-\left(-2 t^{4}+5 t^{2}+1\right) $$

Solve the equation. Tell which method you used. \(x^{2}-3 x-4=0\)

Factor \(x^{2}-10 x-24\) $$ a.\quad(x-4)(x-6) $$ $$ b.\quad(x+4)(x+6) $$ $$ c.\quad(x+2)(x-12) $$ $$ d.\quad(x-2)(x+12) $$

Find the product. $$ (a-2 b)^{2} $$

Find the product. $$ (3 x-4 y)(3 x+4 y) $$

The cross section of the telescope’s dish can be modeled by the polynomial function $$y=\frac{14}{41^{2}}(x+41)(x-41)$$ where \(x\) and \(y\) are measured in feet, and the center of the dish is at \(x=0\) Find the width of the dish. Explain your reasoning.

$$ (4 x+5)(4 x-3) $$

Solve the equation by factoring. $$ 5 x^{2}-3 x-26=0 $$