Chapter 3

Find each quotient. $$\frac{-36 x^{3} y^{5}}{2 y^{5}}$$

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$9 a^{2}-30 a+25$$

Set up an equation and solve each of the following problems. The combined area of two squares is 26 square meters. The sides of the larger square are five times as long as the sides of the smaller square. Find the dimensions of each of the squares.

Solve each of the equations. $$-4 x^{2}+9 x=0$$

Find each quotient. $$\frac{-48 x y z^{2}}{2 x z}$$

Explain how to subtract the polynomial \(-3 x^{2}+2 x-4\) from \(4 x^{2}+6 .\)

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$4 n^{2}+25 n+36$$

Set up an equation and solve each of the following problems. A rectangle is twice as long as it is wide, and its area is 50 square meters. Find the length and the width of the rectangle.

Solve each of the equations. $$4 x^{2}=5 x$$

Find the indicated products. Assume all variables that appear as exponents represent positive integers. $$\left(x^{n}-4\right)\left(x^{n}+4\right)$$

Find each product. Assume that the variables in the exponents represent positive integers. For example, $$ \left(x^{2 n}\right)\left(x^{3 n}\right)=x^{2 n+3 n}=x^{5 n} $$ $$\left(2 x^{n}\right)\left(3 x^{2 n}\right)$$

Is the sum of two binomials always another binomial? Defend your answer.

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$x^{3}-9 x$$

Set up an equation and solve each of the following problems. Suppose that the length of a rectangle is one and onethird times as long as its width. The area of the rectangle is 48 square centimeters. Find the length and width of the rectangle.

Solve each of the equations. $$3 x=11 x^{2}$$

Find the indicated products. Assume all variables that appear as exponents represent positive integers. $$\left(x^{3 a}-1\right)\left(x^{3 a}+1\right)$$

Find each product. Assume that the variables in the exponents represent positive integers. For example, $$ \left(x^{2 n}\right)\left(x^{3 n}\right)=x^{2 n+3 n}=x^{5 n} $$ $$\left(3 x^{2 n}\right)\left(x^{3 n-1}\right)$$

Explain how to simplify the expression $$ 7 x-[3 x-(2 x-4)+2]-x $$

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$n^{3}-49 n$$

Set up an equation and solve each of the following problems. The total surface area of a right circular cylinder is \(54 \pi\) square inches. If the altitude of the cylinder is twice the length of a radius, find the altitude of the cylinder.

Solve each of the equations. $$x-4 x^{2}=0$$

Find the indicated products. Assume all variables that appear as exponents represent positive integers. $$\left(x^{a}+6\right)\left(x^{a}-2\right)$$

Find each product. Assume that the variables in the exponents represent positive integers. For example, $$ \left(x^{2 n}\right)\left(x^{3 n}\right)=x^{2 n+3 n}=x^{5 n} $$ $$\left(a^{2 n-1}\right)\left(a^{2 n+4}\right)$$

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$4 x^{2}+16$$

Set up an equation and solve each of the following problems. The total surface area of a right circular cone is \(108 \pi\) square feet. If the slant height of the cone is twice the length of a radius of the base, find the length of a radius.

Solve each of the equations. $$x-6 x^{2}=0$$

Find the indicated products. Assume all variables that appear as exponents represent positive integers. $$\left(x^{a}+4\right)\left(x^{a}-9\right)$$

Find each product. Assume that the variables in the exponents represent positive integers. For example, $$ \left(x^{2 n}\right)\left(x^{3 n}\right)=x^{2 n+3 n}=x^{5 n} $$ $$\left(a^{5 n-1}\right)\left(a^{5 n+1}\right)$$

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$x^{2}-7 x-8$$

Set up an equation and solve each of the following problems. The sum of the areas of a circle and a square is \((16 \pi+\) 64) square yards. If a side of the square is twice the length of a radius of the circle, find the length of a side of the square.

Solve each of the equations. $$12 a=-a^{2}$$

Find the indicated products. Assume all variables that appear as exponents represent positive integers. $$\left(2 x^{n}+5\right)\left(3 x^{n}-7\right)$$

Find each product. Assume that the variables in the exponents represent positive integers. For example, $$ \left(x^{2 n}\right)\left(x^{3 n}\right)=x^{2 n+3 n}=x^{5 n} $$ $$\left(x^{3 n-2}\right)\left(x^{n+2}\right)$$

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$x^{2}+3 x-54$$

Set up an equation and solve each of the following problems. The length of an altitude of a triangle is one-third the length of the side to which it is drawn. If the area of the triangle is 6 square centimeters, find the length of that altitude.

Solve each of the equations. $$-5 a=-a^{2}$$

Find the indicated products. Assume all variables that appear as exponents represent positive integers. $$\left(3 x^{n}+5\right)\left(4 x^{n}-9\right)$$

Find each product. Assume that the variables in the exponents represent positive integers. For example, $$ \left(x^{2 n}\right)\left(x^{3 n}\right)=x^{2 n+3 n}=x^{5 n} $$ $$\left(x^{n-1}\right)\left(x^{4 n+3}\right)$$

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$3 x^{4}-81 x$$

Explain how you would solve the equation \(4 x^{3}=64 x\).

Solve each equation for the indicated variable. \(5 b x^{2}-3 a x=0\) for \(x \quad\) 82. \(a x^{2}+b x=0\) for \(x\)

Find the indicated products. Assume all variables that appear as exponents represent positive integers. $$\left(x^{2 a}-7\right)\left(x^{2 a}-3\right)$$

Find each product. Assume that the variables in the exponents represent positive integers. For example, $$ \left(x^{2 n}\right)\left(x^{3 n}\right)=x^{2 n+3 n}=x^{5 n} $$ $$\left(a^{5 n-2}\right)\left(a^{3}\right)$$

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$x^{3}+125$$

What is wrong with the following factoring process? $$ 25 x^{2}-100=(5 x+10)(5 x-10) $$ How would you correct the error?

Solve each equation for the indicated variable. \(2 b y^{2}=-3 a y\) for \(y\)

Find the indicated products. Assume all variables that appear as exponents represent positive integers. $$\left(x^{2 a}+6\right)\left(x^{2 a}-4\right)$$

Find each product. Assume that the variables in the exponents represent positive integers. For example, $$ \left(x^{2 n}\right)\left(x^{3 n}\right)=x^{2 n+3 n}=x^{5 n} $$ $$\left(x^{3 n-4}\right)\left(x^{4}\right)$$

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$x^{4}+6 x^{2}+9$$

Find the indicated products. Assume all variables that appear as exponents represent positive integers. $$\left(2 x^{n}+5\right)^{2}$$