Chapter 6

Use Pascal's Triangle to expand each binomial. $$(a+b)^{3}$$

Evaluate each expression. $$ 5 ! $$

For each equation, state the number of complex roots, the possible number of real roots, and the possible rational roots. $$ x^{3}+4 x^{2}+5 x-1=0 $$

Write each expression as a polynomial in standard form. $$ (x+3)(x-2) $$

Use the Rational Root Theorem to list all possible rational roots for each polynomial equation. Then find any actual rational roots. $$ x^{3}-x^{2}+2 x-2=0 $$

Divide using long division. Check your answers. $$ \left(x^{2}-3 x-40\right) \div(x+5) $$

Write each polynomial in standard form. Then classify it by degree and by number of terms. $$ 7 x+3 x+5 $$

Use Pascal's Triangle to expand each binomial. $$ (x-y)^{2} $$

Evaluate each expression. $$ 10 ! $$

For each equation, state the number of complex roots, the possible number of real roots, and the possible rational roots. $$ 3 x^{2}-7=0 $$

Write each expression as a polynomial in standard form. $$ (x+3)(x+4)(x+5) $$

Use the Rational Root Theorem to list all possible rational roots for each polynomial equation. Then find any actual rational roots. $$ x^{3}+4 x^{2}+x-6=0 $$

$$ 3 x^{3}-6 x^{2}-9 x=0 $$

Divide using long division. Check your answers. $$ \left(3 x^{2}+7 x-20\right) \div(x+4) $$

Write each polynomial in standard form. Then classify it by degree and by number of terms. $$ 5-3 x $$

Use Pascal's Triangle to expand each binomial. $$ (a+b)^{4} $$

Evaluate each expression. $$ 13 ! $$

For each equation, state the number of complex roots, the possible number of real roots, and the possible rational roots. $$ -x^{4}=0 $$

Write each expression as a polynomial in standard form. $$ (x-3)^{2}(x-1) $$

Use the Rational Root Theorem to list all possible rational roots for each polynomial equation. Then find any actual rational roots. $$ x^{3}+x^{2}+4 x+4=0 $$

Solve each equation by graphing. Check your answers. $$ 4 x^{3}-8 x^{2}+4 x=0 $$

Divide using long division. Check your answers. $$ \left(x^{3}+3 x^{2}-x+2\right) \div(x-1) $$

Write each polynomial in standard form. Then classify it by degree and by number of terms. $$ 2 m^{2}-3+7 m $$

Use Pascal's Triangle to expand each binomial. $$ (x-y)^{5} $$

For each equation, state the number of complex roots, the possible number of real roots, and the possible rational roots. $$ 2 x^{5}-4 x^{4}-4 x^{2}+5=0 $$

Write each expression as a polynomial in standard form. $$ x(x+2)^{2} $$

Use the Rational Root Theorem to list all possible rational roots for each polynomial equation. Then find any actual rational roots. $$ 2 x^{3}-9 x^{2}-11 x+8=0 $$

Solve each equation by graphing. Check your answers. $$ 6 x^{2}=48 x $$

Divide using long division. Check your answers. $$\left(2 x^{3}-3 x^{2}-18 x-8\right) \div(x-4)$$

Write each polynomial in standard form. Then classify it by degree and by number of terms. $$ -x^{3}+x^{4}+x $$

Use Pascal's Triangle to expand each binomial. $$ (a-b)^{6} $$

Evaluate each expression. $$ \frac{12 !}{6 !} $$

For each equation, state the number of complex roots, the possible number of real roots, and the possible rational roots. $$ x^{7}-x^{3}-2 x-3=0 $$

Write each expression as a polynomial in standard form. $$ x(x+5)^{2} $$

Use the Rational Root Theorem to list all possible rational roots for each polynomial equation. Then find any actual rational roots. $$ x^{3}+2 x^{2}-8 x-16=0 $$

Solve each equation by graphing. Check your answers. $$ x^{3}+3 x^{2}+2 x=0 $$

Divide using long division. Check your answers. $$ \left(9 x^{3}-18 x^{2}-x+2\right) \div(3 x+1) $$

Write each polynomial in standard form. Then classify it by degree and by number of terms. $$ -4 p+3 p+2 p^{2} $$

Use Pascal's Triangle to expand each binomial. $$ (x-y)^{7} $$

Evaluate each expression. $$ 5(4 !) $$

For each equation, state the number of complex roots, the possible number of real roots, and the possible rational roots. $$ 4 x+8=0 $$

Write each expression as a polynomial in standard form. $$ x(x-1)(x+1) $$

Use the Rational Root Theorem to list all possible rational roots for each polynomial equation. Then find any actual rational roots. $$ x^{4}+2 x^{2}-15=0 $$

Divide using long division. Check your answers. $$ \left(9 x^{2}-21 x-20\right) \div(x-1) $$

Write each polynomial in standard form. Then classify it by degree and by number of terms. $$ 5 a^{2}+3 a^{3}+1 $$

Use Pascal's Triangle to expand each binomial. $$ (x+y)^{8} $$

Evaluate each expression. $$ \frac{10 !}{7 ! 3 !} $$

For each equation, state the number of complex roots, the possible number of real roots, and the possible rational roots. $$ -2 x^{6}-x^{2}+x-7=0 $$

Write each polynomial in factored form. Check by multiplication. $$ x^{3}-36 x $$

Find the roots of each polynomial equation. $$ x^{3}-2 x^{2}+5 x-10=0 $$