Chapter 10

Copy the equation and fill in the blanks. $$ (x-4)(x-5)=x^{2}-9 x+\underline{?} $$

Identify the polynomial by degree and by the number of terms. $$ -15 $$

Factor the expression. $$ 18-2 b^{2} $$

Factor the expression. \(x^{3}+64\)

Solve the equation by factoring. $$ 0=x^{2}+x-6 $$

Use a special product pattern to find the product. $$ (a-2)(a+2) $$

Does the graph of the function have x-intercepts of 4 and 5? \(y=3(x+5)(x-4)\)

$$ (x+2)(2 x+1)=?+5 x+2 $$

Factor the expression. $$ 4 x^{2}-4 x+1 $$

Factor the expression. \(27 x^{3}+1\)

Factoring ____ reverses the effects of multiplication.

Tell whether the statement is true or false. If the statement is false, rewrite the right-hand side to make the statement true. $$ (3 x+4)^{2}=9 x^{2}+12 x+16 $$

Use the zero-product property to solve the equation. \((b+1)(b+3)=0\)

Use the distributive property to find the product. $$ (4 x+7)(-2 x) $$

In Exercises 9 and 10, find and correct the error. $$ \begin{aligned} &\left(4 x^{2}-9 x)(-8 x^{2}+3 x-7\right) \\ =&\left(4 x^{2}+8 x^{2}\right)+(-9 x+3 x)-7 \\ =& 12 x^{2}-6 x-7 \end{aligned} $$

Factor the trinomial. $$ 2 x^{2}+17 x+21 $$

Factor the expression. $$ 4 a^{2}-b^{2} $$

Factor the expression. \(125 x^{3}-1\)

In the factoring of a trinomial, if the constant term is positive, then the signs in both binomial factors will ___ be the same.

Tell whether the statement is true or false. If the statement is false, rewrite the right-hand side to make the statement true. $$ (3+2 y)^{2}=9+12 y+4 y^{2} $$

Use the zero-product property to solve the equation. \((t-3)(t-5)=0\)

$$ 2 x\left(x^{2}+x-5\right) $$

Find the sum or the difference of the polynomials. $$ (2 x-9)+(x-7) $$

Factor the trinomial. $$ 2 x^{2}-3 x-2 $$

Solve the equation by factoring. $$ x^{2}+6 x+9=0 $$

Factor the expression completely. \(2 b^{3}-18 b\)

In the factoring of a trinomial, if the constant term is negative, then the signs in both binomial factors will ______ be negative.

Tell whether the statement is true or false. If the statement is false, rewrite the right-hand side to make the statement true. $$ (5 x-1)^{2}=25 x^{2}-10 x+1 $$

Use the zero-product property to solve the equation. \((x-7)^{2}=0\)

$$ -4 x^{2}\left(3 x^{2}+2 x-6\right) $$

Find the sum or the difference of the polynomials. $$ (7 x-3)-(9 x-2) $$

Factor the trinomial. $$ 6 t^{2}-t-5 $$

Solve the equation by factoring. $$ 144-y^{2}=0 $$

Factor the expression completely. \(7 a^{3}-14 a^{2}-21 a\)

Choose the correct factorization. $$ x^{2}+7 x+12 $$ $$ \begin{aligned} &a.\quad(x+6)(x+2)\\\ &b.\quad(x+4)(x+3) \end{aligned} $$

Use the zero-product property to solve the equation. \((y+9)(y-2)(y-5)=0\)

$$ (a+4)(a+5) $$

Find the sum or the difference of the polynomials. $$ \left(x^{2}-4 x+3\right)+\left(3 x^{2}-3 x-5\right) $$

Factor the trinomial. $$ 12 x^{2}-19 x+4 $$

Solve the equation by factoring. $$ s^{2}-14 s+49=0 $$

Factor the expression completely. \(3 t^{3}+18 t^{2}+27 t\)

Choose the correct factorization. $$ x^{2}-10 x+16 $$ $$ \begin{aligned} &a.\quad(x-4)(x-4)\\\ &b.\quad(x-8)(x-2) \end{aligned} $$

Tell whether the expression is a difference of two squares. $$x^{2}-9$$

Sketch the graph of \(y=(x+2)(x-2) .\) Label the vertex and the \(x\) -intercepts.

$$ (y-2)(y+8) $$

Find the sum or the difference of the polynomials. $$ \left(3 x^{2}+2 x-4\right)-\left(2 x^{2}+x-1\right) $$

Factor the trinomial. $$ 6 x^{2}+7 x-20 $$

Solve the equation by factoring. $$ -25+x^{2}=0 $$

Factor the expression completely. \(y^{3}-6 y^{2}+5 y\)

Choose the correct factorization. $$ x^{2}+11 x-26 $$ $$ \begin{aligned} &a.\quad(x-13)(x+2)\\\ &b.\quad(x+13)(x-2) \end{aligned} $$