Chapter 10

Is \(-4 x^{2}+5 x-3 x^{3}+6\) written in standard form? Explain.

What does it mean to say that a polynomial is prime?

Write the three special product factoring patterns. Give an example of each pattern.

What is the difference between factoring quadratic polynomials of the form \(-x^{2}+b x+c\) and \(a x^{2}+b x+c ?\)

What does it mean to factor a trinomial of the form \(x^{2}+b x+c ?\)

What is the zero-product property?

What is the sum and difference pattern for the product of two binomials?

How do the letters in “FOIL” help you remember how to multiply two binomials?

Is \(9 x^{2}+8 x-4 x^{3}+3\) a polynomial with a degree of \(2 ?\) Explain.

Factor the expression. $$ x^{2}-9 $$

Copy and complete the statement. $$ (2 x+1)(x+1)=2 x^{2} \quad ?+1 $$

Is \((x-2)\left(x^{2}-9\right)=0\) in factored form? Explain.

Complete: \((x+3)^{2}=x^{2}+6 x+9\) is an example of the ____? pattern.

Give an example of a monomial, a binomial, and a trinomial.

Identify the polynomial by degree and by the number of terms. $$ -9 y+5 $$

Find and correct the error. \(-2 b^{3}+12 b^{2}-14 b\) \(=-2 b\left(b^{2}+6 b-7\right)\) \(=-2 b(b+7)(b-1)\)

Factor the expression. $$ b^{2}+10 b+25 $$

Copy and complete the statement. $$ (3 x+2)(x-3)=3 x^{2}-7 x ____ $$

Are \(-5,2,\) and 3 the solutions of \(3(x-2)(x+5)=0 ?\) Explain.

Use a special product pattern to find the product. $$ (x-6)^{2} $$

Identify the polynomial by degree and by the number of terms. $$ 6 x^{3} $$

Find the greatest common factor of the terms and factor it out of the expression. \(5 n^{3}-20 n\)

Factor the expression. $$ p^{2}+25 $$

Copy and complete the statement. $$ (3 x-4)(x-5)=3 x^{2} \quad ?+20 $$

Match the trinomial with a correct factorization. $$ \begin{aligned} &A.)\quad (x+5)(x-4)\\\ &B.)\quad(x+4)(x+5)\\\ &C.)\quad(x-4)(x-5)\\\ &D.)\quad(x+4)(x-5) \end{aligned} $$ $$ x^{2}+9 x+20 $$

Use a special product pattern to find the product. $$ (w+11)(w-11) $$

Find and correct the error at the right. \(\begin{aligned}(2 x+4)(x-2) &=0 \\ 2 x+4 &=0 \quad \text { or } \quad x-2=0 \\\ 2 x &=4 \\ x &=2 \end{aligned}\)

$$ (3 x+4)(2 x-1)=3 x(?)+4(?) $$

Identify the polynomial by degree and by the number of terms. $$ 12 x^{2}+7 x $$

Factor the expression. $$ w^{2}-16 w+64 $$

Find the greatest common factor of the terms and factor it out of the expression. \(6 x^{2}+3 x^{4}\)

Copy and complete the statement. $$ (5 x+2)(2 x+1)=?+9 x+2 $$

Match the trinomial with a correct factorization. $$ \begin{aligned} &A.)\quad (x+5)(x-4)\\\ &B.)\quad(x+4)(x+5)\\\ &C.)\quad(x-4)(x-5)\\\ &D.)\quad(x+4)(x-5) \end{aligned} $$ $$ x^{2}-9 x+20 $$

Use a special product pattern to find the product. $$ (6+p)^{2} $$

Does the graph of the function have x-intercepts of 4 and 5? \(y=2(x+4)(x-5)\)

Copy the equation and fill in the blanks. \((x-3)(x+1)=x^{2}-2 x-\)______

Identify the polynomial by degree and by the number of terms. $$ 4 w^{3}-8 w+9 $$

Factor the expression. $$ 16-c^{2} $$

Find the greatest common factor of the terms and factor it out of the expression. \(6 y^{4}+14 y^{3}-10 y^{2}\)

Match the trinomial with a correct factorization. $$ 3 x^{2}-17 x-6 $$ A. \((3 x+2)(x+3)\) B. \((3 x+1)(x-6)\) C. \((3 x-1)(x+6)\) D. \((3 x-2)(x+3)\)

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

Use a special product pattern to find the product. $$ (3 y-1)^{2} $$

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

Copy the equation and fill in the blanks. \((x+2)(x+6)=x^{2}+\underline{?}+12\)

Identify the polynomial by degree and by the number of terms. $$ 7 y+2 y^{3}-y^{2} $$

Factor the expression. $$ 6 y^{2}-24 $$

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

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

Use a special product pattern to find the product. $$ (t-6)(t+6) $$

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