Chapter 3

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$y^{2}+21 y+98$$

Use the difference-of-squares pattern to factor each of the following. $$x^{2} y^{2}-a^{2} b^{2}$$

Classify each number as prime or composite. $$119$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$-a b^{2}\left(5 a+3 b-6 a^{2} b^{3}\right)$$

Find each product. $$\left(-2 x y^{2} z^{2}\right)\left(-x^{2} y^{3} z\right)$$

Determine the degree of the given polynomials. $$5 y^{6}+y^{4}-2 y^{2}-8$$

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$w^{2}-4 w=5$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$x^{2}-5 x-14$$

Use the difference-of-squares pattern to factor each of the following. $$4 x^{2}-y^{4}$$

Classify each number as prime or composite. $$71$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(a+2 b)(x+y)$$

Find each product. $$(5 x y)\left(-6 y^{3}\right)$$

Determine the degree of the given polynomials. $$-12$$

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$s^{2}-4 s=21$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$x^{2}-3 x-54$$

Use the difference-of-squares pattern to factor each of the following. $$x^{6}-9 y^{2}$$

Classify each number as prime or composite. $$101$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(t-s)(x+y)$$

Find each product. $$(-7 x y)\left(4 x^{4}\right)$$

Determine the degree of the given polynomials. $$7 x-2 y$$

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$n^{2}+25 n+156=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$x^{2}+9 x+12$$

Use the difference-of-squares pattern to factor each of the following. $$1-144 n^{2}$$

Factor each of the composite numbers into the product of prime numbers. For example, \(30=2 \cdot 3 \cdot 5 .\) $$28$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(a-3 b)(c+4 d)$$

Find each product. $$\left(3 a^{2} b\right)\left(9 a^{2} b^{4}\right)$$

Add the given polynomials. \(3 x-7\) and \(7 x+4\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$n(n-24)=-128$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$35-2 x-x^{2}$$

Use the difference-of-squares pattern to factor each of the following. $$25-49 n^{2}$$

Factor each of the composite numbers into the product of prime numbers. For example, \(30=2 \cdot 3 \cdot 5 .\) $$39$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(a-4 b)(c-d)$$

Find each product. $$\left(-8 a^{2} b^{2}\right)\left(-12 a b^{5}\right)$$

Add the given polynomials. \(9 x+6\) and \(5 x-3\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$3 t^{2}+14 t-5=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$6+5 x-x^{2}$$

Use the difference-of-squares pattern to factor each of the following. $$(x+2)^{2}-y^{2}$$

Factor each of the composite numbers into the product of prime numbers. For example, \(30=2 \cdot 3 \cdot 5 .\) $$44$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(x+6)(x+10)$$

Find each product. $$\left(m^{2} n\right)\left(-m n^{2}\right)$$

Add the given polynomials. \(-5 t-4\) and \(-6 t+9\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$4 t^{2}-19 t-30=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$x^{2}+8 x-24$$

Use the difference-of-squares pattern to factor each of the following. $$(3 x+5)^{2}-y^{2}$$

Factor each of the composite numbers into the product of prime numbers. For example, \(30=2 \cdot 3 \cdot 5 .\) $$49$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(x+2)(x+10)$$

Find each product. $$\left(-x^{3} y^{2}\right)\left(x y^{3}\right)$$

Add the given polynomials. \(-7 t+14\) and \(-3 t-6\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$6 x^{2}+25 x+14=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$x^{2}+15 x y+36 y^{2}$$