Chapter 3

Find each product. $$(-12 x)(3 y)\left(-\frac{3}{4} x y^{6}\right)$$

Subtract the polynomials using the vertical format. \(4 x^{2}-3 x-7\) from \(-x^{2}-6 x+9\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$35 n^{2}-18 n-8=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$24 n^{2}-2 n-5$$

Factor each of the following polynomials completely. Indicate any that are not factorable using integers. Don't forget to look first for a common monomial factor. $$6 x-6 x^{3}$$

Factor completely. $$5 x+7 x^{2}+9 x^{4}$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(7 x-2)(2 x+1)$$

Raise each monomial to the indicated power. $$\left(3 x y^{2}\right)^{3}$$

Subtract the polynomials using the vertical format. \(x^{3}+x^{2}-x-1\) from \(-2 x^{3}+6 x^{2}-3 x+8\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$8 n^{2}-6 n-5=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$3 n^{2}-16 n-35$$

Factor each of the following polynomials completely. Indicate any that are not factorable using integers. Don't forget to look first for a common monomial factor. $$1-16 x^{4}$$

Factor completely. $$9 x^{2}-17 x^{4}+21 x^{5}$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(6 x-1)(3 x+2)$$

Raise each monomial to the indicated power. $$\left(4 x^{2} y^{3}\right)^{3}$$

Subtract the polynomials using the vertical format. \(2 x^{3}-x+6\) from \(x^{3}+4 x^{2}+1\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$-3 x^{2}-19 x+14=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$5 n^{2}+33 n+18$$

Factor each of the following polynomials completely. Indicate any that are not factorable using integers. Don't forget to look first for a common monomial factor. $$1-x^{4} y^{4}$$

Factor completely. $$15 x^{2} y^{3}+20 x y^{2}+35 x^{3} y^{4}$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(1+t)(5-2 t)$$

Raise each monomial to the indicated power. $$\left(-2 x^{2} y\right)^{5}$$

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$5 x^{2}=43 x-24$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$7 n^{2}+31 n+12$$

Factor each of the following polynomials completely. Indicate any that are not factorable using integers. Don't forget to look first for a common monomial factor. $$20 x-5 x^{3}$$

Factor completely. $$8 x^{5} y^{3}-6 x^{4} y^{5}+12 x^{2} y^{3}$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(3-t)(2+4 t)$$

Raise each monomial to the indicated power. $$\left(-3 x y^{4}\right)^{3}$$

Subtract the polynomials using the vertical format. \(2 x^{2}-7 x-10\) from \(-x^{3}-12\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$n(n+2)=360$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$x^{2}+25 x+150$$

Factor each of the following polynomials completely. Indicate any that are not factorable using integers. Don't forget to look first for a common monomial factor. $$4 x^{2}-64 y^{2}$$

Factor completely. $$x(y+2)+3(y+2)$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(3 t+7)^{2}$$

Raise each monomial to the indicated power. $$\left(-x^{4} y^{5}\right)^{4}$$

Perform the operations as described. Subtract \(2 x^{2}-7 x-1\) from the sum of \(x^{2}+9 x-4\) and \(-5 x^{2}-7 x+10 .\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$n(n+1)=182$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$x^{2}+21 x+108$$

Factor each of the following polynomials completely. Indicate any that are not factorable using integers. Don't forget to look first for a common monomial factor. $$9 x^{2}-81 y^{2}$$

Factor completely. $$x(y-1)+5(y-1)$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(4 t+6)^{2}$$

Raise each monomial to the indicated power. $$\left(-x^{5} y^{2}\right)^{4}$$

Perform the operations as described. Subtract \(4 x^{2}+6 x+9\) from the sum of \(-3 x^{2}-9 x+6\) and \(-2 x^{2}+6 x-4\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$9 x^{4}-37 x^{2}+4=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$n^{2}-36 n+320$$

Factor each of the following polynomials completely. Indicate any that are not factorable using integers. Don't forget to look first for a common monomial factor. $$3 x^{4}-48$$

Factor completely. $$3 x(2 a+b)-2 y(2 a+b)$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(2-5 x)(2+5 x)$$

Raise each monomial to the indicated power. $$\left(a b^{2} c^{3}\right)^{6}$$

Perform the operations as described. Subtract \(-x^{2}-7 x-1\) from the sum of \(4 x^{2}+3\) and \(-7 x^{2}+2 x\)