Chapter 7

Find the greatest common factor of each group of terms. $$45 m^{3}, 20 m^{2}$$

Explain the zero product rule.

Find the following. a) \(6^{2}\) b) \(10^{2}\) c) \(4^{2}\) d) \(11^{2}\) e) \(3^{2}\) f) \(8^{2}\) g) \(12^{2}\) h) \(\left(\frac{1}{2}\right)^{2}\) i) \(\left(\frac{3}{5}\right)^{2}\)

Find two integers whose \(\begin{array}{cccc} & & \text { and whose } & \\ & \text { PRODUCT IS } & \text { SUM IS } & \text { ANSWER } \\ \text { a) } & -50 & 5 & \\ \text { b) } & 27 & -28 & \\ \text { c) } & 12 & 8 & \\ \text { d) } & -72 & -6 & \end{array}\)

Find the length and width of each rectangle. Area \(=40 \mathrm{cm}^{2}\)

Find the greatest common factor of each group of terms. $$18 d^{6}, 21 d^{2}$$

Can we solve \((y+6)(y-11)=8\) by setting each factor equal to 8 like this: \(y+6=8\) or \(y-11=8 ?\) Why or why not?

Find two integers whose \(\begin{array}{lccc} & \text { PRODUCT IS } & \text { and whose } & \\ \text { a) } & 18 & \text { SUM IS } & \text { ANSWER } \\ \text { b) } & -132 & 19 & \\ \text { c) } & -30 & -13 & \\ \text { d) } & 63 & -16 & \end{array}\)

Find the greatest common factor of each group of terms. $$42 k^{5}, 54 k^{7}, 72 k^{9}$$

Fill in the blank with a term that has a positive coefficient. a) \((\quad)^{2}=n^{4}\) b) \(\quad(\quad )^{2}=25 t^{2}\) c) \(\quad(\quad)^{2}=49 k^{2}\) d) \(\quad(\quad)^{2}=16 p^{4}\) e) \(\quad(\quad)^{2}=\frac{1}{9}\) f) \(\quad(\quad)^{2}=\frac{25}{4}\)

Solve each equation.. \((m+9)(m-8)=0\)

Factor by grouping. $$2 k^{2}+10 k+9 k+45$$

If \(x^{2}+b x+c\) factors to \((x+m)(x+n)\) and if \(c\) is positive and \(b\) is negative, what do you know about the signs of \(m\) and \(n ?\)

Find the greatest common factor of each group of terms. $$25 t^{8}, 55 t, 30 t^{3}$$

If \(x^{n}\) is a perfect square, then \(n\) is divisible by what number?

Factor by grouping. $$9 m^{2}+54 m+2 m+12$$

If \(x^{2}+b x+c\) factors to \((x+m)(x+n)\) and if \(b\) and \(c\) are positive, what do you know about the signs of \(m\) and \(n ?\)

Find the greatest common factor of each group of terms. $$27 x^{4} y, 45 x^{2} y^{3}$$

What perfect square trinomial factors to \((z+9)^{2} ?\)

Solve each equation.. \((q-4)(q-7)=0\)

Factor by grouping. $$7 y^{2}-7 y-6 y+6$$

When asked to factor a polynomial, what is the first question you should ask yourself?

Find the greatest common factor of each group of terms. $$24 r^{3} s^{6}, 56 r^{2} s^{5}$$

What perfect square trinomial factors to \((2 b-7)^{2} ?\)

Solve each equation.. \((x-5)(x+2)=0\)

Factor by grouping. $$8 c^{2}-8 c+11 c-11$$

Find the greatest common factor of each group of terms. $$28 u^{2} v^{5}, 20 u v^{3},-8 u v^{4}$$

Factor by grouping. $$8 a^{2}-14 a b+12 a b-21 b^{2}$$

Why isn't \(9 c^{2}-12 c+16\) a perfect square trinomial?

Solve each equation.. \((4 z+3)(z-9)=0\)

After factoring a polynomial, what should you ask yourself to be sure that the polynomial is completely factored?

Why isn't \(k^{2}+6 k+8\) a perfect square trinomial?

Find the greatest common factor of each group of terms. $$-6 a^{4} b^{3}, 18 a^{2} b^{6}, 12 a^{2} b^{4}$$

Factor by grouping. $$ 10 y^{2}-8 y z-15 y z+12 z^{2} $$

Solve each equation.. \((2 n+1)(n-13)=0\)

How do you check the factorization of a polynomial?

Write an equation and solve. A rectangular rug is \(4 \mathrm{ft}\) longer than it is wide. If its area is \(45 \mathrm{ft}^{2},\) what is its length and width?

Factor completely. $$t^{2}+16 t+64$$

Find the greatest common factor of each group of terms. $$21 s^{2} t, 35 s^{2} t^{2}, s^{4} t^{2}$$

Solve each equation.. \(11 s(s+15)=0\)

Complete the factorization. $$n^{2}+12 n+27=(n+9)(\quad)$$

Write an equation and solve. The surface of a rectangular bulletin board has an area of 300 in \(^{2}\). Find its dimensions if it is 5 in. longer than it is wide.

Factor completely. $$x^{2}+12 x+36$$

Find the greatest common factor of each group of terms. $$p^{4} q^{4},-p^{3} q^{4},-p^{3} q$$

Solve each equation.. \(11 s(s+15)=0\)

Complete the factorization. $$p^{2}+11 p+24=(p+3)(\quad)$$

Write an equation and solve. Judy makes stained glass windows. She needs to cut a rectangular piece of glass with an area of 54 in \(^{2}\) so that its width is 3 in. less than its length. Find the dimensions of the glass she must cut.

Factor completely. $$g^{2}-18 g+81$$

How do we know that \((2 x-4)\) cannot be a factor of \(2 x^{2}+13 x-24 ?\)

Solve each equation.. \((6 x-5)^{2}=0\)