Chapter 6

For the following problems, factor the trinomials if possible. $$ 8 a^{2}+10 a b-6 b^{2} $$

For the following problems, factor the polynomials, if possible. $$ s^{2}+9 s+18 $$

For the following problems, factor the binomials. $$ 49-16 a^{2} $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 8 x^{2}+12 x,-4 x $$

Factor \(6 x y+2 a x-3 a y-a^{2}\).

For the following problems, factor the polynomials, if possible. $$ x^{2}+14 x+40 $$

For the following problems, factor the trinomials if possible. $$ 12 a^{2}+54 a-90 $$

For the following problems, factor the binomials. $$ 100-36 b^{4} $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 20 a^{2} b^{2}-10 a^{2}, \quad-10 a^{2} $$

For the following problems, factor the polynomials, if possible. $$ a^{2}-12 a+36 $$

For the following problems, factor the trinomials if possible. $$ 12 b^{4}+30 b^{2} a+12 a^{2} $$

For the following problems, factor the binomials. $$ 128-32 x^{2} $$

Factor \(4 x^{2}+17 x-15\)

For the following problems, factor the polynomials, if possible. $$ n^{2}-14 n+49 $$

For the following problems, factor the trinomials if possible. $$ 30 a^{4} b^{4}-3 a^{2} b^{2}-6 c^{2} $$

For the following problems, factor the binomials. $$ x^{4}-16 $$

Solve the equation \(6(t-1)=4(5-s)\) if \(s=2\).

A quantity plus \(21 \%\) more of that quantity is \(26.25 .\) What is the original quantity?

For the following problems, factor the polynomials, if possible. $$ a^{2}+6 a+5 $$

For the following problems, factor the binomials. $$ 2 a b^{3}-a^{3} b $$

For the following problems, factor the trinomials if possible. $$ 3 a^{6}-3 a^{3} b^{2}-18 b^{4} $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ a-b+c,-1 $$

Given that \(4 a^{3}\) is a factor of \(8 a^{3}-12 a^{2}\), find the other factor.

For the following problems, factor the polynomials, if possible. $$ a^{2}-9 a+20 $$

For the following problems, factor the binomials. $$ a^{4}-b^{4} $$

For the following problems, factor the trinomials if possible. $$ 20 a^{2} b^{2}+2 a b c^{2}-6 a^{2} c^{4} $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 2 x+4 y-z,-1 $$

For the following problems, factor the polynomials, if possible. $$ 6 x^{2}+5 x+1 $$

For the following problems, factor the binomials. $$ a^{16}-b^{4} $$

For the following problems, factor the trinomials if possible. $$ 14 a^{2} z^{2}-40 a^{3} z^{2}-46 a^{4} z^{2} $$

For the following problems, factor the polynomials, if possible. $$ 4 a^{2}-9 a-9 $$

For the following problems, factor the binomials. $$ x^{12}-y^{12} $$

Simplify \(\left(a^{3} b^{6}\right)^{4}\)

For the following problems, factor the polynomials, if possible. $$ 4 x^{2}+7 x+3 $$

For the following problems, factor the binomials. $$ a^{2} c-9 c $$

Find the product. \(x^{2}(x-3)(x+4)\).

How many \(4 y^{2}\) 's are there in \(24 x^{2} y^{3}\) ?

For the following problems, factor the polynomials, if possible. $$ 42 a^{2}+5 a-2 $$

For the following problems, factor the binomials. $$ a^{3} c^{2}-25 a c^{2} $$

Find the product. \((5 m-3 n)^{2}\).

Find the product. \((2 y-3)^{2}\).

For the following problems, factor the polynomials, if possible. $$ 30 y^{2}+7 y-15 $$

For the following problems, factor the binomials. $$ a^{4} b^{4} c^{2} d^{2}-36 x^{2} y^{2} $$

Solve the equation \(5(2 x-1)-4(x+7)=0\).

Solve \(2(2 a-1)-a=7\).

For the following problems, factor the polynomials, if possible. $$ 56 m^{2}+26 m+6 $$

For the following problems, factor the binomials. $$ 49 x^{2} y^{4} z^{6}-64 a^{4} b^{2} c^{8} d^{10} $$

Factor \(x^{5}-8 x^{4}+7 x^{3}\).

Given that \(3 m^{2} n\) is a factor of \(12 m^{3} n^{4}\), find the other factor.

For the following problems, factor the polynomials, if possible. $$ 27 r^{2}-33 r-4 $$