Chapter 7

Factor each trinomial of the form \(x^{2}+b x y+c y^{2}\). \(x^{2}-3 x y-14 y^{2}\)

Factor each trinomial of the form \(x^{2}+b x y+c y^{2}\). \(u^{2}-8 u v-24 v^{2}\)

Factor each trinomial of the form \(x^{2}+b x y+c y^{2}\). \(m^{2}-5 m n+30 n^{2}\)

Factor each trinomial of the form \(x^{2}+b x y+c y^{2}\). \(c^{2}-7 c d+18 d^{2}\)

Factor each expression. \(u^{2}-12 u+36\)

Factor each expression. \(w^{2}+4 w-32\)

Factor each expression. \(x^{2}-14 x-32\)

Factor each expression. \(y^{2}+41 y+40\)

Factor each expression. \(r^{2}-20 r s+64 s^{2}\)

Factor each expression. \(x^{2}-16 x y+64 y^{2}\)

Factor each expression. \(k^{2}+34 k+120\)

Factor each expression. \(m^{2}+29 m+120\)

Factor each expression. \(y^{2}+10 y+15\)

Factor each expression. \(z^{2}-3 z+28\)

Factor each expression. \(m^{2}+m n-56 n^{2}\)

Factor each expression. \(q^{2}-29 q r-96 r^{2}\)

Factor each expression. \(u^{2}-17 u v+30 v^{2}\)

Factor each expression. \(m^{2}-31 m n+30 n^{2}\)

Factor each expression. \(r^{2}+11 r s+36 s^{2}\)

Deirdre is thinking of two consecutive integers whose product is 56. The trinomial \(x^{2}+x-56\) describes how these numbers are related. Factor the trinomial.

Deshawn is thinking of two consecutive integers whose product is 182 . The trinomial \(x^{2}+x-182\) describes how these numbers are related. Factor the trinomial.

Many trinomials of the form \(x^{2}+b x+c\) factor into the product of two binomials \((x+m)(x+n)\). Explain how you find the values of \(m\) and \(n\).

Will factored \(x^{2}-x-20\) as \((x+5)(x-4)\). Bill factored it as \((x+4)(x-5)\). Phil factored it as \((x-5)(x-4) .\) Who is correct? Explain why the other two are wrong.

Identify the best method to use to factor each polynomial. (a) \(10 q^{2}+50\) (b) \(a^{2}-5 a-14\) (c) \(u v+2 u+3 v+6\)

Identify the best method to use to factor each polynomial. (a) \(n^{2}+10 n+24\) (b) \(8 u^{2}+16\) (c) \(p q+5 p+2 q+10\)

Identify the best method to use to factor each polynomial. (a) \(x^{2}+4 x-21\) (b) \(a b+10 b+4 a+40\) (c) \(6 c^{2}+24\)

Identify the best method to use to factor each polynomial. (a) \(20 x^{2}+100\) (b) \(u v+6 u+4 v+24\) (c) \(y^{2}-8 y+15\)

Factor completely. \(5 x^{2}+35 x+30\)

Factor completely. \(12 s^{2}+24 s+12\)

Factor completely. \(2 z^{2}-2 z-24\)

Factor completely. \(3 u^{2}-12 u-36\)

Factor completely. \(7 v^{2}-63 v+56\)

Factor completely. \(5 w^{2}-30 w+45\)

Factor completely. \(p^{3}-8 p^{2}-20 p\)

Factor completely. \(q^{3}-5 q^{2}-24 q\)

Factor completely. \(3 m^{3}-21 m^{2}+30 m\)

Factor completely. \(11 n^{3}-55 n^{2}+44 n\)

Factor completely. \(5 x^{4}+10 x^{3}-75 x^{2}\)

Factor completely. \(6 y^{4}+12 y^{3}-48 y^{2}\)

Factor. \(2 t^{2}+7 t+5\)

Factor. \(5 y^{2}+16 y+11\)

Factor. \(11 x^{2}+34 x+3\)

Factor. \(7 b^{2}+50 b+7\)

Factor. \(4 w^{2}-5 w+1\)

Factor. \(5 x^{2}-17 x+6\)

Factor. \(6 p^{2}-19 p+10\)

Factor. \(21 m^{2}-29 m+10\)

Factor. \(4 q^{2}-7 q-2\)

Factor. \(10 y^{2}-53 y-11\)

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