Chapter 7

Factor completely. \(a^{5}+9 a^{3}\)

Factor completely. \(75 m^{3}+12 m\)

Factor completely. \(121 r^{2}-s^{2}\)

Factor completely. \(49 b^{2}-36 a^{2}\)

Factor completely. \(8 m^{2}-32\)

Factor completely. \(36 q^{2}-100\)

Factor completely. \(25 w^{2}-60 w+36\)

Factor completely. \(49 b^{2}-112 b+64\)

Factor completely. \(m^{2}+14 m n+49 n^{2}\)

Factor completely. \(64 x^{2}+16 x y+y^{2}\)

Factor completely. \(7 b^{2}+7 b-42\)

Factor completely. \(3 n^{2}+30 n+72\)

Factor completely. \(3 x^{3}-81\)

Factor completely. \(5 t^{3}-40\)

Factor completely. \(k^{4}-16\)

Factor completely. \(m^{4}-81\)

Factor completely. \(15 p q-15 p+12 q-12\)

Factor completely. \(12 a b-6 a+10 b-5\)

Factor completely. \(4 x^{2}+40 x+84\)

Factor completely. \(5 q^{2}-15 q-90\)

Factor completely. \(u^{5}+u^{2}\)

Factor completely. \(5 n^{3}+320\)

Factor completely. \(25 x^{2}+35 x y+49 y^{2}\)

Factor completely. \(10 m^{4}-6250\)

Factor completely. \(3 v^{4}-768\)

A fall tradition at the University of California San Diego is the Pumpkin Drop, where a pumpkin is dropped from the eleventh story of Tioga Hall. (a) The binomial \(-16 t^{2}+128\) gives the height of the pumpkin \(t\) seconds after it is dropped. Factor the greatest common factor from this binomial. (b) If the pumpkin is thrown down with initial velocity 32 feet per second, its height after \(t\) seconds is given by the trinomial \(-16 t^{2}-32 t+128\). Completely factor this trinomial.

The difference of squares \(y^{4}-625\) can be factored as \(\left(y^{2}-25\right)\left(y^{2}+25\right)\). But it is not completely factored. What more must be done to completely factor it?

Of all the factoring methods covered in this chapter (GCF, grouping, undo FOIL, 'ac' method, special products) which is the easiest for you? Which is the hardest? Explain your answers.

Solve. \((x-3)(x+7)=0\)

Solve. \((y-11)(y+1)=0\)

Solve. \((3 a-10)(2 a-7)=0\)

Solve. \((5 b+1)(6 b+1)=0\)

Solve. \(6 m(12 m-5)=0\)

Solve. \(2 x(6 x-3)=0\)

Solve. \((y-3)^{2}=0\)

Solve. \((b+10)^{2}=0\)

Solve. \((2 x-1)^{2}=0\)

Solve. \((3 y+5)^{2}=0\)

Solve. \(x^{2}+7 x+12=0\)

Solve. \(y^{2}-8 y+15=0\)

Solve. \(5 a^{2}-26 a=24\)

Solve. \(4 b^{2}+7 b=-3\)

Solve. \(4 m^{2}=17 m-15\)

Solve. \(n^{2}=5 n-6\)

Solve. \(7 a^{2}+14 a=7 a\)

Solve. \(12 b^{2}-15 b=-9 b\)

Solve. \(625=x^{2}\)

Solve. \((y-3)(y+2)=4 y\)

Solve. \((p-5)(p+3)=-7\)

Solve. \((2 x+1)(x-3)=-4 x\)