Exam 13: Factoring Polynomials

Solve. -One leg of a right triangle is 21 inches longer than the smaller leg, and the hypotenuse is 24 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

Represent the given condition using a single variable, x. -The base and height of a triangle whose height is eight less than five times its base.

Solve the equation. - $15 x ^ { 2 } = 8 x$

Factor the trinomial completely. - $15 x ^ { 4 } - 22 x ^ { 3 } + 8 x ^ { 2 }$

Solve the equation. - $16 n ^ { 2 } + 48 n = 0$

Solve. -A triangular piece of glass is being cut so that the height of the triangle is 4 inches shorter than twice the base. If the area of the triangle is 24 square inches, how long is the height of the triangle?

Factor out the GCF from the polynomial. - $x ^ { 10 } y ^ { 8 } - x ^ { 10 } y ^ { 7 } + x ^ { 8 } y ^ { 5 } - x ^ { 7 } y ^ { 5 }$

Solve. -If the cost, C(x), for manufacturing x units of a certain product is given byoduct is given by $C ( x ) = x ^ { 2 } - 50 x + 12,600$ , find the, find th number of units manufactured at a cost of $14,000.

Solve the equation. -(y - 7)(9y + 17)= 0

Factor the trinomial completely. - $6 x ^ { 2 } - 21 x - 12$

Determine whether the trinomial is a perfect square trinomial. - $m ^ { 2 } - 22 m + 121$

The equationn $D = \frac { 1 } { 2 } n ( n - 3 )$ gives the n gives the umber of diagonals D for a polygon with n sides. Use this equation to solve the problem. -Find the number of sides n for a polygon that has 44 diagonals.

Find the GCF for the list. -800, 900

Factor the trinomial completely. - $14 y ^ { 2 } + 63 y - 35$

Factor out the GCF from the polynomial. - $15 x ^ { 2 } + 11 x ^ { 4 }$

Solve the equation. -(8 - 0.8x)(5 - 0.2x)= 0

Factor the trinomial completely. - $9 x ^ { 2 } + 24 x y + 16 y ^ { 2 }$

Solve the equation. - $15 x ^ { 3 } + 90 x ^ { 2 } + 120 x = 0$

Factor the trinomial completely. - $6 x ^ { 2 } - 26 x - 20$

Fill in the blank with one of the words or phrases listed below. -An equation that can be written in the formrm a $a x ^ { 2 } + b x + c = 0$ 0 (with a not 0)0 (with a not 0)is called a_____ .