Exam 7: Factoring, Solving Equations and Problem Solving

Factor the following trinomial assuming that all variables appearing as exponents represent positive integers. $x ^ { 2 a } + 7 x ^ { a } + 6$

Factor the polynomial completely. $45 y + 65 d$

Factor the polynomial completely. $4 x ^ { 7 } + 4 x ^ { 8 } + 4 x ^ { 5 }$

A strip of uniform width is to be cut off of both sides and both ends of a sheet of paper that is 8 inches by 10 inches in order to reduce the size of the paper to an area of 15 square inches. Find the width of the strip. __________ inches

Factor the following trinomial completely. $x ^ { 2 } - 11 x + 24$

Factor the polynomial completely. Don t forget to look for a common monomial factor first. $4 x ^ { 2 } - 16 y ^ { 2 }$

Factor the following trinomial completely. $x ^ { 2 } + 2 x y - 15 y ^ { 2 }$

Factor the polynomial completely. $54 z + 66 c$

Factor the polynomial completely. $4 - 81 y ^ { 2 }$

In an office building, a room contains 81 chairs. The number of chairs per row is 9 less than twice the number of rows. Find the number of rows. __________ rows

Perfect square trinomials are trinomials where the terms are perfect squares.

When solving a word problem involving distances, a solution to the equation might be discarded.

Consider the following approach to factoring. $20 x ^ { 2 } + 39 x + 18$ We need two integers whose sum is 39 and whose product is 360. To help find these integers, let s prime factor 360. $360 = 5 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5$ Now by grouping these factors in various ways, we find that $2 \cdot 2 \cdot 2 \cdot 3 = 24,3 \cdot 5 = 15$ and $24 + 15 = 39$ So the numbers are 15 and 24, and we can express the middle term of the given trinomial, $39 x$ , as $15 x + 24 x$ . Therefore, we can complete the factoring as follows: $20 x ^ { 2 } + 39 x + 18 = 20 x ^ { 2 } + 15 x + 24 x + 18 = 5 x ( 4 x + 3 ) + 6 ( 4 x + 3 ) = ( 4 x + 3 ) ( 5 x + 6 )$ Factor the trinomial. $20 y ^ { 2 } + 23 y + 6$

The length of one leg of a right triangle is 14 centimeters more than the length of the other leg. The length of the hypotenuse is 26 centimeters. Find the lengths of the two legs. Please enter your answer as two numbers without the units, separated by a comma.

An apple orchard contains 104 trees. The number of trees per row is five more than the number of rows. Find the number of rows.

Factor the following polynomial completely. $14 m ^ { 2 } + 38 m + 20$

Solve the equation. $x ^ { 2 } + 6 x = 27$

Set up an equation and solve the problem. Suppose that the width of a certain rectangle is 0.6 of its length and the area of that same rectangle is 0.6 square meters. Find the length of the rectangle. __________ meters

Solve the equation. $16 y ( y + 1 ) = 21$ Please enter your answer as two numbers, separated by a comma.

Solve the equation. $2 x ^ { 3 } - 72 x = 0$