Exam 7: Factoring, Solving Equations and Problem Solving

Factor the trinomial completely. Indicate if it is not factorable using integers. $8 x ^ { 2 } + 22 x - 21$

Solve the equation. $2 x ^ { 2 } = 200$

Solve the equation. $325 x ^ { 3 } = 13 x$ Please enter your answer as three numbers, separated by commas. Leave fractions in your answer.

Solve the equation. $x ^ { 2 } + 2 x = 24$

Factor the polynomial completely. $4 p ( b + 2 ) + 7 f ( b + 2 )$

Factor the following polynomial completely. $2 p ^ { 3 } - 2 p$

Factor the polynomial completely. $14 z ^ { 3 } b ^ { 2 } + 16 z b ^ { 4 } + 26 z b ^ { 2 }$

Find three negative consecutive integers such that the product of the two smaller integers is 142 more than ten times the largest integer.

Factor the following polynomial completely. $14 a ^ { 2 } + 9 a n - 8 n ^ { 2 }$

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. $20 y ^ { 2 } + 9 y + 1$

In an office building, a room contains 70 chairs. The number of chairs per row is 4 less than twice the number of rows. Find the number of rows.

Factor the following polynomial completely. $6 p ^ { 2 } + 33 p + 36$

Solve the equation. $35 y ^ { 2 } + 61 y = - 24$ Please enter your answer as two numbers, separated by a comma.

Factor the polynomial completely. $20 y ^ { 3 } d ^ { 2 } + 32 y d ^ { 4 } + 68 y d ^ { 2 }$

Choose the correct solution set. $4 x ^ { 2 } + 29 x - 24 = 0$

Solve the equation. $3 y ^ { 2 } - 13 y + 4 = 0$ Please enter your answer as two numbers, separated by a comma.

Solve the equation. $9 x ( 9 x + 4 ) = 5$ Please enter your answer as two numbers, separated by a comma.

Factor the polynomial completely. $5 z ^ { 5 } b ^ { 8 } + 11 z ^ { 11 } b ^ { 3 }$

Set up an equation and solve the problem. The sum of the areas of two circles is 612 $\pi$ square meters. Find the length of a radius of the smaller circle if one of them is 4 times as long as the other. __________ meters

The perimeter of a rectangle is 32 centimeters and the area is 48 square centimeters. Find the length and width of the rectangle.