Act Algebra Review

Aria is trying to organize her collection of 5g² + 15g + 10 marbles into groups. Help her factor the expression to find out how she can group them.

• 5(g + 2)(g + 1)

• (5g + 10)(5g + 5)

• 5(g + 5)(g + 2)

• 5(g - 1)(g - 2)

Answer explanation

To factor 5g² + 15g + 10, first factor out the common term 5, giving 5(g² + 3g + 2). Then, factor the quadratic to get 5(g + 2)(g + 1). Thus, the correct answer is 5(g + 2)(g + 1).

Michael is planning to plant a rectangular garden and wants to calculate the area. The area of the garden can be represented by the expression n² + 16n + 63. Help Michael factor this expression to find the possible dimensions of the garden.

• (n-7)(n+4)

• (n+7)(n-9)

• (n-3)(n-10)

• (n+7)(n+9)

Answer explanation

To factor n² + 16n + 63, we look for two numbers that multiply to 63 and add to 16. The numbers 7 and 9 fit this, leading to the factors (n+7)(n+9). Thus, the correct answer is (n+7)(n+9).

Michael is trying to design a rectangular garden. The area of the garden is represented by the expression x² + 2x – 3. Help Michael find the possible dimensions of the garden by factoring the expression.

• (x - 2)(x + 1)

• (x + 1)(x - 3)

• (x + 2)(x - 1)

• (x - 1)(x + 3)

Answer explanation

To factor x² + 2x - 3, we look for two numbers that multiply to -3 and add to 2. The numbers 3 and -1 fit this, leading to (x - 1)(x + 3) as the correct factorization.

Zoe is designing a rectangular garden and the area is 290 meters squared. The length of the garden is 3 times the width minus 1 meter. Find the length.

• Length = 1 meter; Width = -6 meters

• Length = ⅓ meter; Width = -6 meters

• Length = 6 meters; Width = 3 meters

• Length = 6 meters; Width = -⅓ meter

Answer explanation

To solve the equation, factor or use the quadratic formula. The solutions are x = ⅓ and x = -6, which matches the correct answer choice. Other options do not satisfy the equation.

Arjun is designing a rectangular garden. The length of the garden is 14 meters more than its width. If the area of the garden is 15 square meters, find the width of the garden by completing the square.

• Width = -15 meters; Width = -1 meter

• Width = 15 meters; Width = -1 meter

• Width = 0 meters; Width = 7 meters

• Width = ±8 meters

Answer explanation

To solve the equation by completing the square, we rearrange and factor the quadratic. This leads to the solutions x = 15 and x = -1, confirming that the correct answer is x = 15; x = -1.

Emma is planning a garden and wants to create a rectangular area where the length is 5 meters more than the width. The area of the garden is 24 square meters. Solve for the dimensions of the garden by factoring.

• Width = 8 meters; Length = 3 meters

• Width = 3 meters; Length = 8 meters

• Width = 24 meters; Length = 1 meter

• Width = 12 meters; Length = -7 meters

Answer explanation

To solve the equation by factoring, we find the roots. The factors lead to x = -8 and x = 3, which match the correct choice. Thus, the solution is x = -8; x = 3.

What word phrase can you use to represent "5x + 2"?

• five times the sum of a number x and two

• two times the sum of a number x and five

• a number x times the sum of five and two

• the sum of five times a number x and two

Is x = 1 a solution of the equation
2 - 8x = -6?

• yes

• no

Solve for x.
2(-x - 4) = 4x + 16

• 4

• 3

• -3

• -4

Solve for a.
-11- 5a = 6(5a + 4)

• -1

• -2

• -3

• -4