Act Algebra Review

Sophia is planning to build a rectangular garden. The length of the garden is represented by (3x + 2) meters and the width is represented by (2x + 4) meters. What is the expression for the area of the garden?

• 6x² + 16x + 8

• 5x² +11x + 6

• 5x² + 16x + 6

• 6x² + 11x + 8

Answer explanation

To find the product of (3x + 2)(2x + 4), use the distributive property: 3x*2x + 3x*4 + 2*2x + 2*4 = 6x^2 + 12x + 4x + 8 = 6x^2 + 16x + 8. Thus, the correct answer is 6x^2 + 16x + 8.

Aria is planning a garden and wants to calculate the area of a rectangular section. The length of the section is (x − 9) meters and the width is (x − 7) meters. What is the expression for the area of this section?

• x² − 2x − 63

• x² − 16x − 63

• x² − 2x + 63

• x² − 16x + 63

Answer explanation

To find the product of (x − 9)(x − 7), use the distributive property: x^2 - 7x - 9x + 63 = x^2 - 16x + 63. Thus, the correct answer is x^2 - 16x + 63.

Emma is designing a rectangular garden. The length of the garden is represented by (2x + 3) meters and the width is represented by (2x − 3) meters. What is the area of the garden?

• 4x² − 9

• 4x² + 9

• 4x² − 12x − 9

• 4x² + 12x − 9

Answer explanation

To find the product of (2x + 3)(2x - 3), use the difference of squares formula: a^2 - b^2. Here, a = 2x and b = 3. Thus, (2x)^2 - (3)^2 = 4x^2 - 9. The correct answer is 4x² - 9.

Rohan is trying to calculate the area of a rectangular garden. The length of the garden is represented by (3p − 3) meters and the width is represented by (p − 1) meters. What is the expression for the area of the garden?

• 3p² + 6p + 3

• 3p² − 6p + 3

• 3p² − 6p − 3

• 3p² + 6p − 3

Answer explanation

To find the product, use the distributive property: (3p)(p) + (3p)(-1) + (-3)(p) + (-3)(-1) = 3p^2 - 3p - 3p + 3 = 3p^2 - 6p + 3. Thus, the correct answer is 3p^2 - 6p + 3.

Nora is designing a rectangular garden. She wants to calculate the area of the garden if the length is (x - 7) meters and the width is (x + 7) meters. Find the product:

(x − 7)(x + 7)

• x² + 7x − 49

• x² − 7x + 49

• x² − 49

• x² + 49

Answer explanation

The expression (x − 7)(x + 7) is a difference of squares, which simplifies to x² − 49. Thus, the correct answer is x² − 49.

Isla is planning to build a square garden with each side measuring (x + 5) meters. What will be the area of the garden? Hint: try (x + 5)(x + 5)

• x² + 25

• x² + 10x + 25

• x² + 10 x + 10

• x² + 10

Answer explanation

To find (x + 5)², use the hint (x + 5)(x + 5). Applying the distributive property: x² + 5x + 5x + 25 = x² + 10x + 25. Thus, the correct answer is x² + 10x + 25.

Ava is organizing a math competition and she needs to create a problem for the participants. She decides to use the following expression and asks them to factor it completely: 3x³ + 9x

• 3x (x² + 3)

• 3x ( x³ + 9)

• x (3x² + 9)

• 3x (x³ + 3x)

Answer explanation

To factor 3x^3 + 9x, first factor out the common term 3x, resulting in 3x(x^2 + 3). This matches the correct answer choice, confirming that 3x(x^2 + 3) is the complete factorization.

Elijah is organizing a school event and needs to distribute 16xy - 24y flyers equally among different classes. Help him factor the expression completely to find out how many flyers each class will receive.

• 4y (4x - 6)

• 8y (2xy - 3y)

• 8y (2x - 3)

• 2xy (8 - 12y)

Answer explanation

To factor 16xy - 24y, first factor out the greatest common factor, which is 8y. This gives us 8y(2x - 3). Thus, the correct choice is 8y (2x - 3).

Jackson is trying to design a rectangular garden and needs to calculate the area. He has the expression for the area as 10x² + 15x - 5. Help Jackson by factoring the expression completely.

• 25(10x³+45x-15)

• 5(2x³ + 3x²-x)

• x(10x³+15x-5)

• 5(2x²+3x-1)

Answer explanation

To factor 10x² + 15x - 5, first factor out the greatest common factor, which is 5. This gives 5(2x² + 3x - 1). The expression 2x² + 3x - 1 cannot be factored further, making 5(2x² + 3x - 1) the correct choice.

Arjun is trying to design a rectangular garden. The area of the garden can be represented by the expression 10v² + 11v - 8. Help Arjun factor this expression to find the possible dimensions of the garden.

• (5v + 8)(2v + 1)

• (v + 8)(v - 1)

• (5v + 8)(2v - 1)

• (10v - 8)(v + 1)

Answer explanation

To factor 10v² + 11v - 8, we look for two numbers that multiply to -80 (10 * -8) and add to 11. The numbers 16 and -5 work. Thus, we can rewrite and factor as (5v + 8)(2v - 1). This matches the correct choice.