Algebra Ch 1-5 Review

Factor the difference of squares: 4x² - 9

• (2x - 3)(2x + 3)

• (2x - 3)(2x - 3)

• (4x - 3)(x + 3)

• (2x + 3)(2x + 3)

Answer explanation

The expression 4x² - 9 is a difference of squares, which factors as (a - b)(a + b) where a = 2x and b = 3. Thus, it factors to (2x - 3)(2x + 3), making this the correct choice.

Tags

CCSS.HSA.SSE.A.2

Solve the quadratic equation: 4x² + 9x + 2 = 0

• 1/4, 2

• 1/2, 4

• -1/4, -2

• -1/2, -4

Answer explanation

To solve 4x² + 9x + 2 = 0, use the quadratic formula x = (-b ± √(b² - 4ac)) / 2a. Here, a=4, b=9, c=2. This gives roots x = -1/4 and x = -2, making the correct choice -1/4, -2.

Tags

CCSS.HSA.REI.B.4

What is this formula?

• This is the speed of light formula.

• This is the quadratic formula.

• This is the zero product property.

• This is scary.

Answer explanation

The quadratic formula, given by x = (-b ± √(b²-4ac)) / 2a, is used to find the roots of a quadratic equation ax² + bx + c = 0. This formula is essential in algebra for solving such equations.

Tags

CCSS.HSA.REI.B.4

Multiply: (x + 3)(x + 5)

Answer explanation

To multiply (x + 3)(x + 5), use the distributive property: x*x + x*5 + 3*x + 3*5 = x^2 + 5x + 3x + 15 = x^2 + 8x + 15. Thus, the correct answer is x^2 + 8x + 15.

Tags

CCSS.HSA.APR.A.1

Multiply: (x + 2)(x² + 3x + 4)

• x³ + 5x² + 10x + 8

Answer explanation

To multiply (x + 2)(x^2 + 3x + 4), use the distributive property: x(x^2 + 3x + 4) + 2(x^2 + 3x + 4). This results in x^3 + 3x^2 + 4x + 2x^2 + 6x + 8, which simplifies to x^3 + 5x^2 + 10x + 8.

Tags

CCSS.HSA.APR.A.1

Factor the trinomial: x² - 5x - 14

• (x - 7)(x + 2)

• (x - 7)(x - 14)

• (x + 7)(x - 2)

• (x - 7)(x - 2)

Answer explanation

To factor x^2 - 5x - 14, we look for two numbers that multiply to -14 and add to -5. The numbers -7 and 2 fit this, so the factorization is (x - 7)(x + 2). Thus, the correct choice is (x - 7)(x + 2).

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Factor completely: 3x² - 12x - 15

• 3(x - 3)(x + 5)

• 3(x - 5)(x + 1)

• (3x + 15)(x - 1)

• 3(x + 3)(x - 5)

Answer explanation

To factor 3x² - 12x - 15, first factor out 3: 3(x² - 4x - 5). Then, factor the quadratic: (x - 5)(x + 1). Thus, the complete factorization is 3(x - 5)(x + 1), which is the correct answer.

Tags

CCSS.HSA.SSE.A.2

Factor the trinomial: 2x² - 5x - 3

• (2x - 1)(x + 3)

• (2x + 1)(x - 3)

• (2x - 3)(x + 1)

• (2x + 3)(x - 1)

Answer explanation

To factor 2x² + 7x - 3, we look for two numbers that multiply to (2 * -3 = -6) and add to 7. The numbers 6 and -1 work. Thus, we can rewrite the trinomial as (2x + 1)(x - 3). Therefore, the correct choice is (2x + 1)(x - 3).

Tags

CCSS.HSA.SSE.A.2

Solve the quadratic equation by factoring: x² - 9x + 20 = 0

• x = 6, 8

• x = 4, 5

• x = 3, 7

• x = 2, 10

Answer explanation

To factor the equation x^2 - 9x + 20 = 0, we look for two numbers that multiply to 20 and add to -9. The numbers 4 and 5 fit this, so we can write (x - 4)(x - 5) = 0. Thus, the solutions are x = 4 and x = 5.

Tags

CCSS.HSA.REI.B.4

Simplify √-48

• 4√3

• 16i√3

• 4i√3

• -4i√3

Answer explanation

To simplify √-48, first factor it: √(-1) * √48 = i√48. Then, simplify √48 = √(16*3) = 4√3. Thus, √-48 = 4i√3, making the correct answer 4i√3.

Tags

CCSS.HSN.CN.A.1