Advanced Expressions Algebra

Find the difference. 
(3- 2x + 2x²) - (4x -5 +3x²)

• x_² + 6x + 8

• 2x² + 5x - 7

• -x² -6x + 8

• -2x² + 11x - 4

Tags

CCSS.HSA.APR.A.1

Multiply.
(b+3)(b²+2b+1)

• b³+6b²+6b+3

• b³+5b²+7b+3

• 4b³+8b²+3b

• 3b³+6b²+3b

Tags

CCSS.HSA.APR.A.1

Classify by number of terms:
3x³ – 6x

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

A polynomial function contains the factors x, x-3, and x+1. Which graphs could represent the polynomial function. SELECT ALL THAT APPLY

• 
• 
• 
• 
• 

Tags

CCSS.HSA.APR.B.3

Function g is defined by g(x) = 3(x + 8). What is the value of g(12)?

• A. -4

• B. 20

• C. 44

• D. 60

Answer explanation

To find g(12), substitute 12 into the function: g(12) = 3(12 + 8) = 3(20) = 60. Thus, the correct answer is D. 60.

Tags

CCSS.HSF.IF.A.2

Which of the following expressions is equivalent to (x + 7)(x² - 3x + 2)?

• x³ - 3x² + 2x + 14

• x³ + 4x² - 19x + 14

• x³ - 3x + 14

• x² - 2x + 9

Answer explanation

To find the equivalent expression, expand (x + 7)(x² - 3x + 2). This results in x³ + 4x² - 19x + 14, which matches choice B. The other options do not match the expanded form.

Tags

CCSS.HSA.APR.A.1

The graph above shows the cost, in dollars, of apples as a function of the number of pounds of apples purchased at a particular grocery store. The equation above defines the cost C, in dollars, for p pounds of pears at the same store. Which of the following statements accurately compares the cost per pound of apples and the cost per pound of pears at this store?

• Apples cost approximately $0.07 less per pound than pears do.

• Apples cost approximately $0.04 less per pound than pears do.

• Apples cost approximately $0.73 less per pound than pears do.

• Apples cost approximately $0.62 more per pound than pears do.

Answer explanation

To compare costs, calculate the cost per pound for both apples and pears. The graph shows apples cost less per pound than the equation for pears. The difference is approximately $0.07, making A the correct choice.

Tags

CCSS.8.EE.B.5

Which of the following expressions is equivalent to 3x² + 6x – 24?

• 3(x + 2)(x – 4)

• 3(x – 2)(x + 4)

• (x + 6)(x – 12)

• (x – 6)(x + 12)

Answer explanation

To factor 3x² + 6x - 24, first factor out 3: 3(x² + 2x - 8). Then, factor the quadratic: (x - 2)(x + 4). Thus, the expression is 3(x - 2)(x + 4), which matches the correct choice.

x² + 5x – 9 = 5 Which of the following values of x satisfies the equation above

• 7

• 3

• 2

• -7

Answer explanation

To solve x^2 + 5x - 9 = 5, first simplify to x^2 + 5x - 14 = 0. Factoring gives (x + 7)(x - 2) = 0, leading to x = -7 or x = 2. The correct answer is -7.

Tags

CCSS.6.EE.B.5

The graph of y = f(x) is shown in the xy-plane. Which of the following equations could define f(x)?

• f(x) = x^2 – 2x – 8

• f(x) = –x^2 + 2x – 8

• f(x) = (x – 2)(x + 4)

• f(x) = –(x – 1)2 – 9

Answer explanation

The equation f(x) = x^2 – 2x – 8 is a quadratic function that opens upwards, matching the graph's shape. The other options either open downwards or do not fit the graph's characteristics.

Tags

CCSS.HSF-IF.C.7A