Topic 3 - Polynomial Functions

Use the leading coefficient and degree of the polynomial function f(x) = x³ − 7x² + 10x to determine the end behavior of its graph. Select all the true statements.

• As x → ∞ , y → ∞ .

• As x → ∞ , y → −∞ .

• As x → ∞ , y → 0 .

• As x → −∞ , y → ∞ .

• As x → −∞ , y → −∞ .

The graph of a function f is shown. Use the graph to estimate all turning points. Select all x -values that are turning points of f .

• -3

• 0

• -1.5

• 1

• 1.5

Use the graph of the polynomial function f(x) = − x³ + 5x² − 2x − 8 to complete the sentences.

f is ​ (a)   on the intervals (-∞, 1/3) and (3, ∞).

f is ​ (b)   on the intervals (-1, 2) and (4, ∞).

f is ​ (c)   on the intervals (1/3, 3).

f is ​ (d)   on the intervals (-∞, -1) and (2, 4).

• decreasing
• negative
• increasing
• positive

Add (4a²b − 3ab² + 2ab + 5) and (2a²b + 3ab² − 7ab) . Complete the expression in standard form.

Mathematical Equivalence

ON

Tags

CCSS.HSA.APR.A.1

Multiply (x + 2y)( x² − xy + 3y) .

• x³ + x²y + 3xy − 2xy² + 6y²

• x³ − 3x²y + 3xy − 2xy² + 6y²

• x³ + 3xy − xy² + 3y²

• x³ − 3xy + 6y²

Tags

CCSS.HSA.APR.A.1

Jae is constructing an open box from a piece of cardboard that is 9 in. wide and 12 in. long. Jae cuts squares of equal size from each corner of the cardboard, and then folds up the sides of the box. Write and simplify a polynomial function V in standard form for the volume of the box in terms of x . (ASK HELP)

V(x) = ​ (a)   x³ - ​ (b)   x² + ​ (c)   x​

• 4
• 42
• 108
• 26

Use Dfiference of Squares to multiply (5 − 4x³ )(5 + 4x³) .

• 25 − 4x⁹

• 25 − 40x³ + 16x⁶

• 25 − 4x⁶

• 25 − 16x⁶

Tags

CCSS.HSA.APR.A.1

Use the Difference of cubes identity to factor 1 − 125n³ . Select all factors.

• 1 - 5n

• 1 + 5n

• 1 + 5n + 5n²

• 1 - 5n + 5n²

• 1 + 5n + 25n²

Tags

CCSS.HSA.APR.C.4

Expand (a + 4)⁵: a⁵ + ​ ​ (a)   a⁴ + ​ (b)   a³ + ​ (c)   a² + ​ (d)   a + ​ (e)  

• 460
• 20
• 160
• 640
• 1280
• 1024

Tags

CCSS.HSA.APR.C.5

Use long division to divide x³ + x² − 2x + 14 by x + 3 .

Mathematical Equivalence

ON

Tags

CCSS.HSA.APR.D.6