Common Core HSA.APR.D.6 worksheet

Question 1

Divide x³ + 7x² + 13x + 13 by (x + 2). Type the quotient (ignore the remainder).

Answer 

Question 2

Simplify: (x² − 9x + 18)/(x² − 9)

• A. (x − 6)/(x − 3)
• B. (x − 9)/(x − 9)
• C. (x − 6)/(x + 3)
• D. (x + 6)/(x + 3)

Question 3

Find lim(x→−5) (x² + 7x + 10)/(x + 5).

Answer 

Question 4

Omar simplified (x + 7)/x by crossing out the x's and got 1 + 7 = 8. Is this right?

• A. Right
• B. Wrong: only common factors can be cancelled, not terms
• C. Right, but only when x is positive

Question 5

Find lim(x→4) (2x² + 5x).

Answer 

Question 6

Find lim(x→−1) (x² − 1)/(x² + 3x + 2). Give a fraction if needed.

Answer (as a fraction)

Question 7

Write as a single fraction: 3/(x + 6) + 1/(x + 5). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)).

Answer 

Question 8

Simplify: (x² − 3x − 4) / (x − 4)

• A. x − 1
• B. x + 1
• C. x − 4
• D. x − 3

Question 9

Divide x³ − x² − 25x − 20 by (x + 4). The remainder is 0. Type the quotient.

Answer 

Question 10

Find the vertical asymptote of f(x) = (5x − 5)/(2x + 6). Give the x-value.

Answer 

Question 11

Divide x³ − 2x² − 12x + 6 by (x + 3). Type the quotient (ignore the remainder).

Answer 

Question 12

Simplify: (x² − 3x − 18)/(x − 6)

• A. (x − 3)
• B. (x − 18)
• C. (x + 3)
• D. (x + 3)/(x − 6)

Question 13

Find lim(x→−6) (x² + 3x − 18)/(x + 6).

Answer 

Question 14

Kwame simplified (x + 8)/x by crossing out the x's and got 1 + 8 = 9. Is this right?

• A. Right
• B. Wrong: only common factors can be cancelled, not terms
• C. Right, but only when x is positive

Question 15

Find lim(x→−1) (x² − 6x − 9).

Answer 

Question 16

Find lim(x→−5) (x² − 25)/(x² + 3x − 10). Give a fraction if needed.

Answer (as a fraction)