Common Core HSA.SSE.A.2 worksheet

Question 1

Factorise: x² − 18x + 81

• A. (x − 9)²
• B. (x − 18)²
• C. (x + 81)(x + 1)
• D. (x + 9)²

Question 2

Factorise fully: x² + 3x + 2

Answer 

Question 3

Ravi wrote (5x⁵)² = 5x¹⁰. What is the correct simplification?

• A. 10x¹⁰
• B. 25x²⁵
• C. 25x¹⁰
• D. 25x⁷

Question 4

Factorise: 2x² − 6x − 36

• A. (2x + 6)(x − 6)
• B. (2x − 6)(x + 6)
• C. (x + 6)(2x − 6)

Question 5

Ethan says x³ − 16x = x(x² − 16) is fully factorised. What is the full factorisation?

• A. x(x − 4)²
• B. (x + 4)(x − 4)
• C. x²(x − 16)
• D. x(x + 4)(x − 4)

Question 6

Use the difference of two squares to work out 62² − 56² without a calculator.

Answer 

Question 7

Jamal simplified (x + 3)/x by crossing out the x's and got 1 + 3 = 4. Is this right?

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

Question 8

x² + 6x − 27 = (x + 9)(x + ☐). What number goes in the box?

Answer 

Question 9

Simplify: (−2x⁴y⁴)³

Answer 

Question 10

Factorise by grouping: 2x² + 8x + 3x + 12

• A. (2x + 3)(x − 4)
• B. (2x + 4)(x + 3)
• C. (2x + 3)(x + 4)
• D. (2x − 3)(x − 4)

Question 11

Factorise: 8x³ − 27

• A. (2x − 3)³
• B. (2x − 3)(4x² − 6x + 9)
• C. (2x − 3)(4x² + 6x + 9)
• D. (8x − 27)(x² + 1)

Question 12

Simplify: (x² − 1)/(x + 1)

• A. (x − 1)
• B. x − 1
• C. (x + 1)
• D. 1/(x − 1)

Question 13

Factorise: x³ + 8

• A. (x + 2)(x² − 2x + 4)
• B. (x + 2)³
• C. (x + 2)(x² − 4x + 4)
• D. (x + 2)(x² + 2x + 4)

Question 14

What number c makes x² + 14x + c a perfect square?

Answer 

Question 15

Factorise: x² − 36

• A. (x + 6)²
• B. (x + 36)(x − 1)
• C. (x + 6)(x − 6)
• D. (x − 6)²

Question 16

Factorise fully: 5x² + 55x + 150

• A. 5(x² + 11x + 30)
• B. 5(x + 6)(x + 5)
• C. (5x + 6)(x + 5)
• D. 5(x − 6)(x − 5)