Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Factoring Monic Quadratics

Sample Question Videos

Worksheet • 24 Questions • 1 Video

Q1:

Factor π‘₯ + 8 π‘₯ βˆ’ 2 0 2 .

  • A ( π‘₯ + 1 0 ) ( π‘₯ βˆ’ 2 )
  • B ( π‘₯ βˆ’ 2 ) ( π‘₯ βˆ’ 1 0 )
  • C ( π‘₯ βˆ’ 4 ) ( π‘₯ + 5 )
  • D ( π‘₯ βˆ’ 4 ) ( π‘₯ βˆ’ 5 )
  • E ( π‘₯ + 2 ) ( π‘₯ + 1 0 )

Q2:

Find the solution set of π‘₯ ( π‘₯ βˆ’ 1 9 ) = βˆ’ 1 5 π‘₯ in ℝ .

  • A { 0 , 4 }
  • B { 1 9 , βˆ’ 1 5 }
  • C { 0 , βˆ’ 4 }
  • D { βˆ’ 4 }
  • E { 4 }

Q3:

What property is illustrated by the step

  • AThe distributive property of multiplication over addition
  • BThe property of opposites
  • CThe associative property of addition
  • DThe associative property of multiplication
  • EThe commutative property of addition

Q4:

Find the possible values of if .

  • A
  • B
  • C
  • D
  • E

Q5:

Solve the equation ( π‘₯ βˆ’ 3 ) ( π‘₯ + 8 ) = 0 .

  • A π‘₯ = 3 , π‘₯ = βˆ’ 8
  • B π‘₯ = βˆ’ 3 , π‘₯ = 8
  • C π‘₯ = 3 , π‘₯ = 8
  • D π‘₯ = βˆ’ 3 , π‘₯ = βˆ’ 8

Q6:

Identify the solutions to the equation ( π‘₯ βˆ’ 3 ) ( π‘₯ + 8 ) = 0 .

  • A π‘₯ = 3 or π‘₯ = βˆ’ 8
  • B π‘₯ = βˆ’ 3 or π‘₯ = 8
  • C π‘₯ = 3 or π‘₯ = 8
  • D π‘₯ = βˆ’ 3 or π‘₯ = βˆ’ 8

Q7:

If the function 𝑓 ∢ β„• β†’ β„€ , where 𝑓 ( π‘₯ ) = ( π‘₯ + 1 7 ) 2 , and the function 𝑔 ∢ β„• β†’ β„€ , where 𝑔 ( π‘₯ ) = π‘₯ + 1 7 , find the solution set of π‘₯ which makes 𝑓 ( π‘₯ ) = 𝑔 ( π‘₯ ) .

  • A βˆ…
  • B { βˆ’ 1 7 }
  • C { 1 7 , 1 6 }
  • D { βˆ’ 1 6 }

Q8:

Given that π‘₯ + 1 6 π‘₯ = 8 , find π‘₯ + 1 6 π‘₯ 2 2 .

Q9:

At which values of π‘₯ does the graph of the equation 𝑦 = π‘₯ ( π‘₯ βˆ’ 1 0 ) cross the π‘₯ -axis?

  • A0 and 10
  • B0 and βˆ’ √ 1 0
  • C 0 and βˆ’ 1 0
  • D 0 and √ 1 0
  • E √ 1 0 and βˆ’ √ 1 0

Q10:

Find the solution set of the equation ο€» π‘₯ βˆ’ 7 √ 1 1  ο€» π‘₯ + 2 √ 4 1  = 0 in ℝ .

  • A  7 √ 1 1 , βˆ’ 2 √ 4 1 
  • B  βˆ’ 7 √ 1 1 , 2 √ 4 1 
  • C  βˆ’ 7 √ 1 1 , βˆ’ 2 √ 4 1 
  • D  7 √ 1 1 , 2 √ 4 1 

Q11:

Factor π‘₯ + 8 π‘₯ + 1 2 2 .

  • A ( π‘₯ + 6 ) ( π‘₯ + 2 )
  • B ( π‘₯ βˆ’ 6 ) ( π‘₯ βˆ’ 2 )
  • C ( π‘₯ + 3 ) ( π‘₯ + 4 )
  • D ( π‘₯ + 3 ) ( π‘₯ βˆ’ 4 )
  • E ( π‘₯ βˆ’ 6 ) ( π‘₯ + 2 )

Q12:

At which values of π‘₯ does the graph of the equation 𝑦 = ( π‘₯ + 2 ) ( π‘₯ βˆ’ 6 ) cross the π‘₯ -axis?

  • A βˆ’ 2 and 6
  • B 4 and 12
  • C2 and βˆ’ 6
  • D4 and βˆ’ 1 2
  • E βˆ’ 4 and βˆ’ 1 2

Q13:

Factorise fully π‘₯ + 2 π‘₯ βˆ’ 6 3 π‘₯ 3 2 .

  • A π‘₯ ( π‘₯ βˆ’ 7 ) ( π‘₯ + 9 )
  • B π‘₯ ( π‘₯ + 7 ) ( π‘₯ βˆ’ 9 )
  • C π‘₯ ( π‘₯ βˆ’ 2 1 ) ( π‘₯ + 3 )
  • D π‘₯ ( π‘₯ + 7 ) ( π‘₯ + 9 )

Q14:

Factorise fully π‘₯ βˆ’ π‘₯ βˆ’ 1 2 π‘₯ 3 2 .

  • A π‘₯ ( π‘₯ + 3 ) ( π‘₯ βˆ’ 4 )
  • B π‘₯ ( π‘₯ βˆ’ 3 ) ( π‘₯ + 4 )
  • C π‘₯ ( π‘₯ βˆ’ 1 2 ) ( π‘₯ + 1 )
  • D π‘₯ ( π‘₯ βˆ’ 3 ) ( π‘₯ βˆ’ 4 )

Q15:

Find algebraically the solution set of the equation √ π‘₯ βˆ’ 1 6 π‘₯ + 6 4 = 2 2 .

  • A { 6 , 1 0 }
  • B { 1 0 }
  • C { βˆ’ 1 0 }
  • D { βˆ’ 1 0 , βˆ’ 6 }

Q16:

Find the solution set of the equation π‘₯ + 2 1 π‘₯ = βˆ’ 1 0 in ℝ .

  • A { βˆ’ 3 , βˆ’ 7 }
  • B { 1 , βˆ’ 1 }
  • C { βˆ’ 3 }
  • D { 3 , 7 }
  • E  1 , βˆ’ 1 3 3 

Q17:

Factor π‘₯ βˆ’ 8 π‘₯ βˆ’ 2 0 2 .

  • A ( π‘₯ βˆ’ 1 0 ) ( π‘₯ + 2 )
  • B ( π‘₯ βˆ’ 2 ) ( π‘₯ βˆ’ 1 0 )
  • C ( π‘₯ + 4 ) ( π‘₯ βˆ’ 5 )
  • D ( π‘₯ βˆ’ 4 ) ( π‘₯ + 5 )
  • E ( π‘₯ + 2 ) ( π‘₯ + 1 0 )

Q18:

By factoring, solve the equation π‘₯ 4 βˆ’ 3 π‘₯ 4 = 5 2 2 .

  • A π‘₯ = βˆ’ 2 , π‘₯ = 5
  • B π‘₯ = βˆ’ 5 2
  • C π‘₯ = βˆ’ 2
  • D π‘₯ = 5 2
  • E π‘₯ = 2 , π‘₯ = βˆ’ 5

Q19:

Find the solution set of 1 + 6 π‘₯ = 4 0 π‘₯ 2 in ℝ .

  • A { βˆ’ 1 0 , 4 }
  • B { βˆ’ 1 0 , βˆ’ 4 }
  • C { 1 0 , βˆ’ 4 }
  • D { βˆ’ 1 , 4 0 }
  • E { βˆ’ 2 0 , 2 }

Q20:

Find the solution set of ο€Ή π‘₯ βˆ’ 3 π‘₯  = βˆ’ 8 2 3 in ℝ .

  • A { 2 , 1 }
  • B { 2 , βˆ’ 1 }
  • C { 2 }
  • D { βˆ’ 2 , βˆ’ 1 }
  • E { βˆ’ 2 }

Q21:

Find the solution set of the equation ( π‘₯ βˆ’ 1 8 ) = 2 2 2 in ℝ .

  • A  1 8 + √ 2 2 , 1 8 βˆ’ √ 2 2 
  • B  βˆ’ 1 8 + √ 2 2 , βˆ’ 1 8 βˆ’ √ 2 2 
  • C  βˆ’ 1 8 + √ 2 2 , 1 8 βˆ’ √ 2 2 
  • D  1 8 + √ 2 2 , βˆ’ 1 8 βˆ’ √ 2 2 

Q22:

Factor the equation 𝑦 = π‘₯ βˆ’ 9  .

  • A 𝑦 = ( π‘₯ + 3 ) ( π‘₯ βˆ’ 3 )
  • B 𝑦 = ( π‘₯ βˆ’ 4 . 5 ) ( π‘₯ βˆ’ 4 . 5 )
  • C 𝑦 = ( π‘₯ + 9 ) ( π‘₯ βˆ’ 9 )
  • D 𝑦 = ( π‘₯ βˆ’ 3 ) ( π‘₯ βˆ’ 3 )
  • E 𝑦 = ( π‘₯ + 4 . 5 ) ( π‘₯ βˆ’ 4 . 5 )

At which values of π‘₯ does the graph of 𝑦 = π‘₯ βˆ’ 9  cross the π‘₯ -axis?

  • A3 and βˆ’ 3
  • B4.5
  • C9 and βˆ’ 9
  • D3
  • E4.5 and βˆ’ 4 . 5

Q23:

Find the solution set of the equation ο„Ÿ ο€Ό π‘₯ βˆ’ 6 3 π‘₯  + 2 5 2 = 1 6 2 .

  • A { βˆ’ 9 , βˆ’ 7 , 7 , 9 }
  • B { βˆ’ 9 , βˆ’ 7 }
  • C { βˆ’ 6 3 , βˆ’ 9 , βˆ’ 7 , 0 }
  • D { βˆ’ 6 3 , 0 }

Q24:

Find the solution set of ο€Ή π‘₯ βˆ’ 6 π‘₯ + 9  = 3 2 1 2 in ℝ .

  • A { 0 , 6 }
  • B { 0 , βˆ’ 6 }
  • C { βˆ’ 6 }
  • D { 6 }
Preview