Worksheet: Factoring Monic Quadratics

In this worksheet, we will practice factoring quadratics where the coefficient of the leading term is one.

Q1:

Factor 𝑥 + 8 𝑥 2 0 2 .

  • A ( 𝑥 + 2 ) ( 𝑥 + 1 0 )
  • B ( 𝑥 4 ) ( 𝑥 + 5 )
  • C ( 𝑥 4 ) ( 𝑥 5 )
  • D ( 𝑥 + 1 0 ) ( 𝑥 2 )
  • E ( 𝑥 2 ) ( 𝑥 1 0 )

Q2:

Solve the equation 𝑥 8 𝑥 + 1 6 = 0 2 by factoring.

  • A 𝑥 = 8 or 𝑥 = 2
  • B 𝑥 = 8 or 𝑥 = 2
  • C 𝑥 = 4
  • D 𝑥 = 4

Q3:

Solve 𝑥 4 𝑥 + 4 = 0 2 by factoring.

  • A 𝑥 = 4
  • B 𝑥 = 2 , 𝑥 = 2
  • C 𝑥 = 4 , 𝑥 = 1
  • D 𝑥 = 2
  • E 𝑥 = 2

Q4:

Factor 𝑥 + 8 𝑥 + 1 2 2 .

  • A ( 𝑥 6 ) ( 𝑥 + 2 )
  • B ( 𝑥 + 3 ) ( 𝑥 + 4 )
  • C ( 𝑥 + 3 ) ( 𝑥 4 )
  • D ( 𝑥 + 6 ) ( 𝑥 + 2 )
  • E ( 𝑥 6 ) ( 𝑥 2 )

Q5:

Factor 𝑥 8 𝑥 2 0 2 .

  • A ( 𝑥 + 2 ) ( 𝑥 + 1 0 )
  • B ( 𝑥 + 4 ) ( 𝑥 5 )
  • C ( 𝑥 4 ) ( 𝑥 + 5 )
  • D ( 𝑥 1 0 ) ( 𝑥 + 2 )
  • E ( 𝑥 2 ) ( 𝑥 1 0 )

Q6:

Find the solution set of ( 𝑥 + 9 ) = ( 𝑥 + 9 ) 2 in .

  • A { 9 }
  • B { 9 , 8 }
  • C { 1 0 }
  • D { 9 , 8 }
  • E { 9 , 1 0 }

Q7:

Find the solution set of 𝑧 + 1 0 𝑧 + 2 1 = 0 2 in .

  • A { 1 , 2 1 }
  • B { 7 , 3 }
  • C { 1 , 2 1 }
  • D { 7 , 3 }

Q8:

Find the solution set of the equation in .

  • A
  • B
  • C
  • D
  • E

Q9:

Factorise fully 𝑥 + 2 𝑥 6 3 𝑥 .

  • A 𝑥 ( 𝑥 + 7 ) ( 𝑥 + 9 )
  • B 𝑥 ( 𝑥 + 7 ) ( 𝑥 9 )
  • C 𝑥 ( 𝑥 2 1 ) ( 𝑥 + 3 )
  • D 𝑥 ( 𝑥 7 ) ( 𝑥 + 9 )

Q10:

Find the solution set of 𝑥 ( 𝑥 1 9 ) = 1 5 𝑥 in .

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

Q11:

Given that 𝑥 + 1 6 𝑥 = 8 , find 𝑥 + 1 6 𝑥 .

Q12:

Find the solution set of the equation 𝑥 + 2 1 𝑥 = 1 0 in .

  • A 1 , 1 3 3
  • B { 3 }
  • C { 3 , 7 }
  • D { 3 , 7 }
  • E { 1 , 1 }

Q13:

By factoring, solve the equation 𝑥 4 3 𝑥 4 = 5 2 2 .

  • A 𝑥 = 2 , 𝑥 = 5
  • B 𝑥 = 2
  • C 𝑥 = 5 2
  • D 𝑥 = 2 , 𝑥 = 5
  • E 𝑥 = 5 2

Q14:

Find the solution set of 1 + 6 𝑥 = 4 0 𝑥 in .

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

Q15:

Find the solution set of 𝑥 3 𝑥 = 8 2 3 in .

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

Q16:

Find the solution set of the equation ( 𝑥 1 8 ) = 2 2 in .

  • A 1 8 + 2 2 , 1 8 2 2
  • B 1 8 + 2 2 , 1 8 2 2
  • C 1 8 + 2 2 , 1 8 2 2
  • D 1 8 + 2 2 , 1 8 2 2

Q17:

Solve the equation ( 𝑥 3 ) ( 𝑥 + 8 ) = 0 .

  • A 𝑥 = 3 , 𝑥 = 8
  • B 𝑥 = 3 , 𝑥 = 8
  • C 𝑥 = 3 , 𝑥 = 8
  • D 𝑥 = 3 , 𝑥 = 8

Q18:

Identify the solutions to the equation ( 𝑥 3 ) ( 𝑥 + 8 ) = 0 .

  • A 𝑥 = 3 or 𝑥 = 8
  • B 𝑥 = 3 or 𝑥 = 8
  • C 𝑥 = 3 or 𝑥 = 8
  • D 𝑥 = 3 or 𝑥 = 8

Q19:

At which values of 𝑥 does the graph of the equation 𝑦 = 𝑥 ( 𝑥 1 0 ) cross the 𝑥 -axis?

  • A 1 0 and 1 0
  • B 0 and 1 0
  • C 0 and 1 0
  • D0 and 10
  • E0 and 1 0

Q20:

At which values of 𝑥 does the graph of the equation 𝑦 = ( 𝑥 + 2 ) ( 𝑥 6 ) cross the 𝑥 -axis?

  • A 4 and 1 2
  • B2 and 6
  • C4 and 1 2
  • D 2 and 6
  • E 4 and 12

Q21:

Find algebraically the solution set of the equation 𝑥 1 6 𝑥 + 6 4 = 2 .

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

Q22:

Factor the equation 𝑦 = 𝑥 9 .

  • A 𝑦 = ( 𝑥 + 4 . 5 ) ( 𝑥 4 . 5 )
  • B 𝑦 = ( 𝑥 + 9 ) ( 𝑥 9 )
  • C 𝑦 = ( 𝑥 3 ) ( 𝑥 3 )
  • D 𝑦 = ( 𝑥 + 3 ) ( 𝑥 3 )
  • E 𝑦 = ( 𝑥 4 . 5 ) ( 𝑥 4 . 5 )

At which values of 𝑥 does the graph of 𝑦 = 𝑥 9 cross the 𝑥 -axis?

  • A3 and 3
  • B3
  • C4.5 and 4 . 5
  • D9 and 9
  • E4.5

Q23:

Find the solution set of the equation 𝑥 6 3 𝑥 + 2 5 2 = 1 6 .

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

Q24:

What property is illustrated by the step

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

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