Worksheet: Factoring Quadratics When the Leading Coefficient Is 1

In this worksheet, we will practice factoring quadratic trinomial expressions in the form x² + bx + c where the leading coefficient is 1.

Q1:

Factorise fully 𝑥 𝑥 3 0 .

  • A ( 𝑥 + 1 5 ) ( 𝑥 2 )
  • B ( 𝑥 + 5 ) ( 𝑥 6 )
  • C ( 𝑥 5 ) ( 𝑥 + 6 )
  • D ( 𝑥 5 ) ( 𝑥 6 )

Q2:

Factorise fully 𝑥 1 5 𝑥 𝑦 + 5 4 𝑦 .

  • A ( 𝑥 1 8 𝑦 ) ( 𝑥 3 𝑦 )
  • B ( 𝑥 + 9 𝑦 ) ( 𝑥 + 6 𝑦 )
  • C ( 𝑥 + 9 𝑦 ) ( 𝑥 6 𝑦 )
  • D ( 𝑥 9 𝑦 ) ( 𝑥 6 𝑦 )

Q3:

Factorise fully 5 𝑦 + 4 0 𝑧 + 3 0 𝑦 𝑧 .

  • A 5 ( 𝑦 2 𝑧 ) ( 𝑦 4 𝑧 )
  • B 5 ( 𝑦 + 2 𝑧 ) ( 𝑦 4 𝑧 )
  • C 5 ( 𝑦 + 2 𝑧 ) ( 𝑦 + 4 𝑧 )
  • D ( 5 𝑦 2 𝑧 ) ( 𝑦 + 4 𝑧 )
  • E ( 5 𝑦 + 𝑧 ) ( 𝑦 + 8 𝑧 )

Q4:

Which of the following is equivalent to ( 𝑥 3 𝑦 ) ( 𝑥 + 3 𝑦 ) ( 𝑥 1 8 𝑥 𝑦 + 8 1 𝑦 ) ?

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

Q5:

Factorise fully 𝑎 + 1 2 𝑎 𝑏 + 3 6 𝑏 3 6 𝑐 .

  • A 𝑎 + 6 𝑏 + 6 𝑐 𝑎 + 6 𝑏 6 𝑐
  • B ( 𝑎 + 6 𝑏 + 6 𝑐 ) ( 𝑎 + 6 𝑏 6 𝑐 )
  • C ( 𝑎 + 1 4 4 𝑏 + 6 𝑐 ) ( 𝑎 + 1 4 4 𝑏 6 𝑐 )
  • D ( 𝑎 + 6 𝑏 + 6 𝑐 ) ( 𝑎 6 𝑏 6 𝑐 )
  • E ( 𝑎 6 𝑏 + 6 𝑐 ) ( 𝑎 6 𝑏 6 𝑐 )

Q6:

Factorise fully 𝑥 + 3 𝑥 + 2 .

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

Q7:

Factorise fully 𝑥 5 𝑥 + 6 .

  • A ( 𝑥 6 ) ( 𝑥 1 )
  • B ( 𝑥 + 3 ) ( 𝑥 + 2 )
  • C ( 𝑥 3 ) ( 𝑥 2 )
  • D ( 𝑥 + 3 ) ( 𝑥 2 )

Q8:

Factorise fully 𝑥 + 2 𝑥 3 5 .

  • A ( 𝑥 + 5 ) ( 𝑥 + 7 )
  • B ( 𝑥 5 ) ( 𝑥 + 7 )
  • C ( 𝑥 + 5 ) ( 𝑥 7 )
  • D ( 𝑥 + 1 ) ( 𝑥 3 5 )

Q9:

Factorise fully 𝑥 5 𝑥 2 4 .

  • A ( 𝑥 8 ) ( 𝑥 + 3 )
  • B ( 𝑥 + 8 ) ( 𝑥 3 )
  • C ( 𝑥 + 8 ) ( 𝑥 + 3 )
  • D ( 𝑥 + 6 ) ( 𝑥 4 )

Q10:

Factorise fully 𝑥 9 𝑥 + 1 8 .

  • A ( 𝑥 1 8 ) ( 𝑥 1 )
  • B ( 𝑥 + 3 ) ( 𝑥 + 6 )
  • C ( 𝑥 3 ) ( 𝑥 6 )
  • D ( 𝑥 + 3 ) ( 𝑥 6 )

Q11:

Factorise fully 𝑥 1 3 𝑥 + 4 0 .

  • A ( 𝑥 + 5 ) ( 𝑥 + 8 )
  • B ( 𝑥 + 5 ) ( 𝑥 8 )
  • C ( 𝑥 5 ) ( 𝑥 8 )
  • D ( 𝑥 1 0 ) ( 𝑥 4 )

Q12:

Factorise fully 𝑥 + 8 𝑥 9 .

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

Q13:

Factorise fully 𝑥 + 5 𝑥 3 6 .

  • A ( 𝑥 + 4 ) ( 𝑥 + 9 )
  • B ( 𝑥 + 1 8 ) ( 𝑥 2 )
  • C ( 𝑥 + 4 ) ( 𝑥 9 )
  • D ( 𝑥 4 ) ( 𝑥 + 9 )

Q14:

Factorise fully 𝑥 + 3 𝑥 4 .

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

Q15:

Factorise fully 𝑥 9 𝑥 𝑦 + 2 0 𝑦 .

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

Q16:

Factorise fully 𝑥 8 𝑥 𝑦 9 𝑦 .

  • A ( 𝑥 + 3 𝑦 ) ( 𝑥 3 𝑦 )
  • B ( 𝑥 𝑦 ) ( 𝑥 + 9 𝑦 )
  • C ( 𝑥 + 𝑦 ) ( 𝑥 9 𝑦 )
  • D ( 𝑥 𝑦 ) ( 𝑥 9 𝑦 )

Q17:

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

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

Q18:

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

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

Q19:

What property is illustrated by the step 𝑥 + 𝑥 1 2 = 0 , 𝑥 + 4 𝑥 3 𝑥 1 2 = 0 ?

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

Q20:

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

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

Q21:

Find the possible values of 𝑥 if 𝑥 = 1 4 .

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

Q22:

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

Q23:

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

Q24:

If the function 𝑓 , where 𝑓 ( 𝑥 ) = ( 𝑥 + 1 7 ) , and the function 𝑔 , where 𝑔 ( 𝑥 ) = 𝑥 + 1 7 , find the solution set of 𝑥 which makes 𝑓 ( 𝑥 ) = 𝑔 ( 𝑥 ) .

  • A
  • B { 1 7 , 1 6 }
  • C { 1 7 }
  • D { 1 6 }

Q25:

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

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