Worksheet: Solving Quadratic Equations: Factoring

In this worksheet, we will practice solving quadratic equations by factoring.

Q1:

Solve the equation 4π‘₯+40π‘₯+40=βˆ’60 by factoring.

  • Aπ‘₯=βˆ’5
  • Bπ‘₯=1 or π‘₯=25
  • Cπ‘₯=βˆ’1 or π‘₯=βˆ’25
  • Dπ‘₯=5

Q2:

Solve the equation 2(π‘₯+1)+5(π‘₯+1)=0.

  • Aπ‘₯=βˆ’1, π‘₯=βˆ’72
  • Bπ‘₯=βˆ’1, π‘₯=βˆ’52
  • Cπ‘₯=βˆ’ο„ž52
  • Dπ‘₯=1
  • Eπ‘₯=ο„ž52

Q3:

Find the solution set of π‘₯(π‘₯βˆ’19)=βˆ’15π‘₯ in ℝ.

  • A{4}
  • B{0,4}
  • C{βˆ’4}
  • D{19,βˆ’15}
  • E{0,βˆ’4}

Q4:

Find the solution set of (π‘₯+9)=(π‘₯+9) in ℝ.

  • A{βˆ’9,βˆ’10}
  • B{10}
  • C{βˆ’9,βˆ’8}
  • D{9,βˆ’8}
  • E{9}

Q5:

Find the solution set of 6π‘₯βˆ’13π‘₯+6=0 in ℝ.

  • A32,βˆ’23
  • Bο¬βˆ’32,βˆ’23
  • C32,23
  • D{βˆ’3,βˆ’2}
  • E{3,2}

Q6:

Solve the equation π‘₯βˆ’8π‘₯+16=0 by factoring.

  • Aπ‘₯=4
  • Bπ‘₯=βˆ’4
  • Cπ‘₯=βˆ’8 or π‘₯=βˆ’2
  • Dπ‘₯=8 or π‘₯=2

Q7:

Find the solution set of βˆ’π‘₯63+1π‘₯=βˆ’263 in ℝ.

  • A{βˆ’7,βˆ’9}
  • B{3,βˆ’21}
  • C{βˆ’7,9}
  • D{7,βˆ’9}
  • E{βˆ’1,63}

Q8:

Find the solution set of (2𝑦+4)+(𝑦+2)=5 in ℝ.

  • A{βˆ’1,βˆ’3}
  • B{5,3}
  • C{βˆ’5,βˆ’3}
  • D{1,3}

Q9:

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

  • Aπ‘₯=βˆ’3, π‘₯=βˆ’8
  • Bπ‘₯=βˆ’3, π‘₯=8
  • Cπ‘₯=3, π‘₯=8
  • Dπ‘₯=3, π‘₯=βˆ’8

Q10:

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

  • Aπ‘₯=βˆ’3 or π‘₯=βˆ’8
  • Bπ‘₯=3 or π‘₯=βˆ’8
  • Cπ‘₯=βˆ’3 or π‘₯=8
  • Dπ‘₯=3 or π‘₯=8

Q11:

Solve the equation 5π‘₯βˆ’14π‘₯+10=15 by factoring.

  • Aπ‘₯=57
  • Bπ‘₯=75
  • Cπ‘₯=7
  • Dπ‘₯=βˆ’75
  • Eπ‘₯=βˆ’7

Q12:

Solve the equation 9π‘₯+30π‘₯+25=0 by factoring.

  • Aπ‘₯=βˆ’53
  • Bπ‘₯=βˆ’259 or π‘₯=βˆ’1
  • Cπ‘₯=53
  • Dπ‘₯=259 or π‘₯=1

Q13:

Find the solution set of βˆ’7(π‘₯+7)+9(π‘₯+7)=0 in ℝ.

  • Aο¬βˆ’7,587
  • Bο¬βˆ’7,βˆ’407
  • Cο¬βˆ’407
  • D7,βˆ’407
  • E0,βˆ’407

Q14:

Find the solution set of (π‘₯+2)(π‘₯βˆ’7)=βˆ’8 in ℝ.

  • A{βˆ’2,7}
  • B{βˆ’1,6}
  • C{2,βˆ’3}
  • D{βˆ’2,3}
  • E{1,βˆ’6}

Q15:

Find the solution set of the equation ο€»π‘₯βˆ’7√11π‘₯+2√41=0 in ℝ.

  • A7√11,βˆ’2√41
  • B7√11,2√41
  • Cο«βˆ’7√11,2√41
  • Dο«βˆ’7√11,βˆ’2√41

Q16:

Solve π‘₯βˆ’4π‘₯+4=0 by factoring.

  • Aπ‘₯=4
  • Bπ‘₯=4, π‘₯=βˆ’1
  • Cπ‘₯=2
  • Dπ‘₯=2, π‘₯=βˆ’2
  • Eπ‘₯=βˆ’2

Q17:

Find the solution set of 3π‘§βˆ’7𝑧=6 in ℝ.

  • A{βˆ’2,3}
  • B{2,βˆ’3}
  • C23,βˆ’3
  • Dο¬βˆ’23,3
  • Eο¬βˆ’32,3

Q18:

Find the solution set of 2π‘₯+5π‘₯βˆ’7=0 in ℝ.

  • A{βˆ’7,1}
  • B{7,βˆ’1}
  • C72,βˆ’1
  • Dο¬βˆ’72,1
  • Eο¬βˆ’27,βˆ’1

Q19:

Find the solution set of π‘₯+5π‘₯βˆ’36=0 in ℝ.

  • A{βˆ’4,9}
  • B{2,βˆ’18}
  • C{4,βˆ’9}
  • D{βˆ’2,18}
  • E{1,βˆ’36}

Q20:

Find the solution set of the equation π‘₯βˆ’26π‘₯9=βˆ’169 in ℝ.

  • A2,89
  • B{βˆ’2,βˆ’8}
  • Cο¬βˆ’2,βˆ’89
  • D{2,8}
  • Eο¬βˆ’2,89

Q21:

Find the solution set of the equation π‘₯+21π‘₯=βˆ’10 in ℝ.

  • A{3,7}
  • B1,βˆ’133
  • C{1,βˆ’1}
  • D{βˆ’3}
  • E{βˆ’3,βˆ’7}

Q22:

Find the solution set of π‘₯+22=12π‘₯ in ℝ.

  • A{βˆ’6,4}
  • B{6,βˆ’4}
  • C{3,βˆ’8}
  • D{βˆ’3,8}
  • E{βˆ’6,βˆ’4}

Q23:

By factoring, solve the equation π‘₯4βˆ’3π‘₯4=52.

  • Aπ‘₯=βˆ’2, π‘₯=5
  • Bπ‘₯=βˆ’52
  • Cπ‘₯=2, π‘₯=βˆ’5
  • Dπ‘₯=52
  • Eπ‘₯=βˆ’2

Q24:

Find the solution set of π‘₯+12π‘₯=0 in ℝ.

  • A{βˆ’12}
  • B{12}
  • C0,βˆ’βˆš12
  • D{0,βˆ’12}
  • E{0,12}

Q25:

Find the solution set of 1+6π‘₯=40π‘₯ in ℝ.

  • A{βˆ’1,40}
  • B{10,βˆ’4}
  • C{βˆ’10,4}
  • D{βˆ’20,2}
  • E{βˆ’10,βˆ’4}

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