Lesson Worksheet: Solving Quadratic and Quadratic-Like Equations by Factoring Mathematics • 9th Grade

In this worksheet, we will practice solving quadratic and quadratic-like equations using factoring along with questions that involve quadratics at some point in the factorization.

Q1:

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

Q2:

Solve the equation (2π‘₯βˆ’3)(3π‘₯+4)=0.

  • Aπ‘₯=3, π‘₯=4
  • Bπ‘₯=32, π‘₯=βˆ’43
  • Cπ‘₯=βˆ’32, π‘₯=βˆ’43
  • Dπ‘₯=βˆ’32, π‘₯=43
  • Eπ‘₯=βˆ’3, π‘₯=4

Q3:

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

Q4:

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

Q5:

Find the solution set for 2π‘₯=18π‘₯.

  • A{3,βˆ’3}
  • B{0,3}
  • C{2,3,βˆ’3}
  • D{0,3,βˆ’3}
  • E{2,3}

Q6:

Given two positive numbers whose product is 35 and whose difference is 2, find the largest number.

Q7:

Find the value of π‘₯ given that a right triangle has a hypotenuse of length 2π‘₯, and sides of lengths π‘₯+1 and π‘₯+3.

Q8:

Find the solution set for π‘₯βˆ’13π‘₯+36=0οŠͺ.

  • A{2,3}
  • B{βˆ’4,βˆ’9}
  • C{2,βˆ’2,3,βˆ’3}
  • D{4,βˆ’4,9,βˆ’9}
  • E{4,9}

Q9:

Solve 36π‘₯βˆ’97π‘₯+36=0οŠͺ.

  • A49,βˆ’49,94,βˆ’94
  • B23,βˆ’23
  • C23,βˆ’23,32,βˆ’32
  • D23,32
  • E49,94

Q10:

Solve 4π‘₯βˆ’4π‘₯βˆ’15π‘₯=0.

  • A0,βˆ’32,52
  • B32,βˆ’52
  • C0,βˆ’52,32
  • Dο¬βˆ’32,52
  • E0,βˆ’52,βˆ’32

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