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

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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 (𝑥−3)(𝑥+8)=0.

  • A𝑥=−3 or 𝑥=−8
  • B𝑥=3 or 𝑥=−8
  • C𝑥=−3 or 𝑥=8
  • D𝑥=3 or 𝑥=8

Q2:

Solve the equation (2𝑥−3)(3𝑥+4)=0.

  • A𝑥=3, 𝑥=4
  • B𝑥=32, 𝑥=−43
  • C𝑥=−32, 𝑥=−43
  • D𝑥=−32, 𝑥=43
  • E𝑥=−3, 𝑥=4

Q3:

Solve the equation 𝑥−8𝑥+16=0 by factoring.

  • A𝑥=4
  • B𝑥=−4
  • C𝑥=−8 or 𝑥=−2
  • D𝑥=8 or 𝑥=2

Q4:

Solve the equation 4𝑥+40𝑥+40=−60 by factoring.

  • A𝑥=−5
  • B𝑥=1 or 𝑥=25
  • C𝑥=−1 or 𝑥=−25
  • D𝑥=5

Q5:

Find the solution set for 2𝑥=18𝑥.

  • A{3,−3}
  • B{0,3}
  • C{2,3,−3}
  • D{0,3,−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 𝑥 given that a right triangle has a hypotenuse of length 2𝑥, and sides of lengths 𝑥+1 and 𝑥+3.

Q8:

Find the solution set for 𝑥−13𝑥+36=0.

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

Q9:

Solve 36𝑥−97𝑥+36=0.

  • A49,−49,94,−94
  • B23,−23
  • C23,−23,32,−32
  • D23,32
  • E49,94

Q10:

Solve 4𝑥−4𝑥−15𝑥=0.

  • A0,−32,52
  • B32,−52
  • C0,−52,32
  • D−32,52
  • E0,−52,−32

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