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STAAR EOC Algebra I Factoring — practice questions — page 2

Explore 51 free Factoring questions in STAAR EOC Algebra I Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Factoring questions and exercises with answers

Showing questions 31–51 of 51.

Using the ac method, factor: 18n^2 - 37n + 15.Read the answer and worked solution →Factor: 2y^2 + 11y + 12.Read the answer and worked solution →Factor: 3u^2 + 8u + 5.Read the answer and worked solution →Factor completely: 10y^2 - 55y + 70.Read the answer and worked solution →The height of a toy rocket t seconds after launch is modeled by -16t^2 + 80t + 96. What is its completely factored form?Read the answer and worked solution →According to the Binomial Squares Pattern, what does (a+b)^2 expand to?Read the answer and worked solution →Factor: 9x^2 + 12x + 4.Read the answer and worked solution →Factor: 81y^2 - 72y + 16.Read the answer and worked solution →Factor: 36x^2 + 84xy + 49y^2.Read the answer and worked solution →According to the Difference of Squares Pattern, how does a^2-b^2 factor?Read the answer and worked solution →Factor: x^2 - 4.Read the answer and worked solution →Factor: 64y^2 - 1.Read the answer and worked solution →Factor: 121x^2 - 49y^2.Read the answer and worked solution →Factor: 100 - h^2.Read the answer and worked solution →What is the completely factored form of x^4 - y^4?Read the answer and worked solution →What happens when you try to factor a sum of squares like a^2 + b^2?Read the answer and worked solution →Factor completely: 6x^2 + 96.Read the answer and worked solution →Factor completely: 8x^2y - 98y.Read the answer and worked solution →Factor completely: 36x^2y - 48xy + 16y.Read the answer and worked solution →According to the Sum and Difference of Cubes Pattern, how does a^3+b^3 factor?Read the answer and worked solution →Factor: x^3 + 64.Read the answer and worked solution →

Worked practice questions

Using the ac method, factor: 18n^2 - 37n + 15.

  1. (2n-5)(9n-3)
  2. (n-3)(18n-5)
  3. (2n-3)(9n-5)
  4. (9n-1)(2n-15)
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Correct answer: C. (2n-3)(9n-5)

1. Multiply a and c: 18 times 15 equals 270. 2. Find two numbers that multiply to 270 and add to -37: -10 and -27 work, since -10 times -27 is 270 and -10 plus -27 is -37. 3. Split the middle term using -10n and -27n, then factor by grouping: 18n squared - 10n - 27n + 15 groups into 2n(9n - 5) - 3(9n - 5). 4. Factor out the shared binomial to get (2n - 3)(9n - 5). 5. Check by multiplying: 18n squared - 10n - 27n + 15 gives back 18n squared - 37n + 15. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1_

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Factor: 2y^2 + 11y + 12.

  1. (y+3)(2y+4)
  2. (y+6)(2y+2)
  3. (y-4)(2y-3)
  4. (y+4)(2y+3)
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Correct answer: D. (y+4)(2y+3)

1. Multiply a and c: 2 times 12 equals 24. 2. Find two numbers that multiply to 24 and add to 11: 3 and 8 work, since 3 times 8 is 24 and 3 plus 8 is 11. 3. Split the middle term using 3y and 8y, then group: 2y squared + 3y + 8y + 12 becomes y(2y + 3) + 4(2y + 3). 4. Factor out the shared binomial (2y + 3) to get (y + 4)(2y + 3). 5. Check by multiplying: 2y squared + 3y + 8y + 12 gives back 2y squared + 11y + 12. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1_

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Factor: 3u^2 + 8u + 5.

  1. (u+1)(3u+5)
  2. (u+5)(3u+1)
  3. (u-1)(3u-5)
  4. (u-5)(3u-1)
Show answer and solution

Correct answer: A. (u+1)(3u+5)

1. Multiply a and c: 3 times 5 equals 15. 2. Find two numbers that multiply to 15 and add to 8: 3 and 5 work, since 3 times 5 is 15 and 3 plus 5 is 8. 3. Split the middle term using 3u and 5u, then group: 3u squared + 3u + 5u + 5 becomes 3u(u + 1) + 5(u + 1). 4. Factor out the shared binomial (u + 1) to get (u + 1)(3u + 5). 5. Check by multiplying: 3u squared + 5u + 3u + 5 gives back 3u squared + 8u + 5. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1_

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More Mathematics topics

GraphsExponential FunctionsQuadratic EquationsRoots and RadicalsSystems of Linear EquationsFactor Quadratic Trinomials with Leading Coefficient 1Use the Rectangular Coordinate SystemGraph with Intercepts