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Quizzes > Mathematics > Algebra

Master Factoring Trinomials: Take the Quiz Now!

Dive into factoring trinomials questions and boost your algebra skills

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art style shapes on sky blue background featuring factoring trinomials quiz theme with quadratic expressions

Ready to ace factoring trinomials examples and answers? Dive into our Free Factoring Trinomials Quiz: Examples & Answers, designed to turn intimidating quadratic trinomial factoring into an exciting challenge. Whether you're brushing up on factoring trinomials questions or seeking extra factoring trinomials practice, you'll explore how to factor trinomials step-by-step with clear explanations and instant feedback. Interested in more advanced warm-ups? Check out our factoring polynomials practice and test yourself further with a fun factoring to solve quadratic equations quiz . Jump in now and master every trinomial - your next A+ starts here!

Factor the trinomial x^2 + 5x + 6.
(x+1)(x+6)
(x+2)(x+2)
(x+3)(x+3)
(x+2)(x+3)
To factor x^2 + 5x + 6, find two numbers that multiply to 6 and add to 5; these are 2 and 3. Thus the trinomial factors as (x+2)(x+3). Factoring when the leading coefficient is 1 can be done by inspection quickly. See this guide for more examples.
Factor the trinomial x^2 - x - 6.
(x-3)(x+2)
(x-2)(x-3)
(x+1)(x-6)
(x+3)(x-2)
We need two numbers that multiply to -6 and add to -1; those are -3 and +2. Hence x^2 - x - 6 factors into (x-3)(x+2). Checking by expansion verifies the result. For further steps, check this resource.
Factor the trinomial x^2 + 7x + 10.
(x+4)(x+3)
(x+5)(x+2)
(x+2)(x+2)
(x+10)(x+1)
To factor x^2 + 7x + 10, look for two numbers multiplying to 10 and summing to 7: 5 and 2. Thus it factors as (x+5)(x+2). This direct approach works when the quadratic's leading coefficient is 1. More details at Math Is Fun.
Factor the perfect square trinomial x^2 - 4x + 4.
(x-2)(x-2)
(x-1)(x-3)
(x-4)(x+1)
(x-2)(x+2)
Since the trinomial is x^2 - 4x + 4, it matches the form (x - a)^2 with a = 2. Therefore the factorization is (x-2)^2 or (x-2)(x-2). Perfect square trinomials follow this pattern. Learn more at this explanation.
Factor the trinomial x^2 + 3x - 10.
(x+10)(x-1)
(x+5)(x-2)
(x-5)(x-2)
(x+2)(x-5)
For x^2 + 3x - 10, find numbers that multiply to -10 and add to +3: these are +5 and -2. Thus the factorization is (x+5)(x-2). Quick inspection works when a=1. For a deeper dive, visit this page.
Factor the trinomial 2x^2 + 7x + 3.
(2x+1)(x+3)
(2x+3)(x+1)
(2x+1)(2x+3)
(x+7)(2x+3)
We seek numbers that multiply to 2·3=6 and sum to 7: these are 1 and 6. Split the middle term: 2x^2 + x + 6x + 3, factor by grouping: x(2x+1) + 3(2x+1) = (2x+1)(x+3). See this tutorial for grouping methods.
Factor the trinomial 3x^2 - 2x - 8.
(3x+2)(x-4)
(3x-4)(x+2)
(x+4)(3x-2)
(3x+4)(x-2)
The product 3·(-8) = -24 and sum -2 come from -6 and +4. Splitting: 3x^2 - 6x + 4x - 8, group: 3x(x-2) +4(x-2) gives (3x+4)(x-2). For more examples, see this resource.
Factor completely 4x^2 - 12x - 16.
4(x-2)(x-2)
2(x-4)(2x+2)
4(x-4)(x+1)
4(x+4)(x-1)
First factor out the GCF 4, yielding 4(x^2 -3x -4). Then factor x^2 -3x -4 = (x-4)(x+1). The completely factored form is 4(x-4)(x+1). For steps, visit this explanation.
Factor the trinomial x^2 + 11x + 28.
(x+7)(x+4)
(x+1)(x+28)
(x+8)(x+3)
(x+14)(x+2)
We need two numbers that multiply to 28 and add to 11: they are 7 and 4. So x^2 + 11x + 28 = (x+7)(x+4). Direct factorization works for a=1. More practice at this link.
Factor the trinomial x^2 - 15x + 56.
(x-7)(x-8)
(x-6)(x-9)
(x-1)(x-56)
(x-14)(x-4)
Two numbers multiply to 56 and add to -15; those are -7 and -8. Thus x^2 - 15x + 56 = (x-7)(x-8). Always check by FOIL to confirm. See this page for related examples.
Factor the trinomial 6x^2 + 13x + 6.
(3x+6)(2x+1)
(2x+6)(3x+1)
(6x+2)(x+3)
(3x+2)(2x+3)
Multiply 6·6=36 and find two numbers summing to 13: 4 and 9. Split: 6x^2 + 4x + 9x + 6, factor by grouping: 2x(3x+2) +3(3x+2) gives (3x+2)(2x+3). For grouping techniques, see this explanation.
Factor the trinomial 5x^2 - 8x - 4.
(5x+4)(x-1)
(5x+2)(x-2)
(5x-2)(x+2)
(5x-4)(x+1)
Compute 5·(-4)=-20 and find numbers summing to -8: -10 and +2. Splitting: 5x^2 -10x +2x -4, grouping: 5x(x-2) +2(x-2) gives (5x+2)(x-2). Refer to this guide for more.
Factor the trinomial 8x^2 - 2x - 3.
(4x-3)(2x+1)
(8x+1)(x-3)
(2x-3)(4x-1)
(4x+1)(2x-3)
Product 8·(-3)=-24, numbers summing to -2 are -6 and +4. Split: 8x^2 -6x +4x -3, factor groups: 2x(4x-3) +1(4x-3) yields (4x-3)(2x+1). For step-by-step, see this site.
Factor the perfect square trinomial 4x^2 - 12x + 9.
(4x-6)(x-1.5)
(2x-1)(2x-9)
(4x-3)(x-3)
(2x-3)(2x-3)
Recognize 4x^2 - 12x + 9 as (2x)^2 - 2·2x·3 + 3^2, so it factors to (2x-3)^2. Identifying perfect square trinomials speeds factoring. More on this at Math Is Fun.
Factor the trinomial 12x^2 + x - 20.
(3x-5)(4x+4)
(12x+5)(x-4)
(6x-5)(2x+4)
(4x-5)(3x+4)
Multiply 12·(-20)=-240 and find numbers summing to 1: -15 and +16. Split: 12x^2 -15x +16x -20, group: 3x(4x-5)+4(4x-5) gives (4x-5)(3x+4). For advanced techniques, visit this tutorial.
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Study Outcomes

  1. Identify Quadratic Components -

    Recognize the coefficients and constants in a quadratic expression (ax2 + bx + c) to set up the factoring process.

  2. Apply Step-by-Step Factoring -

    Use a clear, systematic method to find factor pairs that multiply to ac and sum to b for accurate trinomial factorization.

  3. Analyze Special Trinomial Patterns -

    Distinguish cases like perfect square trinomials and common factor scenarios to adapt your factoring approach.

  4. Solve Diverse Practice Problems -

    Work through factoring trinomials questions using our free examples and answers to reinforce and test your skills.

  5. Verify Factorization Accuracy -

    Confirm your solutions by expanding the binomial factors back to the original quadratic expression.

  6. Build Confidence with Interactive Quizzes -

    Engage in hands-on factoring trinomials practice to improve speed and mastery of quadratic expressions.

Cheat Sheet

  1. Standard Form and Coefficient Roles -

    To ace quadratic trinomial factoring, always rewrite your expression in standard form ax² + bx + c so the coefficients a, b, and c stand out clearly. Knowing how each coefficient influences the parabola's shape and roots helps when you tackle factoring trinomials questions and interpret factoring trinomials examples and answers. A solid grasp on this foundation sets you up for how to factor trinomials step-by-step.

  2. Factoring When a = 1 by Inspection -

    When the leading coefficient a is 1, scan for two integers whose product equals c and sum equals b to split the middle term - e.g., x² + 5x + 6 = (x + 2)(x + 3). This quick "product-sum" trick makes factoring trinomials practice a breeze and builds confidence before tackling harder examples. Match your work against reliable factoring trinomials examples and answers to confirm accuracy.

  3. AC Method for a ≠ 1 -

    When a ≠ 1, multiply a·c and find two numbers that multiply to that product and sum to b; for 6x² + 11x + 3, 6·3 = 18 gives 2 and 9 (since 2 + 9 = 11), so you rewrite as 6x² + 2x + 9x + 3 and factor by grouping to get (3x + 1)(2x + 3). This how to factor trinomials step-by-step strategy shines in factoring trinomials practice and shows up in many factoring trinomials examples and answers.

  4. Perfect Squares and Special Patterns -

    Recognize perfect square trinomials (like x² + 6x + 9 = (x + 3)²) and difference of squares patterns (a² − b² = (a + b)(a − b)) to speed through certain quadratic trinomial factoring tasks. Spotting these patterns cuts down on time and aligns with many factoring trinomials questions in tests and online quizzes.

  5. Sign Strategies and Final Check -

    Use sign patterns to quickly predict binomial signs - if c and b share a sign, both binomial terms take that sign; if c is negative, the binomial signs differ. Always verify your result by foiling back and comparing with factoring trinomials examples and answers to ensure no sign slip-ups. Regular factoring trinomials practice with varied questions guarantees mastery!

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