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Questions and Answers
Factor completely: 2x²-7x+3
Factor completely: 2x²-7x+3
(2x-1)(x-3)
Factor the trinomial completely: 3w²+14w+8
Factor the trinomial completely: 3w²+14w+8
(w+4)(3w+2)
Factor the trinomial: 5d²-22d+8
Factor the trinomial: 5d²-22d+8
(d-4)(5d-2)
Factor the trinomial: 6h²+8h+2
Factor the trinomial: 6h²+8h+2
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Factor the trinomial: 9x²+6x-8
Factor the trinomial: 9x²+6x-8
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Factor the trinomial: 6q²-13q+6
Factor the trinomial: 6q²-13q+6
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Factor the trinomial: 2x²-11x+15
Factor the trinomial: 2x²-11x+15
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Factor the trinomial: 4t²+15t-4
Factor the trinomial: 4t²+15t-4
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Study Notes
Factoring Trinomials
- Factoring trinomials involves rewriting a quadratic in the form of ( ax^2 + bx + c ) as the product of two binomials.
- The goal is to express the trinomial as ( (px + q)(rx + s) ).
Example Trinomials and Their Factors
- 2x² - 7x + 3 factors to ( (2x - 1)(x - 3) ).
- 3w² + 14w + 8 factors to ( (w + 4)(3w + 2) ).
- 5d² - 22d + 8 factors to ( (d - 4)(5d - 2) ).
- 6h² + 8h + 2 factors to ( (h + 1)(3h + 1) ).
- 9x² + 6x - 8 factors to ( (3x - 2)(3x + 4) ).
- 6q² - 13q + 6 factors to ( (2q - 3)(3q - 2) ).
- 2x² - 11x + 15 factors to ( (x - 3)(2x - 5) ).
- 4t² + 15t - 4 factors to ( (t + 4)(4t - 1) ).
Key Techniques in Factoring
- Look for patterns such as a perfect square trinomial.
- Identify the coefficients and constant terms to determine suitable binomials.
- Confirm the factorization by expanding the binomials to ensure they reconstruct the original trinomial.
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