Frequently Asked Questions
Can you factor x^2 + 1?
Not over the real numbers. The discriminant is -4. Over the complex numbers, x^2 + 1 = (x + i)(x - i).
What if a is not 1?
Use the quadratic formula or AC method. For 6x^2 + 5x - 4, the roots are 1/2 and -4/3, so the factorization is (2x - 1)(3x + 4).
Does factoring work for higher-degree polynomials?
Sometimes. Cubics and quartics have closed-form solutions; quintics and above generally do not. Look for rational roots first using the Rational Root Theorem.
How do you factor a trinomial with a leading coefficient?
Use the AC method: multiply the leading coefficient a by the constant c, find two numbers that multiply to ac and add to the middle coefficient b, split the middle term with them, then factor by grouping.
What is the AC method?
The AC method factors ax² + bx + c by finding two numbers with product a·c and sum b. You rewrite bx as those two terms and factor the four-term expression by grouping. It always works when the trinomial factors over the integers.
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