Factoring Polynomials

Intro: Shows each factoring tactic it tries and why it works.

Worked example

• $x^2+5x+6$



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• Find two numbers such that when you add them, you get $5$, and when you multiply them, you get $6$.



• $2$ and $3$ are the numbers which satisfy this since $2 + 3 = 5$ and $2 × 3 = 6$.



• Let's re-write the polynomial as $x^2 + 2x + 3x + 6$.



• Now we can factor: $x(x + 2) + 3(x + 2)$.



• Take $(x + 2)(x + 3)$, which is the factored form.



• Final answer: $\boxed{(x + 2)(x + 3)}$.





• $\displaystyle 2x^3-5x^2-4x+10$



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• Group terms: $(2x^3-5x^2)+(-4x+10)$.



• Factor each group: $x^2(2x-5)-2(2x-5)$.



• Common binomial $(2x-5)$: $(2x-5)(x^2-2)$.



• Final factorization: $\boxed{(2x-5)(x-\sqrt{2})(x+\sqrt{2})}$ (over reals, last two are irrational factors).

Why choose MathGPT?

• Get clear, step-by-step solutions that explain the “why,” not just the answer.
• See the rules used at each step (power, product, quotient, chain, and more).
• Optional animated walk-throughs to make tricky ideas click faster.
• Clean LaTeX rendering for notes, homework, and study guides.

How this calculator works

• Type or paste your function (LaTeX like \sin, \ln works too).
• Press Generate a practice question button to generate the derivative and the full reasoning.
• Review each step to understand which rule was applied and why.
• Practice with similar problems to lock in the method.

Related

• Quadratic Solver