Solving polynomial equations by factoring
Solve a factorable polynomial equation for all real roots. Unlimited questions, five difficulty levels, and a full worked solution every time, included free with weekly lessons.
Try one
Solve P(x) = 0 for all real roots.
P(x) = x3 - 3x2 - 6x + 8
- x = 2, −1, −4
- x = −2, 1, 4
- x = −2, 1, −4
- x = 1, 4
Answer: x = -2, 1, 4
See one solved, step by step
Solve P(x) = 0 for all real roots.
P(x) = x3 + 4x2 - 25x - 100
- x = −5, −4, −5
- x = 5, 4, −5
- x = −4, 5
- x = −5, −4, 5
📘 Worked solution
1P(x) = (x + 4)(x - 5)(x + 5)Factor the polynomial completely.
2(x + 4)(x - 5)(x + 5) = 0Set the factored form equal to zero.
3x = −5, −4, 5By the zero product property, each factor equal to zero gives one root.
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