Find the zeros of a polynomial in factored form
Read the zeros of a cubic function from its factored form, including a repeated (multiplicity-2) root at higher difficulty. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
The function below is in factored form. Find its zeros.
f(x) = (x - 5)(x - 3)(x + 4)
- x = −5, −4, 3
- x = −3, 3, 5
- x = −4, 3, 5
- x = −5, −3, 4
Answer: x = -4, 3, 5
See one solved, step by step
The function below is in factored form. Find its zeros.
f(x) = −1(x + 7)(x + 8)(x + 3)
- x = −8, −3, 7
- x = −8, −7, −3
- x = −8, −7, −2
- x = 3, 7, 8
📘 Worked solution
1f(x) = −1(x + 7)(x + 8)(x + 3) = 0A zero is a value of x that makes f(x) = 0.
2Set each factor to zero: (x + 7) = 0 or (x + 8) = 0 or (x + 3) = 0A product is zero only when at least one factor is zero.
3x = −8, −7, −3Solving each factor for x gives the zeros. The leading coefficient a = -1 stretches or reflects the graph but never moves the zeros.
4Every factor here appears once, so the graph crosses straight through the x-axis at each zero.The exponent on a factor (its multiplicity) tells you whether the graph crosses or bounces off the x-axis there.
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