Four hands-on tools built around the chapter: classify polynomials by degree, evaluate p(k) to hunt for zeroes, watch a graph's x-intercepts be the zeroes, and verify how zeroes and coefficients are tied together.
Pick a degree, drag the coefficient sliders, and watch the expression update live. A polynomial of degree n needs its leading coefficient a ≠ 0 — try setting it to zero and see what happens.
From the chapter's own examples. Click a card to reveal whether it's linear, quadratic, cubic, higher degree — or not a polynomial at all.
A real number k is a zero of p(x) if p(k) = 0. Set the coefficients, slide k, and watch the substitution happen step by step. Green means you've landed on a zero.
The zeroes of p(x) are exactly the x-coordinates where the graph of y = p(x) crosses the x-axis. Defaults below reproduce the chapter's own figures — drag the sliders to explore every case.
For a quadratic ax² + bx + c with zeroes α, β → α+β = −b⁄a and αβ = c⁄a. For a cubic ax³ + bx² + cx + d with zeroes α, β, γ → α+β+γ = −b⁄a, αβ+βγ+γα = c⁄a, αβγ = −d⁄a. Adjust the coefficients — the identities always hold.