Question

Form a polynomial whose real zeros and degree are given.​
Zeros: -3​, -1​, 1​, 4​; ​ degree: 4
Type a polynomial with integer coefficients and a leading coefficient of 1.​
f(x) = __________.
(Simplify your​ answer.)

Answer 1

Answer:

Step-by-step explanation:

Given that zeroes of a polynomial are

-3, -1, 1, 4

Degree of the polynomial is 4

Also leading coefficient is 1.

So we find easily the polynomial

Since polynomial is 0 at the given four points the polynomial is a product of

$(x+3)(x+1)(x-1)(x-4)\\=(x^2-1)(x^2-x-12)\\= (x^4-x^3-13x^2+x+12)$

Since leading coefficient is given to be 1 we need not multiply an arbitrary constant a

so the required polynomial is

$(x^4-x^3-13x^2+x+12)$