form a polynomial whose degree and zeros are given. don't expand
a) degree 3,zeros,-2,0,4
b)degree 4,zeros, -2 multiplicity 3,1 multiplicity 1
solutions
a)p(x)= x(x+2)(x-4)
B)p(x) =(x+2)^3(x-1)
both are correct
To form a polynomial with given degree and zeros, you need to know the root or zero values. Here's how you can find the correct polynomials:
a) For a degree 3 polynomial with zeros -2, 0, and 4, you can write the polynomial in factored form as p(x) = (x - (-2))(x - 0)(x - 4).
This simplifies to p(x) = (x + 2)(x)(x - 4).
b) For a degree 4 polynomial with zeros -2 (multiplicity 3) and 1 (multiplicity 1), you can write the polynomial as p(x) = (x - (-2))^3(x - 1).
This simplifies to p(x) = (x + 2)^3(x - 1).
Remember that the degree of a polynomial is determined by the highest exponent of x in the polynomial.