Question

1. Identify the name and label the parts of the following polynomial: -2x4+24x2-10

a.Name the polynomial by degree and number of terms
b.Identify the lead coefficient
c.Identify the constant term
d.Identify the degree of the middle term

2. Give an example of a cubic binomial polynomial

3. How many constants can a polynomial have? Explain your answer.

4.Explain in detail why the degree of the polynomial below is not 6.
3x2+6xy-10x5+y6-10x3y5

Answer 1

This is a fourth degree polynomial, since the highest power of x is 4. Ordinarily, a fourth degree poly would have 5 terms, but here two of the coefficients of the powers of x are zero, leaving only 3 terms.

The lead coeff. of P(x) = -2x^4+24x^2-10 is -2.

The constant terms is -10. The exponent of x here is zero (0).

The degree of the middle term is 2 (see 24x^2, above

Explanation:

Answer 2

Please write this polynomial as P(x) = -2x^4+24x^2-10, using " ^ " to denote exponentiation.

This is a fourth degree polynomial, since the highest power of x is 4. Ordinarily, a fourth degree poly would have 5 terms, but here two of the coefficients of the powers of x are zero, leaving only 3 terms.

The lead coeff. of P(x) = -2x^4+24x^2-10 is -2.

The constant terms is -10. The exponent of x here is zero (0).

The degree of the middle term is 2 (see 24x^2, above)

Would you please post your other questions separately. Thank you.