Label each of the following statements as true or false If f

Label each of the following statements as true or false. If false, replace the underlined word(s) to produce a true statement. Adding polynomials will always yield a polynomial answer. Subtracting polynomials will yield a polynomial if and only if their leading coefficients are opposites. The product of two polynomials will be a polynomial regardless of the signs of the leading coefficients of the polynomials. The Remainder Theorem states that if a polynomial, f(x), is divided by (x - k), then the remainder, r, is the value of f(k). By the Factor Theorem, if f(k) = 0 for a polynomial f(x), then the polynomial has a factor (x + k). According to the Rational Zero Theorem, the possible rational zeros for f(x) = 4x^3 - 3x + 2 are plusminus 1, plusminus 2, and plusminus 4. According to the Fundamental Theorem of Algebra, the function f(x) = 2x^4 + /3 x^2 + 7 has exactly three solutions.

Solution

9) Yes , adding two polynomials will always yield polynomials

10) No , Because Subtrcting polynomials wills always yield polynomials

11) Yes , Product of polynomials will be polynomials regardless of the sign of polynomials