Unit 4

The result is $$5x + 4$$ .

The equivalent expression is $$8x^3 + 15.5x^2 + 6.6x + 9$$ .

The linear factors are $$h(x) = (x + 2)(x - 2)(x + 1)^2$$ .

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

A linear factor is a polynomial of degree one, typically in the form $$(x - r)$$ , where $$r$$ is a root of the polynomial.

The degree of a polynomial is the highest power of the variable in the expression.

Polynomial long division is a method for dividing a polynomial by another polynomial, similar to numerical long division.

The Remainder Theorem states that the remainder of the division of a polynomial $$f(x)$$ by $$(x - r)$$ is equal to $$f(r)$$ .

Synthetic division is a simplified form of polynomial long division used when dividing by linear factors.

A root of a polynomial is a value of $$x$$ that makes the polynomial equal to zero.