Test #11 - Algebra 2

1

(x - 1)(x + 2)(x + 5)

@@ ext{Solutions: } \\ \\ ext{±}i ext{√10, ±√3}$$

Yes, $$x + 3$$ is a factor.

@@x^3 + 3x^2 - 12x$$

The Factor Theorem states that a polynomial $$f(x)$$ has a factor $$(x - c)$$ if and only if $$f(c) = 0$$ .

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

Set the polynomial equal to zero and solve for $$x$$ .

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

A polynomial function is a function that can be expressed in the form $$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ , where $$a_n, a_{n-1}, ..., a_0$$ are constants.