91Ó°ÊÓ

Fill in the blanks. When a real zero of a polynomial function is of even multiplicity, the graph of \(f\) __________ the \(x\)-axis at \(x=a,\) and when it is of odd multiplicity, the graph of \(f\) __________ the \(x\)-axis at \(x=a\).

Find the domain of the function and discuss the behavior of \(f\) near any excluded \(x\) -values. $$f(x)=\frac{1}{x-1}$$

Fill in the blanks. quadratic factor that cannot be factored further as a product of linear factors containing real numbers is said to be _____ over the _______ .

When the graph of a quadratic function opens downward, its leading coefficient is ___ and the vertex of the graph is a __ .

Fill in the blanks. A factor \((x-a)^{k}, k>1,\) yields a ______ _______ \(x=a\) of _______ \(k.\)

Determine whether each value of \(x\) is a solution of the inequality. Inequality \(x^{2}-x-12 \geq 0\) Values (a) \(x=5\) (b) \(x=0\) (c) \(x=-4\) (d) \(x=-3\)

Fill in the blanks. The _______ Theorem states that if a polynomial \(f(x)\) is divided by \(x-k,\) then the remainder is \(r=f(k)\).

Fill in the blanks. The numbers \(a+b i\) and \(a-b i\) are called ___________ __________ and their product is a real number \(a^{2}+b^{2}\).

Find the domain of the function and discuss the behavior of \(f\) near any excluded \(x\) -values. $$f(x)=\frac{5 x}{x+2}$$

Fill in the blanks. A polynomial function is written in _______ form when its terms are written in descending order of exponents from left to right.