 Recent questions in Polynomials
Polynomials
ANSWERED ### Linear and quadratic approximation a. Find the linear approximating polynomial for the following functions centered at the given point a. b. Find the quadratic approximating polynomial for the following functions centered at a. c. Use the polynomials obtained in parts (a) and (b) to approximate the given quantity. $$\displaystyle{f{{\left({x}\right)}}}={x}^{{\frac{{1}}{{3}}}},{a}={8}$$ approximiate $$\displaystyle{7.5}^{{\frac{{1}}{{3}}}}$$

Polynomials
ANSWERED ### Solve equation: $$\displaystyle{2}{x}+{1}-{12}={0}$$

Polynomials
ANSWERED ### Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. $$\displaystyle{1}-{27}{a}^{{3}}$$

Polynomials
ANSWERED ### Given $$\displaystyle{P}{\left({x}\right)}={3}{x}^{{2}}+{4}{y}^{{2}}$$ and $$\displaystyle{R}{\left({x}\right)}=-{7}{x}^{{2}}+{4}{x}{y}-{3}{y}^{{2}}$$, find $$P(x)-R(x)$$.

Polynomials
ANSWERED ### Find the roots of the quadratic polynomials: a) $$\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{2}}-{3}{x}-{1}$$ b) $$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{2}{x}-{1}$$

Polynomials
ANSWERED ### Find the zeros ofcthe polynomials $$\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}-{12}{x}^{{2}}+{39}{x}-{28}$$, if it's is given that the zeros in AP

Polynomials
ANSWERED ### Divide the polynomials $$\displaystyle-{13}{x}^{{2}}+{4}{x}^{{3}}+{2}{x}-{7}$$ and explain each step. State the answer in full sentence and ecxpress it as one expression. Check your solution.

Polynomials
ANSWERED ### $$(2x − 1)$$ is a factor of the polynomial $$\displaystyle{6}{x}^{{6}}+{x}^{{5}}-{92}{x}^{{4}}+{45}{x}^{{3}}+{184}{x}^{{2}}+{4}{x}-{48}$$. Determine whether the statement is true or false. Justify your answer.

Polynomials
ANSWERED ### Subtract the polynomials using the horizontal format. $$\displaystyle{2}{x}^{{3}}+{x}^{{2}}-{7}{x}-{2}$$ from $$\displaystyle{5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}$$

Polynomials
ANSWERED ### Add the polynomials. $$\displaystyle{\left({7}{x}^{{2}}-{6}{x}+{6}\right)}+{\left({3}{x}^{{3}}-{9}{x}\right)}$$

Polynomials
ANSWERED ### List all of the polynomials of degrees 2 and 3 in $$\displaystyle{\mathbb{{{Z}}}}_{{2}}{\left[{x}\right]}$$. Find all of the irreducible polynomials of degrees 2 and 3 in $$\displaystyle{\mathbb{{{Z}}}}_{{2}}{\left[{x}\right]}$$.

Polynomials
ANSWERED ### Do the polynomials $$\displaystyle{x}^{{3}}-{2}{x}^{{2}}+{1},{4}{x}^{{2}}-{x}+{3}$$, and $$3x-2$$ generate $$\displaystyle{P}_{{3}}{\left({R}\right)}$$? Justify your answer.

Polynomials
ANSWERED ### Find the roots of the quadratic polynomials: $$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{2}{x}-{1}$$

Polynomials
ANSWERED ### Determine whether the following polynomials u,v, w in P(t) are linearly dependent or independent: $$\displaystyle{u}={t}^{{3}}-{4}{t}^{{2}}+{3}{t}+{3},$$ $${v}={t}^{{3}}+{2}{t}^{{2}}+{4}{t}-{1},$$ $${w}={2}{t}^{{3}}-{t}^{{2}}-{3}{t}+{5}$$

Polynomials
ANSWERED ### Find the difference of the polynomials. $$\displaystyle{\left({3}{x}^{{2}}+{2}{x}-{1}\right)}-{\left(-{5}{x}^{{2}}+{8}{x}+{4}\right)}$$

Polynomials
ANSWERED ### Find the product of $$\displaystyle{2}{x}^{{3}}+{3}{x}^{{2}}+{1}$$ and $$\displaystyle{2}{x}^{{2}}+{4}$$ in $$z_5[x]/$$

Polynomials
ANSWERED ### Find a cubic polynomial function f with real coefficients that has the given complex zeros and x-intercept. (There are many correct answers. Expand your answer completely.) Complex Zeroes $$\displaystyle{x}={2}\pm\sqrt{{{2}}}{i}$$ X-Intercept (5,0)

Polynomials
ANSWERED ### a) Find the derivative of $$f(x)=(2x+9)(8x−7)$$ by first expanding the polynomials. b) Find the derivative of $$f(x)=(2x+9)(8x−7)$$ by using the product rule. Let $$\displaystyle g{{\left({x}\right)}}={2}{x}+{9}{\quad\text{and}\quad}{h}{\left({x}\right)}={8}{x}-{7}$$

Polynomials
ANSWERED ### If the directions is to simplify the following polynomials, then explain what I perhaps did wrong or explain what the answer should be. $$\displaystyle{3}{x}^{{2}}{\left({5}{x}\right)}{\left(-{\frac{{{2}}}{{{3}}}}{x}^{{3}}\right)}\to{15}{x}^{{3}}-{2}{x}^{{5}}$$
ANSWERED 