R Chandra Solutions for Chapter: Polynomials, Exercise 3: TEST YOUR SKILLS

Find the remainder when:
$3{\mathrm{x}}^2+\mathrm{x}-1$ is divided by $\mathrm{x}+1$.

Find the remainder when:
$3{\mathrm{x}}^4-3{\mathrm{x}}^3-3\mathrm{x}-1$ is divided by $\mathrm{x}–1$.

Find the remainder when:
${\mathrm{x}}^3+1$ is divided by $\mathrm{x}+1.$

Find the remainder when:
${\mathrm{x}}^4+{\mathrm{x}}^3-2{\mathrm{x}}^2+\mathrm{x}+1$ is divided by $\mathrm{x}–1.$

Check whether the polynomial
$\mathrm{q}\left(\mathrm{t}\right)=4{\mathrm{t}}^3+4{\mathrm{t}}^2-\mathrm{t}-1$ is a multiple of $2\mathrm{t}\mathrm{}+\mathrm{}1$.
Hint: If $(2\mathrm{t}+1)$ is a factor of $\mathrm{q}\left(\mathrm{t}\right)$, then $\mathrm{q}\left(\mathrm{t}\right)$ is a multiple of $(2\mathrm{t}+1)$.