R Chandra Solutions for Chapter: Polynomials, Exercise 4: TEST YOUR SKILLS

Is $(\mathrm{x}\mathrm{}+\mathrm{}2)$ a factor of $2{\mathrm{x}}^2+6\mathrm{x}+4$?

Examine whether $(\mathrm{x}+2)$ is a factor of ${\mathrm{x}}^3+3{\mathrm{x}}^2+5\mathrm{x}+6$.

Find the value of $\mathrm{k}$, if $(\mathrm{x}–1)$ is a factor of $4{\mathrm{x}}^3+3{\mathrm{x}}^2-4\mathrm{x}+\mathrm{k}$.

Factorise $6{\mathrm{x}}^2+17\mathrm{x}+5$

Using factor theorem, factorise ${\mathrm{y}}^2-5\mathrm{y}+6$.

Factorise ${\mathrm{x}}^3-23{\mathrm{x}}^2+142\mathrm{x}-120$.

Show that $(\mathrm{x}–2)$ is a factor of ${\mathrm{x}}^3-2{\mathrm{x}}^2-2\mathrm{x}+4$.

For what value of $\mathrm{‘}\mathrm{a}\mathrm{’},\mathrm{}(\mathrm{x}–\mathrm{a})$ is a factor of ${\mathrm{x}}^5-{\mathrm{a}}^2{\mathrm{x}}^3+3\mathrm{x}+\mathrm{a}-4$.