# Write each of the following polynomials in the standard form. Also, write their degree.

Question:

Write each of the following polynomials in the standard form. Also, write their degree.

(i) x2 + 3 + 6x + 5x4

(ii) a2 + 4 + 5a6

(iii) (x3 − 1)(x3 − 4)

(iv) (y3 − 2)(y3 + 11)

(v) $\left(a^{3}-\frac{3}{8}\right)\left(a^{3}+\frac{16}{17}\right)$

(vi) $\left(a+\frac{3}{4}\right)\left(a+\frac{4}{3}\right)$

Solution:

(i) Standard form of the given polynomial can be expressed as:

$\left(5 x^{4}+x^{2}+6 x+3\right)$ or $\left(3+6 x+x^{2}+5 x^{4}\right)$

The degree of the polynomial is 4 .

(ii) Standard form of the given polynomial can be expressed as:

$\left(5 \mathrm{a}^{6}+\mathrm{a}^{2}+4\right)$ or $\left(4+\mathrm{a}^{2}+5 \mathrm{a}^{6}\right)$

The degree of the polynomial is 6 .

(iii) $\left(\mathrm{x}^{3}-1\right)\left(\mathrm{x}^{3}-4\right)=\mathrm{x}^{6}-5 \mathrm{x}^{3}+4$

Standard form of the given polynomial can be expressed as:

$\left(x^{6}-5 x^{3}+4\right)$ or $\left(4-5 x^{3}+x^{6}\right)$

The degree of the polynomial is 6 .

(iv) $\left(\mathrm{y}^{3}-2\right)\left(\mathrm{y}^{3}+11\right)=\mathrm{y}^{6}+9 \mathrm{y}^{3}-22$

Standard form of the given polynomial can be expressed as:

$\left(\mathrm{y}^{6}+9 \mathrm{y}^{3}-22\right)$ or $\left(-22+9 \mathrm{y}^{3}+\mathrm{y}^{6}\right)$

The degree of the polynomial is 6 .

(v) $\left(\mathrm{a}^{3}-\frac{3}{8}\right)\left(\mathrm{a}^{3}+\frac{16}{17}\right)=\mathrm{a}^{6}+\frac{77}{136} \mathrm{a}^{3}-\frac{6}{17}$

Standard form of the given polynomial can be expressed as:

$\left(\mathrm{a}^{6}+\frac{77}{136} \mathrm{a}^{3}-\frac{6}{17}\right)$ or $\left(-\frac{6}{17}+\frac{77}{136} \mathrm{a}^{3}+\mathrm{a}^{6}\right)$

The degree of the polynomial is 6 .

(vi) $\left(\mathrm{a}+\frac{3}{4}\right)\left(\mathrm{a}+\frac{4}{3}\right)=\mathrm{a}^{2}+\frac{25}{12} \mathrm{a}+1$

Standard form of the given polynomial can be expressed as:

$\left(\mathrm{a}^{2}+\frac{25}{12} \mathrm{a}+1\right)$ or $\left(1+\frac{25}{12} \mathrm{a}+\mathrm{a}^{2}\right)$

The degree of the polynomial is 2 .