Question

write the following polynomials in standard form -7y+y5+3y3-1/2+2y4-y2

Answer 1

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Answer 2

The standard form of polynomial is $\bf {y}^{5} + 2 {y}^{4} + 3 {y}^{3} - {y}^{2} - 7y - \frac{1}{2}$

Given:

• A polynomial
• $- 7y + {y}^{5} + 3 {y}^{3} - \frac{1}{2} + 2 {y}^{4} - {y}^{2}$

To find:

• Write the polynomial in its standard form.

Solution:

Standard form of polynomial:

$\bf a_0 {x}^{n} + a_1 {x}^{n - 1} + a_2 {x}^{n - 2} + ... + a_{n - 1}x + a_n$

here,

a0,a1,a2...an are coefficients of respective terms.

Step 1:

Find the highest power of y.

It is 5.

Thus,

In standard form it should be written in 1st place.

${y}^{5} - 7y + 3 {y}^{3} - \frac{1}{2} + 2 {y}^{4} - {y}^{2}$

Step 2:

Find the next term of y, i.e. y with power 4.

Arrange that after first term.

${y}^{5} + 2 {y}^{4} - 7y + 3 {y}^{3} - \frac{1}{2} - {y}^{2}$

repeat the process

Step 3:

Final arrangement and the standard form.

${y}^{5} + 2 {y}^{4} + 3 {y}^{3} - {y}^{2} - 7y - \frac{1}{2}$

Thus,

The standard form is

$\bf {y}^{5} + 2 {y}^{4} + 3 {y}^{3} - {y}^{2} - 7y - \frac{1}{2}$

Learn more:

1) Write the degree of the polynomial :

4z3

– 3z5

+ 2z4

+ z + 1

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2) Which polynomial is written in ascending order? t2 − t + 4 t2 + 4 − t 4 + t2 − t 4 − t + t2

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