Question

If P (m) = 3m 5 - 7m + 5m 3 +2 write the polynomial in coefficient form​

Answer 1

(i) 3m(power 5) + 5m( power 3) -7m + 2

(ii) 3+5-7+2

Answer 2

Given,

P(m) = 3m^5-7m+5m³+2

To find,

The coefficient and standard form of the given polynomial.

Solution,

The coefficient and standard form of the given polynomial will be (3,0,5,0,-7,2) and 3m^5+5m³-7m+2 respectively.

We can easily solve this problem by following the given steps.

According to the question,

P(m) = 3m^5-7m+5m³+2

We will get the standard form by arranging the terms in their decreasing order of power.

So, the highest power is 5, then 3, 1 and 0.

Therefore,

The standard form = 3m^5+5m³-7m+2

The coefficient form of the polynomial is the form in which we write the coefficients of all the terms in brackets with a comma. For example, if a polynomial is x³+5 then the coefficient form will be as (1,0,0,5) because we write the coefficients of all the terms even if they are not present. (After x³, we should have x² and x but they are not present so their coefficient is zero.)

So, the coefficient form of 3m^5+5m³-7m+2 is:

(3,0,5,0,-7,2)

Hence, the coefficient and standard form of the given polynomial are (3,0,5,0,-7,2) and 3m^5+5m³-7m+2 respectively.