Find the constant term after adding the following polynomials:
$4 + 2 y - 3 y^{3}$ , $- 8 + 4 y + 7 y^{3}$ and $5 - 6 y + 8 y^{3} - 6 y^{2}$

Open in App

Solution

We find the sum of the given polynomials $(4 + 2 y - 3 y^{3}) + (- 8 + 4 y + 7 y^{3}) + (5 - 6 y + 8 y^{3} - 6 y^{2})$ by combining the like terms as shown below:

$(4 + 2 y - 3 y^{3}) + (- 8 + 4 y + 7 y^{3}) + (5 - 6 y + 8 y^{3} - 6 y^{2}) = (- 3 y^{3} + 7 y^{3} + 8 y^{3}) + (- 6 y^{2}) + (2 y + 4 y - 6 y) + (4 - 8 + 5) = y^{3} (- 3 + 7 + 8) - 6 y^{2} + y (2 + 4 - 6) + 1 = 12 y^{3} - 6 y^{2} + 1$

We know that the constant term of a polynomial is the term of degree $0$ ; it is the term in which the variable does not appear.

In the resulting polynomial $12 y^{3} - 6 y^{2} + 1$ , the constant term is $1$ because there is no variable.

Hence, the constant term is $1$ .

Suggest Corrections

Similar questions

4 + 2 y - 3 y^{3}, - 8 + 4 y + 7 y^{3}

a n d 5 - 6 y + 8 y^{3} - 6 y^{2}

Add $(3 + 2 y - 5 y^{2} + 6 y^{3}), (- 8 + 3 y + 7 y^{3})$ and $(5 - 6 y - 8 y^{3} + y^{2})$ .

Adding $3 + 2 y - 5 y^{2} + 6 y^{3}, - 8 + 3 y + 7 y^{3}$ and $5 - 6 y - 8 y^{3} + y^{2}$ , we get

\frac{2}{3} y^{3} - \frac{1}{3} y^{2} + \frac{5}{6} y + 7

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

Join BYJU'S Learning Program