Question

Find the product (x+2) (x+7) Why is the product also a polynomial?

Answer 1

The given product is, (x + 2) (x + 7).

We can expand the product as,

`(x+a)(x+b)=x^2+x(a+b)+ab`

Applying the expansion, we have,

`\begin{gathered} (x+2)(x+7)=x^2+x(2+7)+(2*7) \\ \text{ =x}^2+9x+14 \end{gathered}`

A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Since the resultant satisfies this condition, the resultant is also a polynomial.