Question

Write the polynomial P(x) = x² - 9 as the product of two first degree polynomials​

Answer 1

Answer:

Step-by-step

p(x) = xsq - 9

so x= root of 9

that is = (x+3) (x-3)

Answer 2

Given,

A polynomial P(x) = x² - 9

To find,

To simplify P(x) as the product of two first-degree polynomials.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

The degree of any polynomial is the highest of all the degrees of the polynomial's individual terms (monomials) with non-zero coefficients. {Statement-1}

Now, according to the question and statement-1:

The given polynomial P(x) has a degree equal to 2.

Now, on factorizing the given polynomial P(x), we get;

P(x) = x² - 9

= (x)^2 - (3)^2

= (x+3)(x-3)

{using the algebraic identity: (a)^2 - (b)^2 = (a+b)(a-b)}

= the P(x) as the product of two first degree polynomials = (x+3)(x-3)

{According to statement-1, both (x+3) and (x-3) have degree equal to 1}

Hence, the given polynomial P(x) can be represented as the product of two first-degree polynomials as (x+3)(x-3).