Question

Select all the factors of: 2x2−32

Answer 1

Hence, all the factors of the given algebraic expression are:

`2, (x+4), (x-4)`

Explanation:

We have to factor the given expression as:

`2x^2-32`

Now to factor a algebraic expression means:

" Factorisation of an algebraic expression is similar to finding factors of real numbers ".

Now we know that both the terms of the algebraic equation
`2x^2` and 32 are separated by a negative sign and both have 2 as a common factor.

i..e we may write:

`2x^2-32=2(x^2-16)=2(x^2-4^2)`

Also we know that:

`a^2-b^2=(a-b)(a+b)`

Here we have:

`a=x, b=4`

Hence,

`2x^2-32=2(x-4)(x+4)`

Hence, all the factors of the given algebraic expression are:

`2, (x+4), (x-4)`