Answer:
Hence, all the factors of the given algebraic expression are:
[tex]2, (x+4), (x-4)[/tex]
Step-by-step explanation:
We have to factor the given expression as:
[tex]2x^2-32[/tex]
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 [tex]2x^2[/tex] and 32 are separated by a negative sign and both have 2 as a common factor.
i..e we may write:
[tex]2x^2-32=2(x^2-16)=2(x^2-4^2)[/tex]
Also we know that:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Here we have:
[tex]a=x, b=4[/tex]
Hence,
[tex]2x^2-32=2(x-4)(x+4)[/tex]
Hence, all the factors of the given algebraic expression are:
[tex]2, (x+4), (x-4)[/tex]
