Identify the factors of the expression x^3 +4x^2-16x-64.

Question

asked Apr 17, 2023 164k views

1 Answer

Timothy Kanski · Answer 1 · 2023-04-21T05:50:21+0000

Solution:

Consider the following polynomial:

By grouping terms, we get that the above polynomial is equivalent to the following expression:

Now, we can apply common factor:

$x^2(x^{}+4^{})-16(x+4)$

again, applying a common factor, we get:

Note that the left factor is a difference of squares, therefore, the above expression is equivalent to:

this is equivalent to:

So that, we can conclude that the factors of the given expression are:

and

$(x+4)^{2^{}}$

and we can conclude that: