Question

How do you factorize `40x ^ { 2} + 24x`?

Answer 1

`8x(5x+3)`

Explanation:

`40x^2+24x` taking 8x out as is common in both terms,
`8x(5x+3)`

Answer 2

`40x^2+24x=8x(5x+3)`

Explanation:

When factoring something, what it is really asking to do is find what are the simplest terms in which the expression can be written which is in the terms of the expression's greatest common factors of its parts. Factoring basically allows one to simply an expression.

So looking at.. `40x^2+24x`, one can break down that `x` is multiplied to both terms (`40x^2` and `-24x`)so one can "divide/remove" that part of the expression and multiply the x separately which would look like this

`40x^2+24x=x(40x+24)`

You are basically doing the applying the distributive property of multiplication in reverse. However, this is not the simplest terms that the expression can be written in. One can note that 40 and 24 both have a common factor of 8. `8*5=40 and 8*3=24`

So one can once again "remove" (remove in quotations because you are not really removing something but rather separating it from the rest) the factor 8 from the expression, giving:

`x(40x+24)=8x(5x+3)`

If it is hard to imagine that 8 fits both into 40 and 24 on the spot (as may be the case with larger factorizations) you can simply keep dividing the coefficients by low common factors like 2 or 3 or 5 until one has completely simplified the expression and then multiply the low common factors used at the end. For example, one could have divided the `40x-24` by the number `2` continuously and would have found this:

`x(40x+24)=2x(20x+12)=4x(10x+6)=8x(5x+3)`

You still get the same answer. I hope this helps.