30x^4y^3+24x^3y^2?

Question

i have to factor 30x^4y^3+24x^3y^2 and to be blunt i have no idea on how to do it

Answer 1

What is the greatest common factor of 30 and 24?

6, right? 6 x 5 = 30, 6 x 4 = 24.

What is the greatest common factor of x^4 and x^3?

x^3, right? x^3 times x = x^4, and x^3 times 1 = x^3

What is the greatest common factor of y^3 and y^2?

y^2, right? y^2 times y = y^3, and y^2 times 1 = y^2

So you factor out all those things, and figure out what's left

30x^4y^3+24x^3y^2
= 6x^3y^2 (5xy + 4(1)(1)) = 6x^3y^2 (5xy + 4)

Make sense?

Answer 2

what you need to do is to look at both parts and find what they have in common

30x^4y^3 part one

24x^3y^2 part two

in otherwords

partone is 30 x x x x 4 y y y

parttwo is 24 x x x 3 y y

so we can remove 3 of the x's and 2 y's to get

partone becomes x^3y^2 (30 x 4 y)

parttwo becomes x^3y^2 (24 . 3)

then take common factors out of the numerical aspects of part one and part two

IE 3, 4, 2 which gives (4 x 3 x 2 = 24)

partone becomes 24x^3y^2(5y)

part two becomes 24x^3y^2(3)

then combining both parts would give

24x^3y^2 (5y +3)

Answer 3

30x^4y^3 + 24x^3y^2 = x^3y^2(30xy+24) = 6x^3y^2(5xy + 4)

Answer 4

30x^4y³ + 24x³y² --- You can factor out 6x³y²
6x³y²(5xy + 4)