Question

Find the GCF of 4x³ + 2x²y + 24x.​

Answer 1

Answer:

GCF = 2x

Step-by-step explanation:

Find the prime factors of each term in order to find the greatest common factor (GCF).

Answer 2

We have given that

$4x^{3}+2x^{2} y+24x$

and find the greatest common factor

Lets Solve,

Since, $4x^{3}, 2x^{2} y, 24x$ contain both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numeric part then find GCF for the variable part.

The factors for $4$ are 1, 2, 4

The factors for 2 are 1 and 2

The factors for 24 are 1, 2, 3, 4, 6, 8, 12, 24

List all the factors for 4, 2, 24 to find the common factors.

4: 1, 2, 4

2: 1, 2

24: 1, 2, 3, 4, 6, 8, 12, 24

The common factors for 4, 2, 24 are 1,2.

The GCF for the numerical part is 2.

Now,

find the common factors for the variable part:

$x^{3}, x^{2} , y, x$

The factors for $x^{3}$ are $x.x.x$

The factors for $x^{2}$ are $x.x$

The factor for $y^{1}$ is y itself.

The factor for $x^{1}$ is x itself.

List all the factors for $x^{3}, x^{2} , y^{1} , x^{1}$ to find the common factors.

$x^{3} =x.x.x\\x^{2} =x.x\\y^{1} =y\\x^{1} =x$

Multiply the GCF of the numerical part 2 and the GCF of the variable part x

$2x$