Which of the following is the greatest common factor of the terms 48s⁵t³u² and 40s³tu⁴?

Solution:

Given, the terms are 48s⁵t³u² and 40s³tu⁴

We have to find the greatest common factor of the terms.

48s⁵t³u² = 2 × 2 × 2 × 2 × 3 × s⁵ × t³ × u²

40s³tu⁴ =  2 × 2 × 2 × 5 × s³ × t × u⁴

The greatest common factor = 2³ × s³ × t × u²

= 8s³tu²

Therefore, the greatest common factor is  8s³tu².

Example: What is the greatest common factor of the terms in the polynomial 12x⁴ + 2x³ - 30x²?

Solution:

Given, the polynomial is 12x⁴ + 2x³ - 30x²

We have to find the greatest common factor.

Check for the largest number that can be divided in all 3 numbers.

In this case, the largest number would be 2.

Now, the coefficient of the polynomial divided by 2,

12/2 = 6

2/2 = 1

30/2 = 15

The largest common variable would be x².

x⁴/x² = x²

x³/x² = x

x²/x² = 1

Putting the terms together, we get 2x².

Therefore, the greatest common factor is 2x².

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Which of the following is the greatest common factor of the terms 48s⁵t³u² and 40s³tu⁴?

Summary:

The greatest common factor of the terms 48s⁵t³u² and 40s³tu⁴ is  8s³tu².