Greatest Common Factor and Polynomials

This video tutorial covers factoring polynomials, focusing on finding the greatest common factor (GCF) and using it to factor expressions. It explains how to identify the GCF in numbers and variables, handle negative coefficients, and recognize prime expressions. The tutorial also applies these concepts to solve area problems involving rectangles and circles.

What is the Greatest Common Factor (GCF)?

• The sum of all factors of a number.

• The smallest number that divides a group of numbers.

• The product of all factors of a number.

• The largest number that divides a group of numbers.

Which of the following is a correct factor list for the number 48?

• 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

• 1, 2, 4, 8, 16, 32, 48

• 1, 2, 3, 6, 12, 24, 48

• 1, 2, 4, 6, 8, 12, 24, 48

When factoring the polynomial 48G^4H and 64G^3H^2, what is the GCF?

• 16G^3H

• 8G^4H^2

• 32G^3H

• 16G^4H

What should you do if the leading coefficient of a polynomial is negative?

• Ignore the negative sign.

• Multiply the GCF by -1.

• Add a positive sign to the GCF.

• Add a negative sign to the GCF.

What is the factored form of the polynomial 15HM^2 + 20N - 35M?

• 5M(3H + 4N - 7M)

• 5M(3H + 4N - 7)

• 5(3HM + 4N - 7M)

• 5(3H + 4N - 7M)

What do you call an expression that cannot be factored further?

• Simplified

• Factorable

• Prime

• Composite

If a polynomial has no common factors other than 1, what is it called?

• Composite

• Prime

• Factorable

• Simplified

What is the GCF of the numbers 14 and 35?

• 2

• 5

• 7

• 14

In an area problem, if the width of a rectangle is 7GH^4, what is the GCF of the areas 14G^2H^4 and 35GH^5?

• 7GH^4

• 14GH^4

• 35GH^5

• 7G^2H^4

How do you find the shaded area of a square with a circle inside it?

• Divide the area of the square by the area of the circle.

• Multiply the area of the square by the area of the circle.

• Subtract the area of the circle from the area of the square.

• Add the area of the square and the circle.