Factoring Polynomials with Coefficients Greater than 1

The video tutorial explains how to factor polynomials when the leading coefficient is greater than one. It begins by multiplying the first and last coefficients to find a product, then identifies factor pairs that sum to the middle term. The process involves grouping terms and factoring out common factors, ultimately using distribution properties to complete the factoring. The example used is 5x^2 - 3x + 6, which is factored into (5x - 3)(x - 2).

What is the first step in factoring polynomials with a leading coefficient greater than one?

• Divide the polynomial into groups

• Multiply the first and last coefficients

• Identify the middle term

• Find the factors of the middle term

What is the product of the first and last coefficients in the given polynomial?

• -13

• 15

• 18

• 30

Which two factors of 30 add up to -13?

• -3 and -10

• 1 and 30

• 2 and 15

• 3 and 10

How do we rewrite the polynomial for easier factoring?

• By adding factors of the middle term

• By subtracting the last term

• By grouping similar terms

• By dividing each term by the leading coefficient

What common factor is taken out from the first group (5x^2 - 10x)?

• -3

• x

• 10x

• 5x

What is left inside the parentheses after factoring out the common term from the first group?

• 5x + 2

• 5x - 2

• x - 2

• x + 2

What does factoring out common terms from each group help to achieve?

• Multiplying the coefficients

• Simplifying the polynomial

• Increasing the degree of the polynomial

• Changing the signs of the terms

What common factor is taken out from the second group (-3x + 6)?

• 6

• -3

• 3

• x

After factoring, what expression do we get inside both parentheses?

• x + 2

• 5x + 2

• 5x - 2

• x - 2

How do we rearrange the expression using the property of distribution?

• (5x - 3)(x - 2)

• (x - 2)(5x - 3)

• (5x + 3)(x - 2)

• (5x - 3)(x + 2)