Factoring Trinomials with a Leading Coefficient of 1

This video tutorial explains how to factor trinomials with a leading coefficient of one, focusing on expressions in the form x^2 + BX + C. It covers the different sign combinations that can appear in trinomials and how these affect the signs of the resulting binomials. The tutorial provides examples and uses the FOIL method to verify the correctness of factored expressions. It also discusses advanced strategies for factoring trinomials with different sign configurations, emphasizing the importance of understanding the relationship between the signs and the terms in the trinomial.

What is the standard form of a trinomial with a leading coefficient of one?

• ax^2 + bx + c

• x^2 + bx + c

• x^2 - bx + c

• ax^2 + bx - c

If the second sign in a trinomial is positive, what does it indicate about the signs of the factors?

• One sign is positive and one is negative

• Cannot determine the signs

• Both signs are positive

• Both signs are negative

What is required to get a positive third term in a trinomial when factoring?

• Multiply two positive numbers

• Multiply two negative numbers

• Multiply a positive and a negative number

• Any of the above

Which pair of factors of 21 adds up to 10?

• 6 and 15

• 1 and 21

• 3 and 7

• 2 and 19

In the example with a trinomial needing factors of 27 that add up to -12, which pair of factors is correct?

• 1 and 27

• 5 and 22

• 3 and 9

• 6 and 21

How do you verify if you have factored a trinomial correctly?

• By solving the quadratic equation

• By plotting the graph

• By foiling the factors

• By checking the discriminant

What does the commutative property of multiplication imply in the context of factoring?

• The order of factors affects the product

• The order of factors does not affect the product

• Only one factor is needed

• None of the above

If the sign of 'c' in a trinomial is negative, what can be inferred about the signs of the factors?

• Cannot determine the signs

• One sign is positive and one is negative

• Both signs are negative

• Both signs are positive

What is the effect of the sign of 'b' in a trinomial on the signs of the factors?

• Determines the sign of both factors

• Has no effect on the signs of the factors

• Changes the factors numerically

• Only affects one of the factors

What encouragement does the video provide for mastering trinomial factoring?

• Practice makes perfect

• Keep working hard at it

• It comes naturally with time

• No specific encouragement given