Quadratic Expressions and Common Binomial Factors

The video tutorial explains how to find a common binomial factor between two quadratic expressions: M squared minus 4m minus 45 and 6m squared minus 150. The instructor demonstrates the process of factoring each expression into binomials and identifies the shared factor, M plus 5. The tutorial emphasizes understanding the relationships between coefficients and products in quadratic expressions to successfully factor them.

What is the main goal of the problem discussed in the video?

• To simplify a polynomial expression

• To find the roots of a quadratic equation

• To identify a common binomial factor between two expressions

• To solve a linear equation

How can the expression M^2 - 4M - 45 be factored?

• (M + 4)(M - 11)

• (M - 4)(M + 11)

• (M - 5)(M + 9)

• (M + 5)(M - 9)

What condition must a and b satisfy for the expression M^2 - 4M - 45?

• a + b = 4 and a * b = -45

• a + b = -4 and a * b = 45

• a + b = -4 and a * b = -45

• a + b = 4 and a * b = 45

Which pair of numbers satisfies the conditions for a and b in the expression M^2 - 4M - 45?

• 9 and -5

• 5 and -9

• 3 and 15

• 1 and -45

What is the first step in factoring the expression 6M^2 - 150?

• Divide by 3

• Subtract 6 from both sides

• Factor out a 6

• Add 150 to both sides

How is the expression 6M^2 - 150 rewritten after factoring out a 6?

• 6(M - 25)

• 6(M^2 + 25)

• 6(M^2 - 25)

• 6(M + 25)

What type of expression is M^2 - 25?

• Perfect square trinomial

• Linear expression

• Sum of squares

• Difference of squares

What is the factored form of M^2 - 25?

• (M + 5)(M + 5)

• (M - 5)(M - 5)

• (M + 5)(M - 5)

• (M - 5)(M + 5)

What is the common binomial factor shared by both expressions?

• M - 9

• M + 5

• M + 9

• M - 5

Why is M + 5 considered a common factor?

• It is the only factor of M^2 - 4M - 45

• It is the only factor of 6M^2 - 150

• It is a factor of neither expression

• It appears in the factored form of both expressions