Factoring Quadratic Expressions

The video tutorial explains how to factor a quadratic polynomial, t^2 + 8t + 15, by finding two numbers whose sum is 8 and product is 15. It demonstrates the use of the distributive property and FOIL method to expand binomials, identifies coefficients, and shows how to factor by grouping. The tutorial concludes with the final factorization of the polynomial as (t + 3)(t + 5).

What is the first step in factoring the expression t^2 + 8t + 15?

• Divide two binomials

• Subtract two binomials

• Add two binomials

• Multiply two binomials

Which property is used to expand the expression (t + a)(t + b)?

• Distributive Property

• Identity Property

• Associative Property

• Commutative Property

What is the coefficient of the second degree term in the expression t^2 + 8t + 15?

• 0

• 15

• 1

• 8

What are the two numbers whose sum is 8 and product is 15?

• 4 and 4

• 2 and 7

• 1 and 15

• 3 and 5

How can the expression 8t be rewritten for factoring by grouping?

• 4t + 4t

• 2t + 6t

• 3t + 5t

• 1t + 7t

What common factor is found in the terms t^2 + 3t?

• 3

• 15

• 5

• t

What is the final factored form of the expression t^2 + 8t + 15?

• (t + 1)(t + 15)

• (t + 2)(t + 7)

• (t + 4)(t + 4)

• (t + 3)(t + 5)

Which method can be used to verify the factorization of a quadratic expression?

• Substitution

• Grouping

• Graphing

• Completing the square

What is the purpose of factoring a quadratic expression?

• To increase the degree of the polynomial

• To change the variable

• To find the roots of the equation

• To simplify the expression

What is the result of factoring by grouping the expression t^2 + 8t + 15?

• (t + 1)(t + 15)

• t(t + 5) + 3

• (t + 3)(t + 5)

• t(t + 8) + 15