Factoring Trinomials and Solving Quadratic Equations

This video tutorial covers factoring trinomials in the form ax^2 + bx + c, where the leading coefficient a is 1. It explains the steps to factor such quadratics, find the zeroes of quadratic functions, and solve quadratic equations by factoring. The tutorial includes examples and addresses cases where the leading coefficient is not 1. It also demonstrates using the zero product property to solve equations.

What is the first step in factoring a quadratic trinomial where the leading coefficient is 1?

• Find the zeroes of the function.

• Factor out the greatest common factor if present.

• Set up two sets of parentheses.

• List all factors of the constant term.

When setting up the parentheses for factoring, what should be placed in the first position of each set?

• Factors of x².

• Factors of the leading coefficient.

• Factors of the middle term.

• Factors of the constant term.

In the example of factoring x² - 14x - 32, which pair of factors is used?

• x - 16 and x + 2

• x + 16 and x - 2

• x - 8 and x + 4

• x + 8 and x - 4

What is the correct factorization of y² - 15y + 36?

• y - 3 and y - 12

• y + 3 and y + 12

• y - 6 and y - 6

• y + 6 and y + 6

How do you handle a quadratic trinomial where the leading coefficient is not 1?

• Ignore the leading coefficient.

• Factor out the leading coefficient if possible.

• Add the leading coefficient to the middle term.

• Multiply the leading coefficient by the constant term.

What is the final factored form of 3x² - 9x + 14?

• 3(x - 7)(x - 2)

• 3(x + 7)(x + 2)

• 3(x + 7)(x - 2)

• 3(x - 7)(x + 2)

What is the greatest common factor in the expression 2y² - 6y + 40?

• 2y

• 6

• y

• 2

What does finding the zeroes of a function mean graphically?

• Finding the axis of symmetry.

• Finding the x-intercepts.

• Finding the y-intercepts.

• Finding the vertex of the parabola.

If x = 7 is a zero of the function, what is one of the factors?

• x + 8

• x - 7

• x - 8

• x + 7

What does the zero product property state?

• If two numbers multiply to zero, both must be zero.

• If two numbers multiply to zero, neither can be zero.

• If two numbers multiply to zero, they must be equal.

• If two numbers multiply to zero, one or both must be zero.