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 video 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.

• Set up two sets of parentheses.

• Factor out the greatest common factor if present.

• 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?

• The factors of the x term.

• The zeroes of the function.

• The factors of x².

• The 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 + 6 and y + 6

• y - 6 and y - 6

• y + 3 and y + 12

• y - 3 and y - 12

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

• Add the leading coefficient to the x term.

• Multiply the leading coefficient by the constant term.

• Factor out the leading coefficient if possible.

• Ignore the leading coefficient.

What is the final factored form of 2y² - 6y + 40?

• 2y(y² - 6y + 40)

• 2y(y - 4)(y + 10)

• 2y(y - 6)(y + 6)

• 2y(y - 5)(y + 8)

What does finding the zeroes of a function mean?

• Finding the y-intercepts of the graph.

• Determining the x-values where the function equals zero.

• Calculating the maximum value of the function.

• Identifying the slope of the function.

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

• x + 8

• x + 7

• x - 7

• x - 8

What does the zero product property state?

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

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

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

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

What are the solutions to the equation x(x - 9) = 0?

• x = 0 and x = 9

• x = 0 and x = -9

• x = 9 and x = -9

• x = 0 and x = 1