How to factor a quadratic in your head when a=1

The video tutorial explains how to factor a quadratic expression by identifying two numbers that multiply to a given product and add to a specific sum. The instructor demonstrates the process of determining these numbers, emphasizing the need for both factors to be negative in this case. The tutorial concludes with a verification step, ensuring the factored form is correct by multiplying it back out.

What is the first step in factoring a quadratic expression like x^2 - 11x + 28?

• Find two numbers that add to 28 and multiply to -11.

• Find two numbers that add to -28 and multiply to 11.

• Find two numbers that multiply to 28 and add to -11.

• Find two numbers that multiply to -28 and add to 11.

If two numbers multiply to a positive product but add to a negative sum, what can be inferred about the numbers?

• Both numbers are positive.

• One number is positive, and the other is negative.

• Both numbers are negative.

• The numbers are zero.

Which of the following pairs of numbers multiply to 28 and add to -11?

• -7 and -4

• -14 and 2

• 7 and 4

• 14 and -2

What is the factored form of the quadratic expression x^2 - 11x + 28?

• (x - 7)(x + 4)

• (x + 7)(x - 4)

• (x - 7)(x - 4)

• (x + 7)(x + 4)

How can you verify that the factored form of a quadratic expression is correct?

• By dividing the factors by the original expression.

• By multiplying the factors to see if they expand to the original expression.

• By adding the factors together.

• By subtracting the factors from the original expression.