Factoring Quadratics Using the Box Method

Why can't x be isolated when solving a quadratic equation with three terms?

• Because the equation doesn't have a constant term

• Because there is only one x term

• Because the equation is linear

• Because the terms are not like terms

What is the product of the coefficient of the first term and the last term in the equation 4x^2 + 5x - 6?

• 20

• -20

• 24

• -24

Which pair of factors of -24 adds up to the middle term's coefficient, 5?

• 8 and -3

• -6 and 4

• 6 and -4

• -8 and 3

Why is the factoring x(x + 8)(x - 3) = 0 incorrect for the equation 4x^2 + 5x - 6?

• Because it doesn't have a constant term

• Because it doesn't produce 4x^2 when multiplied

• Because it equals 0

• Because it uses the wrong method

What is the correct factoring of 4x^2 + 5x - 6 using the box method?

• (x - 3)(x + 2) = 0

• (x + 3)(x - 2) = 0

• (4x + 3)(x - 2) = 0

• (4x - 3)(x + 2) = 0

What are the solutions to the equation 4x^2 + 5x - 6 = 0?

• x = 3/4, x = -2

• x = 3/4, x = 2

• x = -3/4, x = 2

• x = -3/4, x = -2

How does the box method differ from factoring by grouping?

• It is a simpler method

• It visualizes the equation as an area problem

• It only works for equations with a leading coefficient of 1

• It doesn't require finding the GCF

What does factoring by grouping involve?

• Guessing and checking solutions

• Multiplying the first and last coefficients

• Using the diamond method

• Rewriting the middle term and factoring out the GCF

Why can't a 4 be factored out of the equation 4x^2 + 5x - 6?

• Because not all terms are divisible by 4

• Because it would change the equation's value

• Because it would simplify to a linear equation

• Because it would eliminate the x term

What is the purpose of rewriting the middle term in factoring by grouping?

• To simplify the equation for easier factoring

• To find the GCF more easily

• To create like terms

• To identify the factors that add up to the middle term's coefficient