Solving quadratics by factoring and finding square roots

Factor x² + 7x + 10

Mathematical Equivalence

ON

What type of factoring would be required to solve 81x²=25?

• Basic trinomial where a=1

• Difference of squares

• GCF

Answer explanation

To solve 81x² = 25, we can rewrite it as 81x² - 25 = 0. This is a difference of squares, which factors as (9x - 5)(9x + 5) = 0. Thus, the correct type of factoring required is the difference of squares.

Match the equation to the solutions.

• x = 5 and x = -6

• x = 5 and x = 4

• x = 9 and x = 2

• x = 2 and x = 5

• x = -3 and x = 6

e

f

g

h

d

c

b

a

4x

11

44

x

+

11x

4

Answer explanation

To solve the equation x^2 - 100 = 0, we factor it as (x - 10)(x + 10) = 0. This gives us the solutions x = 10 and x = -10, making the correct answer x = -10, 10.

-5x² = -50

• ± 5

• ± 10

• ± √10

• -10

Answer explanation

To solve -5x² = -50, divide both sides by -5 to get x² = 10. Taking the square root gives x = ±√10. Thus, the correct answer is ±√10.

7x² + 1 = 8

• ± 1

• ± 7

• ± √7

• ± 8

Answer explanation

To solve 7x² + 1 = 8, subtract 1 from both sides to get 7x² = 7. Dividing by 7 gives x² = 1. Taking the square root results in x = ±1, making the correct answer ±1.

Answer explanation

The expression x^2 - 14x + 49 is a perfect square trinomial. It can be factored as (x - 7)(x - 7) or (x - 7)^2, which is the correct choice.

Mathematical Equivalence

ON

Answer explanation

Tags

A2.A-REI.B.4