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Lesson Example Discussion Quiz: Class Homework

Step-4

Title: Quadratic-Equations and Factors

Grade: 1300-a Lesson: S2-L1

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Solve the quadratic equation \$2x^2 + 7x + 3 = 0\$ using factors.
2	Step	Find the components of the given equation	\$ 2x^2 + 6x + x + 3 = 0 \$
3	Step	Organize the terms into groups and extract the largest common factor	\$ (2x^2 + 6x) + (x + 3) = 0 \$ ⇒ 2x(x + 3) + 1(x + 3) = 0
4	Step	Identify the common binomial factor (x + 3) in both expressions.
5	Hint	Combine the terms by finding and using the common factor	(x + 3)(2x + 1) = 0
6	Step	To determine the x-values, we equate each factor to zero	x + 3 = 0 and 2x + 1 = 0
7	Step	Therefore, the solutions to the quadratic equation \$2x^2 + 7x + 3 = 0\$ are	\$x = -3 and x = -1/2\$
8	Choice.A	The solutions to the quadratic equations lack precision and are not exact	\$x = 3 and x = -1/2\$
9	Choice.B	The solutions found for the quadratic equation are both accurate	\$x = -3 and x = -1/2\$
10	Choice.C	The solutions to the quadratic equations lack precision and are not exact	\$x = 3 and x = 1/2\$
11	Choice.D	The solutions to the quadratic equations lack precision and are not exact	\$x = -3 and x = 1/2\$
12	Answer	Option	B
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Solve the quadratic equation \$2x^2 + 7x + 3 = 0\$ using factors.

Step

Find the components of the given equation

\$ 2x^2 + 6x + x + 3 = 0 \$

Step

Organize the terms into groups and extract the largest common factor

\$ (2x^2 + 6x) + (x + 3) = 0 \$

⇒ 2x(x + 3) + 1(x + 3) = 0

Step

Identify the common binomial factor (x + 3) in both expressions.

Hint

Combine the terms by finding and using the common factor

(x + 3)(2x + 1) = 0

Step

To determine the x-values, we equate each factor to zero

x + 3 = 0 and 2x + 1 = 0

Step

Therefore, the solutions to the quadratic equation \$2x^2 + 7x + 3 = 0\$ are

\$x = -3 and x = -1/2\$

Choice.A

The solutions to the quadratic equations lack precision and are not exact

\$x = 3 and x = -1/2\$

Choice.B

The solutions found for the quadratic equation are both accurate

\$x = -3 and x = -1/2\$

Choice.C

The solutions to the quadratic equations lack precision and are not exact

\$x = 3 and x = 1/2\$

Choice.D

The solutions to the quadratic equations lack precision and are not exact

\$x = -3 and x = 1/2\$

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?