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Lesson Example Discussion Quiz: Class Homework

Step-3

Title: Dividing polynomials

Grade: 8-a Lesson: S1-L3

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

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	\$(6x^2 + 19x + 10)/(2x + 5)\$ If ax + b represents the simplified form of the expression shown, then what is the value of a + b?
2	Step	Given polynomial expression is	\$(6x^2 + 19x + 10)/(2x + 5)\$
3	Step	We divide \$(6x^2 + 19x + 10) by (2x + 5)\$	$3$
4	Step	After the division, we get 3x + 2.
5	Step	Now equate 3x + 2 to ax+b to find the values of a and b.So, we have:	3x + 2 = ax + b ⇒ a = 3 ⇒ b = 2
6	Step	Finally, we find the sum of the coefficients:	a + b = 3 + 2 = 5
7	Step	Thus, the value of a + b = 5.
8	Choice.A	This option represents the sum of the coefficients a and b in the expression ax + b. However, we found that a = 3 and b = 2, so a + b = 3 + 2 = 5, not 2. Therefore, option A is incorrect	2
9	Choice.B	Again, this represents the sum of the coefficients a and b in the expression ax + b. As we found earlier, a + b = 3 + 2 = 5, not 3. So, option B is incorrect	3
10	Choice.C	This option represents the sum of the coefficients a and b in the expression ax + b. As we found earlier, a + b = 3 + 2 = 5, which matches this option. Therefore, option C is the correct answer	5
11	Choice.D	Similar to the other options, this represents the sum of the coefficients a and b in the expression ax + b. However, we found that a + b = 3 + 2 = 5, not 6. Therefore, option D is incorrect	6
12	Answer	Option	C
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

\$(6x^2 + 19x + 10)/(2x + 5)\$
If ax + b represents the simplified form of the expression shown, then what is the value of a + b?

Step

Given polynomial expression is

\$(6x^2 + 19x + 10)/(2x + 5)\$

Step

We divide \$(6x^2 + 19x + 10) by (2x + 5)\$

$3$

Step

After the division, we get 3x + 2.

Step

Now equate 3x + 2 to ax+b to find the values of a and b.So, we have:

3x + 2 = ax + b
⇒ a = 3
⇒ b = 2

Step

Finally, we find the sum of the coefficients:

a + b = 3 + 2 = 5

Step

Thus, the value of a + b = 5.

Choice.A

This option represents the sum of the coefficients a and b in the expression ax + b. However, we found that a = 3 and b = 2, so a + b = 3 + 2 = 5, not 2. Therefore, option A is incorrect

Choice.B

Again, this represents the sum of the coefficients a and b in the expression ax + b. As we found earlier, a + b = 3 + 2 = 5, not 3. So, option B is incorrect

Choice.C

This option represents the sum of the coefficients a and b in the expression ax + b. As we found earlier, a + b = 3 + 2 = 5, which matches this option. Therefore, option C is the correct answer

Choice.D

Similar to the other options, this represents the sum of the coefficients a and b in the expression ax + b. However, we found that a + b = 3 + 2 = 5, not 6. Therefore, option D is incorrect

Answer

Option

Sumup

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