Answer:
The remainder is 3x - 4
Step-by-step explanation:
[Remember]
So,
In this case our dividend is always P(x).
<u>Part 1</u>
When the divisor is , the remainder is , so we can say
In order to get rid of "Quotient" from our equation, we must multiply it by 0, so
When solving for , we get
When ,
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<u>Part 2</u>
When the divisor is , the remainder is , so we can say
In order to get rid of "Quotient" from our equation, we must multiply it by 0, so
When solving for , we get
When ,
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<u>Part 3</u>
When the divisor is , the quotient is , and the remainder is , so we can say
From Part 1, we know that , so we can substitute and into
When we do, we get:
We will call equation 1
From Part 2, we know that , so we can substitute and into
When we do, we get:
We will call equation 2
Now we can create a system of equations using equation 1 and equation 2
By adding both equations' right-hand sides together and both equations' left-hand sides together, we can eliminate and solve for
So equation 1 + equation 2:
Now we can substitute into either one of the equations, however, since equation 1 has less operations to deal with, we will use equation 1.
So substituting into equation 1:
Now that we have both of the values for and , we can substitute them into the expression for the remainder.
So substituting and into :
Therefore, the remainder is .