What is the remainder when $P(x)=-x^3-2x^2-3x+8$ is divided by $x+2$? - HSC - SSCE Mathematics Extension 1 - Question 3 - 2021 - Paper 1
Question 3
What is the remainder when $P(x)=-x^3-2x^2-3x+8$ is divided by $x+2$?
Worked Solution & Example Answer:What is the remainder when $P(x)=-x^3-2x^2-3x+8$ is divided by $x+2$? - HSC - SSCE Mathematics Extension 1 - Question 3 - 2021 - Paper 1
Step 1
Find the value of $x$
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Answer
To find the remainder when P(x) is divided by x+2, we apply the Remainder Theorem, which states that the remainder of the division of a polynomial P(x) by x−c is P(c). Here, we substitute x=−2.
Step 2
Evaluate $P(-2)$
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Answer
Now, substituting −2 into P(x):
P(−2)=−(−2)3−2(−2)2−3(−2)+8
Calculating this, we have:
−(−2)3=−(−8)=8
−2(−2)2=−2(4)=−8
−3(−2)=6
So,
P(−2)=8−8+6+8=14
Step 3
State the remainder
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Answer
Thus, the remainder when dividing P(x) by x+2 is 14.
