What is the remainder when $2x^3 - 10x^2 + 6x + 2$ is divided by $x - 2$?
(A) -66
(B) -10
(C) $-x^3 + 5x^2 - 3x - 1$
(D) $x^3 - 5x^2 + 3x + 1$ - HSC - SSCE Mathematics Extension 1 - Question 2 - 2016 - Paper 1
Question 2
What is the remainder when $2x^3 - 10x^2 + 6x + 2$ is divided by $x - 2$?
(A) -66
(B) -10
(C) $-x^3 + 5x^2 - 3x - 1$
(D) $x^3 - 5x^2 + 3x + 1$
Worked Solution & Example Answer:What is the remainder when $2x^3 - 10x^2 + 6x + 2$ is divided by $x - 2$?
(A) -66
(B) -10
(C) $-x^3 + 5x^2 - 3x - 1$
(D) $x^3 - 5x^2 + 3x + 1$ - HSC - SSCE Mathematics Extension 1 - Question 2 - 2016 - Paper 1
Step 1
Step 1: Identify the Function
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Answer
We have the polynomial function given by
f(x)=2x3−10x2+6x+2. We need to find the remainder when this polynomial is divided by x−2.
Step 2
Step 2: Apply the Remainder Theorem
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Answer
According to the Remainder Theorem, the remainder of the division of a polynomial f(x) by x−c is equal to f(c). Here, we will substitute c=2 into the polynomial.
Calculating:
f(2)=2(2)3−10(2)2+6(2)+2
This evaluates as follows:
=2(8)−10(4)+12+2=16−40+12+2=16−40+14=−24+14=−10
Step 3
Step 3: Conclusion
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Answer
Thus, the remainder when 2x3−10x2+6x+2 is divided by x−2 is -10. Hence, the correct answer is (B) -10.
