What is the remainder when $2x^3 - 10x^2 + 6x + 2$ is divided by $x - 2$? - 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 $x - 2$?
Worked Solution & Example Answer:What is the remainder when $2x^3 - 10x^2 + 6x + 2$ is divided by $x - 2$? - HSC - SSCE Mathematics Extension 1 - Question 2 - 2016 - Paper 1
Step 1
Substituting $x = 2$ into the polynomial
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Answer
To find the remainder when dividing by x−2, we can use the Remainder Theorem. We need to substitute x=2 into the polynomial:
R=2(2)3−10(2)2+6(2)+2
Calculating this step by step:
Calculate 2(2)3=2⋅8=16.
Calculate −10(2)2=−10⋅4=−40.
Calculate 6(2)=12.
Now adding these values together:
R=16−40+12+2
Simplifying further:
R=16−40=−24R=−24+12=−12R=−12+2=−10
Step 2
Identifying the correct answer
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Answer
From our calculations, the remainder when 2x3−10x2+6x+2 is divided by x−2 is −10. Therefore, the correct answer is (B) -10.
