Math Is Fun Forum

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

[ASK] Polynomial

11. Given a polynomial with the degree 3. If it is divided by

, the remainder is 2x + 1. If it is divided by

, the remainder is 3x - 2. The polynomial is ....
A.

B.

C.

D.

E.

The book says that the answer is A, but I don't understand the part when they suddenly substitute f(-2) = -8, where does that come from? I tried doing it myself and got a (the coefficient of

) as

. Can you tell me what's wrong?

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: [ASK] Polynomial

hi Monox D. I-Fly

I also get the x^3 coefficient as -1/3  Looks like the question has a typo as none of those answers works.

I get

and this checks out correctly with the given information.

I did this by substituting x = -3, 1, 0 and -2 into ax^3 + bx^2 + cx + d and then solving for a, b, c, and d.

When you put x = -2 , 3x - 2 becomes 3 times -2 -2 = -8.   

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
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Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: [ASK] Polynomial

I get it. Thank you, bob!

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.