# Thread: can somebody help me with these polynomials

1. ## can somebody help me with these polynomials

A)The polynomial x3 is divided by x +3. Calculate the remainder.
B)The polynomial p(x)is given by p(x)=ax3 +16x2+cx – 120, where a and c are constants. The three zeros of p(x)are –2, 3 and α. Find the value of α.
c)The function ƒ()x =tanx −loge xhas a zero near x =4.Use one application of Newton’s method to obtain another approximation to this zero. Give your answer correct to two decimal places.
d)The polynomial P(x)=x2+ax +b has a zero at x =2. When P(x)is divided by x +1, the remainder is 18.Find the values of a and b.
e)The cubic polynomial P(x) =x3 +rx2 +sx +t
, where r, s and t are real numbers, has three real zeros, 1, αand –α.
(i) Find the value of r.
(ii) Find the value of s +t.
P(x) =x3 +rx2 +sx +t.

p.s im sorry if this is in the wrong part of the forum this is my first post ever.

2. Originally Posted by andy69
A)The polynomial x3 is divided by x +3. Calculate the remainder.
B)The polynomial p(x)is given by p(x)=ax3 +16x2+cx – 120, where a and c are constants. The three zeros of p(x)are –2, 3 and α. Find the value of α.
c)The function ƒ()x =tanx −loge xhas a zero near x =4.Use one application of Newton’s method to obtain another approximation to this zero. Give your answer correct to two decimal places.
d)The polynomial P(x)=x2+ax +b has a zero at x =2. When P(x)is divided by x +1, the remainder is 18.Find the values of a and b.
e)The cubic polynomial P(x) =x3 +rx2 +sx +t
, where r, s and t are real numbers, has three real zeros, 1, αand –α.
(i) Find the value of r.
(ii) Find the value of s +t.
P(x) =x3 +rx2 +sx +t.

p.s im sorry if this is in the wrong part of the forum this is my first post ever.
A) Use the remainder theorem.

If P(x) is divided by x - a, the remainder is the same as P(a). What do you think "a" has to be in this case?

3. Originally Posted by Prove It
A) Use the remainder theorem.

If $\displaystyle P(x)$ is divided by $\displaystyle x - \alpha$, the remainder is the same as $\displaystyle P(\alpha)$. What do you think $\displaystyle \alpha$ is in this case?
does the post have to be over 10 to view the links

4. Originally Posted by andy69
does the post have to be over 10 to view the links
I didn't post any links. I've just used the LaTeX math type, it should just show up...

5. Originally Posted by Prove It
I didn't post any links. I've just used the LaTeX math type, it should just show up...
this is what it says about your latex math type.To view links or images in signatures your post count must be 10 or greater. You currently have 2 posts.
can you post it up in a different way please because i need to practice these urgently.

6. Edited

7. Originally Posted by Prove It
Edited
sorry you just posted the same thing and it says the same thing of the post i previously posted if you dont get what i mean then dont worry about it

8. I edited my post so that it can be read by new posters. I have also basically given you the answer.

Again - the remainder theorem states that if P(x) is divided by "x - a", then the remainder is the same as P(a).

If you're dividing by "x + 3", what do you think "a" has to be? Work out P(a).

9. Originally Posted by Prove It
I edited my post so that it can be read by new posters. I have also basically given you the answer.

Again - the remainder theorem states that if P(x) is divided by "x - a", then the remainder is the same as P(a).

If you're dividing by "x + 3", what do you think "a" has to be? Work out P(a).
ok then does this method work for all my questions.

10. Originally Posted by andy69
ok then does this method work for all my questions.
Why not first make sure you understand the first question, then have a think about which ones you think the remainder theorem would apply to..?