Subject: More related to "If a polynomial p(x) is divided by x-a, what is the remainder?"
From: Quora <[email-masked]>
To: [email-masked]
Date: Fri, 07 Aug 2020 10:19:20 +0000

Stories from your activity

-----

Question: Polynomial p(x) when divided by (x-a) gives the remainder p(a), which means x=a, but then x-a=0, so we are dividing by 0. How is this possible?

Answer from Mark Gritter

When a polynomial is divided by a polynomial, we are operating over polynomials, not numbers. [math]x-a[/math], as a polynomial, is not zero. It is a degree-one polynomial. At
Read More: https://www.quora.com/Polynomial-p-x-when-divided-by-x-a-gives-the-remainder-p-a-which-means-x-a-but-then-x-a-0-so-we-are-dividing-by-0-How-is-this-possible?top_ans=44859531
-----
Question: If polynomial [math]P(x)[/math] leaves a remainder of [math]1[/math] when divided by [math]x-1,[/math] and a remainder of [math]-1[/math] when divided by [math]x+1[/math], what is the remainder when it is divided by [math]x^{2}-1[/math]?

Answer from Sayan Acharya

Other people here have already provided the best methods but I can show another special method that is pretty easy.

Let’s give you an example first.

When dividing [math](x^3
Read More: https://www.quora.com/If-polynomial-P-x-leaves-a-remainder-of-1-when-divided-by-x-1-and-a-remainder-of-1-when-divided-by-x+1-what-is-the-remainder-when-it-is-divided-by-x-2-1?top_ans=79783120
-----
Question: When a polynomial p(x) is divided by (x-1), the remainder is 3. When p(x) is divided by (x-3), the remainder is 5. If r(x) is the remainder when p(x) is divided by (x -3) (x-1) then what will be the value of r(-2)?

Answer from Ved Prakash Sharma

p(x) is divided by (x-1) , the remainder is 3. Then

p(1)=3…………….(1)

p(x) is divided by (x-3) , the remainder is 5. Then

p(3)=5……………..(2)

p(x) is divided by (x-3).(x-1), th
Read More: https://www.quora.com/When-a-polynomial-p-x-is-divided-by-x-1-the-remainder-is-3-When-p-x-is-divided-by-x-3-the-remainder-is-5-If-r-x-is-the-remainder-when-p-x-is-divided-by-x-3-x-1-then-what-will-be-the-value-of-r-2?top_ans=148033946
-----
Question: When a polynomial f(x) is divided by (x –3) the remainder is –9 and when divided by (2x–1), the remainder is -6. What is the remainder when f(x) is divided by (x –3) (2x–1). [4]?

Answer from Ramkhilari Kushwah (रामखिलाड़ी कुशवाह)

When a polynomial f(x) is divided by (x –3) the remainder is –9

So using the remainder theorem: f(3)=-9

Also when a polynomial f(x) is divided by (2x -1) the remainder is –3
Read More: https://www.quora.com/When-a-polynomial-f-x-is-divided-by-x-3-the-remainder-is-9-and-when-divided-by-2x-1-the-remainder-is-6-What-is-the-remainder-when-f-x-is-divided-by-x-3-2x-1-4?top_ans=208045552
-----
Question: If for polynomial p(X),p(-1) =3, then what will be the remainder when p(X) is divided by (X+1)?

Answer from Goh Kim Tee

By the remainder theorem ,

p(a)= the remainder when p(x) is divided by (x-a)

p(-1)= the remainder when p(x) is divided by {x-(-1)}, i.e.(x+1)

Since it is given that p(-1)=3
Read More: https://www.quora.com/If-for-polynomial-p-X-p-1-3-then-what-will-be-the-remainder-when-p-X-is-divided-by-X-1?top_ans=80772352
-----
Question: A polynomial leaves remainder [math]2[/math] when divided by [math]x-1[/math] and remainder [math]1[/math] when divided by [math]x-2[/math]. If the polynomial is divided by [math](x-1)(x-2)[/math], then what would be the remainder?

Answer from Sayan Acharya

Let’s give you an example first.

When dividing [math](x^3+x)[/math] by [math]x^2[/math]

It can be written as::::

[math]\dfrac{x^3+x}{x^2}[/math]

[math]=x+\dfrac{x}{x^2}[/m
Read More: https://www.quora.com/A-polynomial-leaves-remainder-2-when-divided-by-x-1-and-remainder-1-when-divided-by-x-2-If-the-polynomial-is-divided-by-x-1-x-2-then-what-would-be-the-remainder?top_ans=79781741
-----
Question: When a polynomial p(x) is divided by x-a, then how do you find the remainder?

Answer from Adithya V

Substitute a in the polynomial and the answer you get is the remainder

Eg f(x) = x³-3x²+2x-9

When dividing by x-2 we substitute x = 2

f(2) = 8–12+4–9 = -9 … So remainder is
Read More: https://www.quora.com/When-a-polynomial-p-x-is-divided-by-x-a-then-how-do-you-find-the-remainder?top_ans=41925757
-----
Question: Let [math]p(x) = 1+x+x^2+x^3+x^4+x^5.[/math] What is the remainder of division of [math]p(x^{12})[/math] by [math]p(x)?[/math]

Answer from Gram Zeppi

Thanks for the A2A.  The answer is [math]6.[/math]

Note that  [math]p(x) = \dfrac{x^6-1}{x-1}.[/math]

Let's compute  [math]p(x^{12}) \mod x^6-1.[/math]

This amounts to repl
Read More: https://www.quora.com/Let-p-x-1+x+x-2+x-3+x-4+x-5-What-is-the-remainder-of-division-of-p-x-12-by-p-x?top_ans=16560113
-----
Question: When a polynomial P(x) is divided by 2x - 4, the remainder is -3. If P(-1) = -6, what is the remainder when P(x) is divided by (2x - 4) (x+1)?

Answer from Pustam Raut (पुस्तम राउत)

Given:
P(4/2)=P(2)=-3 & P(-1)=-6
We can write, P(x)=D(x)*Q(x)+R(x)
Since D(x)=(2x-4)(x+1) is quadratic, R(x) will be linear
Let P(x)=(2x-4)(x+1)*Q(x)+(ax+b)
Put x=2, -3=2a+b..
Read More: https://www.quora.com/When-a-polynomial-P-x-is-divided-by-2x-4-the-remainder-is-3-If-P-1-6-what-is-the-remainder-when-P-x-is-divided-by-2x-4-x+1?top_ans=37814979
-----
Question: When a polynomial P(x) is divided by x^2 - 1, the remainder is 3x-1. What is the remainder when P(x) is divided by x - 1?

Answer from Aditya Krishna Das

P(x)=q(x)*(x^2–1)+(3x-1)………(1)

The remainder when P(x) is divided by (x-1) is P(1).

Therefore,

P(1)=q(1)(1^2–1)+(3*1–1)

P(1)=2

The answer is 2.
Read More: https://www.quora.com/When-a-polynomial-P-x-is-divided-by-x-2-1-the-remainder-is-3x-1-What-is-the-remainder-when-P-x-is-divided-by-x-1?top_ans=54002514
-----

-----
To control which emails we send you, visit: https://www.quora.com/qemail/track_click?aoid&aoty=14&aty=4&cp=0&ct=1596795559480774&et=130&id=fda5c649343c4f27ba72506742b6091a&source&src=1&st=1596795559500028&stories=1_bx5LntIJqPh%7C1_Ll8n5vYRBoQ%7C1_IY48PBLe3PP%7C1_mSLGQ5FvMSm%7C1_j6bv80RXzi%7C1_MD19LQLNTuS%7C1_dNYFodCjeSx%7C1_miQuNWMJvbU%7C1_8iXWhAeGfIq%7C1_9j2d3SWbE2a&ty&ty_data&uid=b6jAo0lU8Fa&v=0

To unsubscribe from this type of email, visit: https://www.quora.com/email_optout/qemail_unsubscribe?email_track_id=fda5c649343c4f27ba72506742b6091a&t=1596795559941747&token=c20d8e6a13bfa75781a5eddd3c4614762f2942011507a16e218c934cb0f5453f943fb65dadbf506892e23e16201586b103dd68d69daee885cb8c94772fc317a3&type=130&uid=1238123655