MHB What is the Polynomial P(x) Given a Specific Quotient and Remainder?

  • Thread starter Thread starter missnerdist
  • Start date Start date
  • Tags Tags
    Polynomial
AI Thread Summary
To find the polynomial P(x), use the formula P = AQ + R, where A is the divisor (2x + 1), Q is the quotient (x^2 - x + 2), and R is the remainder (5). Substitute these values into the equation to get P(x) = (2x + 1)(x^2 - x + 2) + 5. Expand the product and simplify to derive the complete polynomial. The final result will provide the expression for P(x). This method effectively utilizes the relationship between polynomials, quotients, and remainders.
missnerdist
Messages
6
Reaction score
0
I can't seem to figure this out.

When a polynomial P(x) is divided by (2x+1) the quotient is x^2-x+2 and the remainder is 5. What is P(x)?
 
Mathematics news on Phys.org
A hint: When 7 is divided by 3 the quotient is 2 and the remainder is 1.
 
If P divided by A has quotient Q with remainder R, P/A= Q+ R/A, then P= AQ+ R. You are told what A, Q, and R are. Just do the algebra to find P.
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Similar threads

B About a definition: What is the number of terms of a polynomial P(x)?
Replies
48
Views
3K
MHB Find Polynomial Given Remainder After Division
Replies
6
Views
2K
B Intermediate Value Theorem and Synthetic Division
Replies
4
Views
2K
MHB Solve Polynomial Division: -5a + 4b = x^2+1 Rem -A-2
Replies
1
Views
1K
I A doubt about the multiplicity of polynomials in two variables
Replies
8
Views
2K
MHB Proving $x-1$ is a Factor of $P(x)$ with Polynomials
Replies
1
Views
1K
MHB [ASK] polynomial f(x) divided by (x - 1)
Replies
2
Views
2K
Does Division of Polynomials Follow a Pattern of Degree Decrease?
Replies
5
Views
2K
MHB Prove Polynomial Remainder: -2x+5 When Divided by (x-1)(x-2)
Replies
4
Views
2K
MHB Prove Root of Polynomial $P(x)=x^{13}+x^7-x-1$ Has 1 Positive Zero
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top