On dividing a polynomial p(x) by x2 - 4, quotient and remainder
found to be x and 3 respectively. The polynomial p(x) is
Answers
Given : a polynomial p(x) divided by x² - 4 , Quotient = x & remainder = 3
To find : Polynomial p(x)
Solution:
As we know that
p(x) = q(x) . g(x) + r(x)
where
q(x) = x
g(x) = x² - 4
r(x) = 3
Substituting all known values
p(x) = x . (x² - 4) + 3
=> p(x) = x³ - 4x + 3
Polynomial p(x) = x³ - 4x + 3 which on dividing by x² - 4 give Quotient x & remainder = 3
Learn more:
on dividing x3-3x2+x+2 by a polynomial g(x),the quotient and ...
https://brainly.in/question/3135153
Divide 9x^3+3x^2-5x+7 by (3x-1) write the quotient and remainder ...
https://brainly.in/question/6190809
Divide the polynomial (6x³ + 11x² - 10x - 7) by the binomial (2x + 1 ...
https://brainly.in/question/4743553
Given: when p(x) / (x² - 4) we get remainder as 3 and quotient as x .
To find: polynomial p(x)
Solution:
- To find the polynomial, we have the formula which states that p(x) can be found out by multiplication of quotient and dividend and then adding it to the remainder.
- Formula for p(x) is:
p(x) = ( q(x) x g(x) ) + r(x)
- Here, q(x) = x, g(x) = x² - 4 and r(x) = 3
- So to find p(x) lets substitute all the values, we get
p(x) =( x × (x² - 4) )+ 3
p(x) =( x³ - 4x )+ 3
Answer:
So the polynomial obtained is p(x) = x³ - 4x + 3