By remainder theorem, find the remainder
when p(x) is divided by g(x)
ii. p(x) = x3 - 3x² + 4x+50, g(x) =x-3
Answers
Answer:
62
Step-by-step explanation:
Zero of g(x)
x-3=0
x=3
put X =3 in p(x)
p(3)=
answer is 62.(By remainder theorem)
Question: Using the Remainder Theorem, find the remainder when p(x) is divided by g(x), where p(x) = x³ - 3x² + 4x + 50 and g(x) = x - 3
Answer:
62
Step-by-step explanation:
We've been given that,
p(x) = x³ - 3x² + 4x + 50
g(x) = x - 3
We've been asked to use the "Remainder Theorem" to find out the remainder obtained when p(x) is divided by g(x).
According to the Remainder theorem, when a polynomial p(x) is divided by a binomial g(x), where g(x) = (x - a), the remainder obtained will be equal to p(a).
Using the Remainder Theorem, let's divide p(x) by g(x). [Kindly check the attachment]
Steps:
- x³ is the first term in p(x), in order to obtain x³, we'll have to multiply g(x) with x². Doing so will give us x³ - 3x²
- After changing the signs before subtracting, we get -x³ + 3x². On subtracting x³ - 3x² and - x³ + 3x², we get 0
- Now we'll bring down the next two terms of p(x), i.e, 4x + 50. In order to obtain 4x, we'll have to multiply g(x) with 4. Doing so will give us 4x - 12
- After changing the signs before subtracting, we get -4x + 12. On subtracting 4x + 50 and -4x + 12, we get 62.
Therefore, 62 is the remainder, obtained with the help of the Remainder theorem.
Verification of the answer using the factor theorem:
We know that, p(x) = x³ - 3x² + 4x + 50
It's given that g(x) = (x - 3), implying that x = 3.
p(x) = x³ - 3x² + 4x + 50
On substituting 3 in x's place we get,
⇒ p(3) = (3)³ - 3(3)² + 4(3) + 50
⇒ p(3) = 27 - 3(9) + 12 + 50
⇒ p(3) = 27 - 27 + 12 + 50
⇒ p(3) = 12 + 50
⇒ p(3) = 62
Hence solved.