Question

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 ​

Answer 1

Answer:

62

Step-by-step explanation:

Zero of g(x)

x-3=0

x=3

put X =3 in p(x)

p(3)=

${3}^{3} - 3 ({3}^{2} ) + 4(3) + 50$

$27 - 27 + 12 + 50$

$= 62$

answer is 62.(By remainder theorem)

Answer 2

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.