Question

14. By remainder theorem find the
remainder when p(x) is divided by g(x).
(0) P(x)=x3 - 3x2 + 4x + 50,
q(x) = x - 3​

Answer 1

ANSWER :-

$\\ \circ \: \boxed{ \bf{Remainder = </p><p>62}}$

GIVEN :-

• p(x) = x³ - 3x² + 4x + 50
• g(x) = x - 3

TO FIND :-

• The reminder by remainder theorem.

SOLUTION :-

➠ Remainder theorem :- If p(x) is is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial x - a , Then the reminder is p(a).

★ Let x - 3 = 0

★ x = 3

★ ACCORDING TO QUESTION ★

→ p(x) = x³ - 3x² + 4x + 50

→ p(3) = (3)³ - 3 × (3)² + 4 × (3) + 50

→ 27 - 3 × 9 + 12 + 50

→ 27 - 27 + 62

→ 0 + 62

→ 62

★ Hence the remainder is 62.

ADDITIONAL INFORMATION :-

◉ Polynomial :- An algebraic expression in which the power of variable in a non negative integers.

Degree of polynomial,

◉ The highest power of variable in given polynomial is called degree.

Example :- x² + x + 4

Here the degree of polynomial is 2.

Answer 2

Step-by-step explanation:

Given that, p(x) is divided by g(x) and p(x)=x³ - 3x² + 4x + 50 & q(x) = x - 3.

We have the remainder by remainder theorem.

→ x - 3 = 0

→ x = 3

What we have to do is, simply substitute the value of x in x³ - 3x² + 4x + 50

→ 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

On solving we get,

→ p(3) = 62

Hence, the remainder is 62.