Question

f(x)=2x^3-7x^2+x+6,g(x)=2x-4 find quotient and remainder when p(x) is divided by g(x)​

Answer 1

Answer:

f(x) =2x³-7x²+x+6, g(x) = 2x-4

Answer 2

$\texttt{\textsf{\large{\underline{Solution}:}}}$

Given,

→ f(x) = 2x³ - 7x² + x + 6

→ g(x) = 2x - 4

We have to find out the remainder when f(x) is divided by g(x)

So,

→ 2x - 4 = 0

→ x = 4/2

→ x = 2

Therefore, remainder = f(2) [By Remainder Theorem]

So, remainder will be,

= f(2)

= 2 × (2)³ - 7 × (2)² + 2 + 6

= 16 + 28 + 8

= 16 + 36

= 52

★ So, the remainder when f(x) is divided by g(x) is 52.

$\texttt{\textsf{\large{\underline{Answer}:}}}$

• Remainder = 52.

$\texttt{\textsf{\large{\underline{Concept}:}}}$

• Remainder Theorem: If a polynomial f(x) is divided by (x - a), then remainder = f(a).
• Cor 1: If it is divided by (x + a), then remainder = f(-a)
• Cor 2: If it is divided by (ax + b), the remainder = f(-b/a).