Question

If p(x) = x^ - 60 x + 18 the divisor of its x + 4, then find the remainder.​

Answer 1

Answer:

The remainder for the given division is 274 .

Given:

• $p(x) = x^{2} - 60 x + 18$

• $p(x)$ is divided by $(x+4)$

To find:

• The remainder after division of p(x) by (x+4) .

Concepts Used:

• Remainder Theorem -
• If an expression p(x) is divided by (x-a) -
• the remainder is given by p(a) where -
• p(a) is the expression with 'x' replaced with the value of 'a' at all occurrences.

Comparing (x-a) and (x+4) -

• x-a = x+4
• x-a = x - (-4)  (x -(-4) = x + 4)
• ∴ a = -4  

Now,

• Applying remainder theorem, we get,

=> p(a) = remainder

=> p( -4 ) = remainder

=> p( -4) = $-4^{2} - 60 * -4 + 18$

=> p(-4) = 16 + 240 + 18

=> p(-4) = 274

=> p(-4) = p(a) = remainder = 274

=> remainder = 274