Question

please answer,question no 14

Answer 1

Concepts used :

1) Remainder theorem

2) Factor theorem

3) Substitution of a value in a variable

4) Equation

Answer 2

$\bf \LARGE \it{Hey \: User!!}$

according to the question, when p(x) = x⁴ - 2x³+ 3x² - ax + 3a - 7 is divided by (x + 1) leaves the remainder 19.

>> x + 1 = 0
>> x = -1

therefore p(-1) = (-1)⁴ - 2(-1)³ + 3(-1)² - a(-1) + 3a - 7 = 19
>> 1 + 2 + 3 + a + 3a - 7 = 19
>> 6 + 4a - 7 = 19
>> -1 + 4a = 19
>> 4a = 19 + 1
>> 4a = 20
>> a = 20/4
>> a = 5

hence, the value of a is 5.

now, we have to find the remainder when p(x) is divided by (x + 2)

given p(x) = x⁴ - 2x³+ 3x² - ax + 3a - 7

g(x) = x + 2
therefore x = -2

on putting values :-

p(-2) = (-2)⁴ - 2(-2)³ + 3(-2)² - 5(-2) + 15 - 7
= 16 + 16 + 12 + 10 + 15 - 7
= 62

remainder is 62 when p(x) is divided by (x + 2).

$\bf \LARGE \it{Cheers!!!}$