Question

The polynomial p(x) = x⁴ - 2x³ + 3x² - ax + 3a - 7 when divided by x + 1 leaves the
remainder 19. Find the value of a. Also, find the remainder when p(x) is divided by x+2.​
please help me

Answer 1

Answer:

step 1 take x=-2 as X+1 has been divided

Answer 2

Answer:

x+1=0

Or, x=-1

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

p(-1)= 19

Or, (-1)^4 - 2.(-1)^3+3(-1)^2-a.(-1) +3a -7 = 19

Or, 1+2+3+a+3a-7=19

Or, 4a-1 =19

Or, 4a =20

Or, a = 5.

If p(x) is divided by x+2

Here, x+2 = 0

Or, x=-2

Now, f(-2) = (-2)4 - 2(-2)3 + 3(-2)2 -a(-2) +3a-7

= -8+12-12+2a+3a-7

= 5a-15

This is remainder.