Question

please solve the 28th question

Answer 1

Let p(x) = x⁴ - 2x³ + 3x²- 9x - 7 + 3b
Let g(x) = ( x + 1 )
Zero of ( x + 1 )
x + 1 = 0  
x = -1

Now,  p(-1) = (-1)⁴ = 2(-1)³ + 3(-1)² - 9(-1) + 3b
                  = 1- (-2) + 3 - (-9) -7 + 3b
                  = 1+2+3+9-7+3b
                  = 15 - 7 + 3b
                  =  8 + 3b

Remainder given = 29
So,   8 + 3b = 29
         3b = 29 - 8
         3b = 21`
           b = 21/3   
           b = 7
Hence, the value of b is 7.

Let f(x) = (x - 2)
Zero of f(x)
x - 2 = 0
x = 2

Now,  p(2) = (2)⁴ - 2(2)³ + 3(2)² - ( 9X2 ) - 7 + ( 3X 7 )
           p(2) = 16 = (2X8) + (3X4) - 18 - 7 + 21
           p(2) =16 - 16 + 12 - 8 - 7 + 21
           p(2) = 0 + (-6) + 14
           p(2) = 0+8
           p(2) = 8
Hence, when p(x) is divided by (x-2), the remainder we get is 8