Question

if the polynomial 2x³+ax²+3x-5 and x³+x²-4x+a leave the same remainder when divided by (x-2).Find a​

Answer 1

Answer:

    a    = - 13/3

Step-by-step explanation:

2x³ + ax² + 3x -5 and x³ + x² - 4x + a

To divide the first polynomial with (x-2)

f (2) = 2(2)³ + a(2)² + 3(2) -5

      = 16 + 4a + 6 - 5

      = 17 + 4a

To divide the second polynomial with (x-2)

f (2) = (2)³ + (2)² - 4(2) + a

      = 8 + 4 - 8 + a

      = 4 + a

Because both polynomials leave the same remainder, we can assume these are equal :

17 + 4a = 4 + a

Now it's simply do the math

17 - 4 = a - 4a

  13   = - 3a

  3a   = - 13

    a    = - 13/3

Hope this helped.

I'm not very good at maths. I always tend to have careless errors when solving problems. But I hope you get the principle of this.