Question

the polynomial 2 x cube + x square minus A X + 2 and 2 x cube minus 3 x square - 3 x + a divided by x minus two leave the same remainder find the value of a​

Answer 1

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Answer 2

Answer:

Value of a is 8.

Step-by-step explanation:

let, p(x) = 2x³ + x² - ax + 2

g(x) = 2x³ - 3x² - 3x + a

To find : Value of a when p(x) & g(x) divided by x - 2 leaves the same remainder.

We use remainder theorem,

Remainder Theorem: When a polynomial p(x) is divided by a linear polynomial of the form x - a then the remainder of the division is given by p(a).

So, Remainder when p(x)  divided by x - 2

remainder we get , p(2) = 2(2)³ + (2)² - a(2) + 2 = 2 × 8 + 4 - 2a + 2 = 22 - 2a

Remainder when g(x)is divided by x - 2

g(2) = 2(2)³ - 3(2)² - 3(2) + a = 2 × 8 - 3 × 4 - 6 + a = a - 2

p(2) = g(2)

22 - 2a = a - 2

3a = 24

a = 8

Therefore, Value of a is 8.