Question

if the polynomial 2x^3+3x^2-a and ax^3-5x+2 leave the same remainder when each is divided by (x-2) , find the value of a

Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

If the polynomial 2x³ + 3x² - a & ax³ - 5x + 2 leave the same remainder when each is divided by (x-2) .

$\underline{\bf{Explanation\::}}$

We have factor of f(x) = (x-2) & factor f(x) = 0.

→ f(x) = x - 2 = 0

→ f(x)  = 2

A/q

f(x) = ax³ - 5x + 2

g(x) = 2x³ + 3x² - a

$\mapsto\tt{(Remainder_1) = (remainder_2)}$

$\mapsto\tt{f(x) = g(x)}$

$\mapsto\tt{f(2) = g(2)}$

$\mapsto\tt{ax^{3} - 5x + 2 = 2x^{3} + 3x^{2} -a}$

$\mapsto\tt{a(2)^{3} - 5(2) + 2 = 2(2)^{3} + 3(2)^{2} -a}$

$\mapsto\tt{a8 - 10 + 2 = 2\times 8 + 3\times 4-a}$

$\mapsto\tt{8a -8 = 16 + 12-a}$

$\mapsto\tt{8a -8 = 28-a}$

$\mapsto\tt{8a +a= 28+8}$

$\mapsto\tt{ 9a= 36}$

$\mapsto\tt{ a= \cancel{36/9}}$

$\mapsto\bf{a=4}$

Thus;

The value of a will be 4 .