Question

On dividing p(x) by x-3, the remainder is -2. Then the value of a is p(x) = x^2−ax+10

No need to explain just give the answer.​

Answer 1

$\sf{\large{\pink{\underline{Given:-}}}}$

• p(x) = x² - ax + 10
• p(x) is divided by x - 3
• Remainder is -2

$\sf{\large{\blue{\underline{To\:find:-}}}}$

Value of a

$\sf{\large{\orange{\underline{Answer:-}}}}$

Division algorithm:

Dividend = Divisor * Quotient + Remainder

p(x) = q(x) * g(x) + r

So apply division algorithm here:

p(x) = (x - 3) * g(x) + r

at x = 3

p(3) = (3 - 3) * g(x) + r

p(3) = 0 * g(x) + r

p(3) = r

And we know p(x) = x² - ax + 10

We also know r = - 2

So,

at x = 3

p(3) = 3² - 3a + 10 = r = -2

p(3) = 9 - 3a + 10 = -2

p(3) = 19 - 3a = -2

p(3) = - 3a = - 21

p(3) = 3a = 21

p(3) = a = 21/3

p(3) = a = 7

$\huge{\red{\boxed{\boxed{a\:=\:7}}}}$