If p(x) ax³ + bx-c is divisible by g(x) x²+ bx+c, then find the value of ab?

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Note: I have put signs according to me as it was not Clear in ur question plzz check ur question once........!!!

If f(x) is divisible by g(x), then the 'remainder' of a long division would equal zero.

The remainder after dividing f(x) by g(x) is

[(ab² - ac + b)x + c(ab - 1)]/(x² + bx + c)

For the numerator to equal zero, both terms in parentheses have to be equal to zero

ab² - ac + b = 0 and ab - 1 = 0

ab = 1.......(i)
or a=1/b

ab² - ac + b = 0

ac = ab² + b

ab = 1...........(from (i))

ac = b + b = 2b c=2b/a c = 2b/(1/b).......substituting value of a or c = 2b2...........

Answer

Answer

Can anyone explain why ab² -ac+b=0 and ab-1=0

Answer

I think your question is wrong .
please type your question correctly

Answer

Explanation:

Given:
p(x) = ax³ + bx - c
g(x) = x² + bx + c

Condition:
p(x) is divisible by g(x)

Expressing the Division:
When p(x) is divided by g(x), the remainder should be zero. Therefore,
ax³ + bx - c = (x² + bx + c) * q(x) + 0
where q(x) is the quotient of the division.

Expanding the Expression:
ax³ + bx - c = x²q(x) + bqx + cq(x)

Comparing Coefficients:
1. Coefficient of x³:
a = q
2. Coefficient of x:
b = bq + c
3. Constant term:
- c = cq

Substituting the Values:
1. q = a
2. b = ab + c
3. -c = ac

Solving for ab:
Substitute q = a into the second equation:
b = ab + c
b = a*b + c
Substitute -c = ac into the third equation:
-c = ac
-c = a*(-c)
Comparing the above two equations:
a*b + c = a*(-c)
a*b + c = -a*c
a*b = -a*c - c
a*b = -c(1 + a)

Result:
ab = -c(1 + a)

Answer

It is right question pls u check

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