Question
What number should be subtracted from x3−4x2−8x+11 to make the number divisible by (x+2)?
The correct answer is
3
Step-by-Step Solution:
Substitute x = -2 into the polynomial:
The polynomial is: f(x) = x³ - 4x² - 8x + 11
Substituting x = -2 into the polynomial:
f(-2) = (-2)³ - 4(-2)² - 8(-2) + 11
Now, simplify:
f(-2) = -8 - 4(4) + 16 + 11
Result:
f(-2) = -8 - 16 + 16 + 11 = 3
Interpret the result:
The remainder when x³ - 4x² - 8x + 11 is divided by (x + 2) is 3. To make the number divisible by (x + 2), we need to subtract the remainder (3) from the polynomial.
Conclusion:
The number that should be subtracted is 3.
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Important Questions from Quadratic equation
- Find the value of K if the quadratic equations $2x^2 + Kx + 8 = 0$ and $3x^2 + 4x + 12 = 0$ have both roots common.
- If sum and product of the roots of a quadratic equation are $(4-3\sqrt{2})$ and -28, respectively, then find the quadratic equation.
- If the quadratic equations $4x^2 + bx + 3 = 0$ and $8x^2 + 4x + c = 0$ have both the roots common, find the values for b and c, respectively.
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