The polynomial x³ + ax² + bx + 10 is exactly divisible by (x − 2) and leaves the remainder 6 when divided by (x + 1). The value of a + b is:

Question

Accepted Answer

−5. p(2) = 8 + 4a + 2b + 10 = 0 gives 2a + b = −9, and p(−1) = −1 + a − b + 10 = 6 gives a − b = −3. Adding, 3a = −12, so a = −4 and b = −1, hence a + b = −5. Check with x³ − 4x² − x + 10: p(2) = 0 and p(−1) = 6.

The polynomial $x^{3} + a x^{2} + b x + 10$ is exactly divisible by $(x - 2)$ and leaves the remainder 6 when divided by $(x + 1)$ . The value of $a + b$ is:

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The polynomial x3+ax2+bx+10 is exactly divisible by (x−2) and leaves the remainder 6 when divided by (x+1). The value of a+b is:

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Algebra practice

The polynomial $x^{3} + a x^{2} + b x + 10$ is exactly divisible by $(x - 2)$ and leaves the remainder 6 when divided by $(x + 1)$ . The value of $a + b$ is: