You need you algebra basics part 1!

Algebra Level 3

When the polynomial $x^3 + 2x^2 - 5ax - 7$ is divided by $x + 1$ , the remainder is $R1$ . When the polynomial $x^3 + ax^2- 12x + 6$ is divided by $x - 2$ , the remainder is $R2.$ If $2R1 + R2 = 6$ , find the value of a.

The answer is 2.

1 solution

Brian Charlesworth
Jul 2, 2014

Let the first polynomial be p(x) and the second q(x).

Then p(x) = (x + 1) * r(x) + R1 and q(x) = (x - 2) * u(x) + R2 for some polynomials r(x) and u(x). Next, we have p(-1) = 5a - 6 = R1 and q(2) = 4a - 10 = R2.

Solving these simultaneously, we find that 4 * R1 - 5 * R2 = 26. We are (in effect) given that 4 * R1 + 2 * R2 = 12, so 7 * R2 = -14.

Thus R2 = -2, and so 4a = R2 + 10 = 8, giving us a = $\boxed{2}$ .

You need you algebra basics part 1!

The answer is 2.

1 solution

0 pending reports