#### Question

What should be subtracted from 3x^{3} – 8x^{2} + 4x – 3, so that the resulting expression has x + 2 as a factor?

#### Solution

Let the required number be k.

Let f(x) = 3x^{3} – 8x^{2} + 4x – 3 – k

According to the given information,

f (-2) = 0

3(-2)^{3} – 8(-2)^{2} + 4(-2) – 3 – k = 0

-24 – 32 – 8 – 3 – k = 0

-67 – k = 0

k = -67

Thus, the required number is -67.

Is there an error in this question or solution?

Solution What Should Be Subtracted from 3x3 – 8x2 + 4x – 3, So that the Resulting Expression Has X + 2 as a Factor? Concept: Factor Theorem.