Question

What should be added to x²-8, so that the
result is exactly divisible by (x + 3).
A. 1 B. - 1 C. 3 D. - 3​

Answer 1

Answer:

possibilities:

±1, ±2 and ±4

We’ll examine each of these numbers to find which ones are solutions of the equation.

f(1) = 13 − 12 – 4×1 + 4 = 0 1 is a solution

f(−1) = (−1)3 − (−1)2 – 4×(−1) + 4 = 6

f(2) = 23 − 22 – 4×2 + 4 = 0 2 is a solution

f(−2) = (−2)3 − (−2)2 – 4×(−2) + 4 = 0 −2 is a solution

We have now found three solutions so we don’t need to try 4 and −4 as a cubic equation has a maximum of three solutions.

These three numbers give us the values of a, b and c and we can factorise the equation.

x3 − x2 – 4x + 4 = (x − 1)(x − 2)(x + 2) = 0

Answer 2

Answer:

B.-1

Step-by-step explanation:

Let p(x) = x²-8

x+3= 0

x = -3

p(-3) =x²-8

= (-3)²-8

= 9-8

= 1

So, -1 should be added.