Answer:
q = - 9 and r = - 10
Step-by-step explanation:
since g(x) is divided by (x - 1) with remainder - 12, then
g(1) = 4(1)³ + q(1)² + r + 3 = - 12, that is
4 + q + r + 3 = - 12
q + r + 7 = - 12 ( subtract 7 from both sides )
q + r = - 19 → (1)
Since (x - 3) is a factor of g(x), then
g(3) = 4(3)³ + q(3)² + 3r + 3 = 0, that is
108 + 9q + 3r + 3 = 0
9q + 3r + 111 = 0 ( subtract 111 from both sides )
9q + 3r = - 111 → (2)
The 2 equations to be solved simultaneously are (1) and (2)
Multiply (1) by - 3
- 3q - 3r = 57 → (3)
Add (2) and (3) term by term to eliminate r
6q = - 54 ( divide both sides by 6 )
q = - 9
Substitute q = - 9 into (1)
- 9 + r = - 19 ( add 9 to both sides )
r = - 10
Answer:
Step-by-step explanation:
When g(x) is divide by (x -1), the remainder = -12
g(1) = -12
4 + q + r + 3 = -12
q+r + 7 = -12
Subtract 7 form both sides.
q + r +7 -7 = -12 - 7
q + r = -19 --------------------(i)
(x -3) is a factor of g(x). So, the remainder = 0
g(3) = 0
4*(3)³ + q*(3)² + r*3 + 3 = 0
4*27 + 9q + 3r + 3 = 0
108 + 9q + 3r +3 = 0
9q +3r + 111 = 0
Subtract 111 from both sides
9q + 3r = -111 -----------------(ii)
Multiply equation (i) by (-3).
(i)*(-3) -3q - 3r = +57
(ii0 9q + 3r = -111 {Now add & r will be eliminated}
6q = -54
q = -54/6
q = -9
Plugin the value of q in equation (i)
-9 + r = -19
Add 9 to both the sides
r = -19 + 9
r = -10
