When x3+ cx + 4 is divided by (x + 2), the remainder is 4. Find the value of c.
1 answer:
Answer:
-4
Step-by-step explanation:
x³ + cx + 4 divided by x + 2 has a remainder of 4, so:
(x³ + cx + 4) / (x + 2) = ax² + bx + d + 4 / (x + 2)
Multiply both sides by x + 2:
x³ + cx + 4 = (ax² + bx + d) (x + 2) + 4
Distribute:
x³ + cx + 4 = ax²(x + 2) + bx(x + 2) + d(x + 2) + 4
x³ + cx + 4 = ax³ + 2ax² + bx² + 2bx + dx + 2d + 4
x³ + cx + 4 = ax³ + (2a + b)x² + (2b + d)x + 2d + 4
Match the coefficients.
a = 1
2a + b = 0
2b + d = c
2d + 4 = 4
Solving, a = 1, b = -2, and d = 0. So c = -4.
We can also solve this using long division (see picture).
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<h2> 22.2</h2>Step-by-step explanation:
Step one
given the coordinates
ABCD with vertices A(-2,-2), B(-1,3), C(5, 3), and D(4, -2)
AB=(-2,-2),(-1,3)
BC=(-1,3), (5, 3)
CD=(5, 3),(4, -2)
DA=(4, -2),(-2,-2)
The distance between points AB=
The distance between points BC=
The distance between points CD
The distance between points DA
Hence the perimeter = 5.1+6+5.1+6
= 22.2