Answer:
899.5
Step-by-step explanation:
Answer:
a = 8
Step-by-step explanation:
x-1 = 0
x = 1
let x³ + ax² -x -8 be p(x)
hence, p(1) = (1)³ + a(1)² -1 -8 = 0 (since, x-1 is a factor)
= 1 + a - 1-8
= a - 8 = 0
therefore, a = 8
Answer:
Mia would have a 55$ interest :)
Step-by-step explanation:
f(x, y) = 4x + 7y - 6
substitute x=5 and y=-5
f(5,-5) = 4(5) + 7(-5) - 6
f(5,-5) =20-35-6
= -15-6
=-21
Answer:
f(x) = (x + 1)*(4*x² - 3*x + 4) - 12
Step-by-step explanation:
We have:
f(x) = 4*x³ + x² + x - 8
We want to write this in:
f(x) = (x - k)*q(x) + r.
with k = -1
Then we want to write:
4*x³ + x² + x - 8 = (x - (-1))*q(x) + r
4*x³ + x² + x - 8 = (x + 1)*q(x) + r
Because f(x) is polynomial of degree 3, we know that q(x) must be a polynomial of degree 2.
then:
q(x) = a*x² + b*x + c
Then:
4*x³ + x² + x - 8 = (x + 1)*(a*x² + b*x + c) + r
4*x³ + x² + x - 8 = a*x³ + b*x² + c*x + a*x² + b*x + c + r
if we take common factors in the right side we get:
4*x³ + x² + x - 8 = a*x³ + (b + a)*x² + (c + b)*x + (c + r)
Now, we must have:
4*x³ = a*x³
then:
4 = a
We also must have:
x² = (b + a)*x²
1 = (b + 4)
1 - 4 = b
-3 = b
We also must have:
x = (c + b)*x
1 = (c + (-3))
1 + 3 = c
4 = c
And finally:
- 8 = (c + r)
-8 = 4 + r
-8 - 4 = r
-12 = r
Then:
f(x) = (x + 1)*(4*x² - 3*x + 4) - 12
