Interesting problem!
P(x)=x^3+3*x^2-2Ax+3
is a third degree polynomial.
The divisor,
D(x)=x^2+1
is a second degree polynomial.
We are given
P(x)/D(x) has a remainder of R(x)= -5x, note that the constant term of the remainder is zero.
The fact that the the quotient Q(x) is a linear expression, and constant term of R(x) equals zero allows us to deduce that the quotient equals Q(x)=x^3/x^2 + 3/1 = x+1, i.e. the sum of the quotients of the leading coefficient divided by that of D(x), or x^2, and the constant term divided by the constant term of D(x), or 1.
Using Q(x)=x+1, the product of the divisor D(x) and the quotient Q(x) added to the remainder R(x) should be equal to the original polynomial P(x), i.e.
P(x) = D(x)*Q(x)+R(x)
=(x^2+1)(x+3)-5x
=x^3+3x^2-4x+3
(To check, divide (using synthetic division) P(x) by D(x) and we should get R(x))
Now solve for A
-2A = -4
A = (-4)/(-2) = 2
Answer:
9
Step-by-step explanation:
When the numbers are relatively close together, it is often useful to see if their difference is a factor:
36 -27 = 9
Checking ...
36 = 4×9
27 = 3×9
9 is the greatest common factor of 27 and 36.
_____
<em>How to find the greatest common factor (GCF)</em>
The Euclidean algorithm has you find the remainder from division of the larger by the smaller. If that remainder is zero, the smaller is the GCF. If the remainder is nonzero, it replaces the larger number and the process is repeated. When the larger number is less than twice the smaller, the remainder is their difference.
A ratio is a comparison of two values. In this case, there are 6 boys to every 15 girls. So, this means the ratio is 6:15.
Hopefully, this helps!
The angle measure of ∠SRV in the parallelogram is 48°
A parallelogram is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel to each other. Opposite angles of a parallelogram are also congruent.
∠TUV + ∠TVU + ∠VTU = 180° (sum of angles in a triangle)
∠VTU + 78 + 54 = 180
∠VTU = 48°
∠SRV = ∠VTU ()
∠SRV = 48°
The angle measure of ∠SRV in the parallelogram is 48°
Find out more on parallelogram at: brainly.com/question/970600
Answer:
8Parallel lines always have the same slope.
[I attached a picture that might help show you]
The lines do
NOT Intersect.