Factor the expression 2x^3-3x^2-5x
1 answer:
You might be interested in
Answer:
The quotient of this division is . The remainder here would be
.
Step-by-step explanation:
The numerator is a polynomial about
with degree
.
The divisor is a polynomial, also about
, but with degree
.
By the division algorithm, the quotient should be of degree , while the remainder shall be of degree
(i.e., the remainder would be a constant.) Let the quotient be
with coefficients
,
, and
.
.
Start by finding the first coefficient of the quotient.
The degree-three term on the left-hand side is . On the right-hand side, that would be
. Hence
.
Now, given that , rewrite the right-hand side:
.
Hence:
Subtract from both sides of the equation:
.
The term with a degree of two on the left-hand side has coefficient . Since the only term on the right hand side with degree two would have coefficient
,
.
Again, rewrite the right-hand side:
.
Subtract from both sides of the equation:
.
By the same logic, .
Hence the quotient would be .
Answer: D) Reflect over x-axis
=======================================================
Explanation:
When we do this type of reflection, a point like (1,2) moves to (1,-2).
As another example, something like (5,-7) moves to (5,7)
The x coordinate stays the same but the y coordinate flips in sign from positive to negative, or vice versa.
We can say that as a general way to represent the transformation. Note how y = f(x), so when we make f(x) negative, then we're really making y negative.
If we apply this transformation to every point on f(x), then it will flip the f(x) curve over the horizontal x axis.
There's an example below in the graph. The point A(2,8) moves to B(2,-8) after applying that reflection rule.
