Answer:

Explanation:
Given

x is a factor
Required
Solve for k
x is a factor means that the polynomial can be divided successfully by x.
In other words, x is a zero of the polynomial.
i.e.
and 
Substitute 0 for x in P(x)





Substitute 0 for P(x)

Collect Like Terms

Divide both sides by 5

The rule used to translate the image is
.
In this question we are going to speak of point translations. Vectorially speaking, a translation between two points is defined by this expression:
(1)
Where:
- Original point.
- Translation vector.
- Translated point.
If we know that
and
, then the translation vector is:



Therefore, the rule used to translate the image is
.
We kindly invite to see this question on translations: brainly.com/question/17485121
Pythagorean theorem should be used to determine the length of any of the three sides of a right-angled triangle.
<h3>What is Pythagorean Theorem?</h3>
Pythagorean theorem can be defined as a fundamental mathematical equation in Euclidean geometry and it can be used to determine the length of any of the three (3) sides of a right-angled triangle.
Mathematically, Pythagorean's Theorem is given by this formula:
c² = a² + b²
<u>Where:</u>
<u>For example:</u>
c² = 3² + 4²
c² = 9 + 16
c² = 25
c = √25
c = 5 units.
Read more on Pythagorean Theorem here: brainly.com/question/16176867