Spencer is asked to factor the polynomial 256x^4y^2−y^2 completely over the integers. His work is shown below.

256x^4 y^2−y^2=y^2(256x^4−1)
y2(256x^4−1)=y^2(16x^2−1)(16x^2+1)< br />
Did Spencer factor the polynomial completely over the integers? Why or why not?

a. Spencer did factor the polynomial completely; he identified the GCF and applied the difference of squares method.
b. Spencer did not factor the polynomial completely; 16x^2−1 can be factored over the integers.
c. Spencer did not factor the polynomial completely; 16x^2+1 can be factored over the integers.
d. Spencer did factor the polynomial completely; he identified the GCF and applied the difference of cubes method.

Option B, Spencer did not factor the polynomial completely; 16x^2−1 can be factored over the integers.

Step-by-step explanation:

Step 1:  Factor

256x^4y^2−y^2

y^2(256x^4 - 1)

y^2(16x^2 - 1)(16x^2 + 1)

y^2(4x + 1)(4x - 1)(16x^2 + 1)

 Option B, Spencer did not factor the polynomial completely; 16x^2−1 can be factored over the integers.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).