Vinculum

I don't think you can apply the quadratic formula to get question one.

1 and 2)

Using the Rational root theorem

\(\left(x-3\right)\frac{x^3+2x^2-17x+6}{x-3}\)

\(\frac{x^3+2x^2-17x+6}{x-3} = x^2+5x-2\)

\(\left(x-3\right)\left(x^2+5x-2\right)\)

3)

 \(0^3+0x^2-17\cdot \:0+6=6\)

-Vinculum

I really don't know how to do ii)

i) \(\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i\)

\(\sum _{i=0}^6\binom{6}{i}\cdot \:2^{\left(6-i\right)}\left(3x\right)^i\)

*After Plugging in Calc*

\(\frac{6!}{0!\left(6-0\right)!}\cdot \:2^6\left(3x\right)^0+\frac{6!}{1!\left(6-1\right)!}\cdot \:2^5\left(3x\right)^1+\frac{6!}{2!\left(6-2\right)!}\cdot \:2^4\left(3x\right)^2+\frac{6!}{3!\left(6-3\right)!}\cdot \:2^3\left(3x\right)^3+\frac{6!}{4!\left(6-4\right)!}\cdot \:2^2\left(3x\right)^4+\frac{6!}{5!\left(6-5\right)!}\cdot \:2^1\left(3x\right)^5+\frac{6!}{6!\left(6-6\right)!}\cdot \:2^0\left(3x\right)^6\)

\(64+576x+2160x^2+4320x^3+4860x^4+2916x^5+729x^6\)

Also please don't post any more questions:  

This is English and I don't  think it is allowed

I think you can maybe post science-related questions if it relates to math

But that is up to the mods to tell.

Uses someone who is not an expert on the issue: Authority

Identifies only two choices, one of which is not viable: False Dichotomy

One thing always leads to another: A slippery Slope

Appeals to the desire to be in the majority: popularity

The Radius of a circle inscribed in a triangle can be found using the formula Area of triangle/semi perimeter of the triangle:

We can find the semi perimeter by adding all the known sides and dividing by 2.

That would be (15+41+42)/2 = 98/2 = 49

We can find the area of the triangle using the heron's formula:

sqrt(49(49-15)(49-41)(49-42))

= 28*sqrt(119) = approx 305.44393

Substituting that in the Area of triangle/semi perimeter of the triangle formula:

28*sqrt(119)/49

= (4sqrt(17))/sqrt(7) or approx.  6.23354 units

If you want, rationalise the radical. Its up to you 

-Vinculum

(deleted)

The three emojis with sunglasses look familiar somewhere...

I wonder where they are from...

You can call me Vin