These are Computer Science questions not Math. So please answer them according to the computer science. Answer all of them and complete step by step

Please answer them complete. show all the steps $.$

$1.$ Find the following summation:

${37}^2+{39}^2+{41}^2+.............+{157}^2.$

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$2.$ Given a polynomial with the following formula

$Q(x)=b_2{x}^2+b_5{x}^5+b_8{x}^8+$ cdots $+b_{322}{x}^{372},$

how many additions do we need if we use the brute force method to calculate it$?$

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$3.$ We are given a polynomial with the following structure

$P(x)=(a_0+a_{1}x)(b_0+b_{1}x)(c_0+c_{1}x),$

where $a_0,a_1,b_0,b_1,c_0,$ and $c_1$ are arbitrarily given coefficients. What is the minimum

number of multiplications do you need to find the value of $P(x)$ for any value of $x?$

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$4.$ Find the following summation:

$(5+6)+(10+11)+(15+16)+.......+(500+501)$

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We are given a polynomial with the following structure

$5.P(x)=(a_0+a_{1}x{)}^4(b_0+b_{1}x{)}^4(c_0+c_{1}x{)}^4,$

where $a_0,a_1,b_0,b_1,c_0,$ and $c_1$ are arbitrarily given coefficients. What is the minimum

number of multiplications do you need to find the value of $P(x)$ for any value of $x?$

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$6.$ Given a $4$ element array, say $\{x_1,x_2,x_3,x_4\},$ with $x^{45}x\{x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8,x_9,x_{10},x_{11}\}{x}_6{x}_1,$ how many more

comparisons do you need to find the $2nd$ largest element for the worst case?

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$7.$ To evaluate a monomial $x^{45}$ for a given value $x,$ what is the minimum number of

multiplications that you need?

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$8.$ Given $11$ elements: $\{x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8,x_9,x_{10},x_{11}\},$ it is known that $x_6$ is

not in place. What is the maximum number of inversions in this array?

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$9.$ Given a $100-$ element array, we want to find an element that is neither the maximum nor minimum. What is the minimum number of comparisons you

need to solve this problem for the worst case?

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