Can someOne please help with the correct answer to problem including steps

Possible rational roots: ±1,±3,±5,±15.

Please correct me If I am wrong

Step-by-step explanation:

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient (coefficient of the constant term) is 15.

Find its factors (with plus and minus): ±1,±3,±5,±15. These are the possible values for p.

he leading coefficient (coefficient of the term with the highest degree) is 1.

Find its factors (with plus and minus): ±1. These are the possible values for q.

Find all possible values of pq: ±11,±31,±51,±151.

Simplify and remove duplicates (if any), these are possible rational roots: ±1,±3,±5,±15.

Next, check the possible roots: if a is a root of the polynomial P(x), the remainder from the division of P(x) by x−a should equal 0.

Check 1: divide x3+3x2+6x+15 by x−1.The quotient is x2+4x+10 and the remainder is 25

Check −1: divide x3+3x2+6x+15 by x+1.The quotient is x2+2x+4 and the remainder is 11

Check 3: divide x3+3x2+6x+15 by x−3.The quotient is x2+6x+24 and the remainder is 87

Check −3: divide x3+3x2+6x+15 by x+3.The quotient is x2+6 and the remainder is −3

Check 5: divide x3+3x2+6x+15 by x−5.The quotient is x2+8x+46 and the remainder is 245

Check −5: divide x3+3x2+6x+15 by x+5.The quotient is x2−2x+16 and the remainder is −65

Check 15: divide x3+3x2+6x+15 by x−15.The quotient is x2+18x+276 and the remainder is 4155

Check −15: divide x3+3x2+6x+15 by x+15.The quotient is x2−12x+186 and the remainder is −2775

Possible rational roots: ±1,±3,±5,±15.

Please correct me if I am wrong I did my best its been so long I haven't done rational roots

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.