It could be 42:112, 63:168, or 84:224 :)
35x-37 because 3x×15=35 and 3×-17=-37.
First I will present the polynomial itself: it is
5x^3 - 22x^2 - 3x - 53.
Let's show that when this poly. is divided by (x-5), the quotient is 5x^2 + 3x + 12 and the remainder is 7. Use synthetic division here. Let the divisor be 5 (this comes from the factor (x-5). Then:
__________________
5 / 5 -22 -3 -53
25 15 60
----------------------------
5 3 12 7 where 5 3 12 are the coeff. of the quotient and 7
is the remainder.
Now work backwards. Multiply (x-5) and (5x^2 + 3x + 12) together. We get
5x^3 + 3x^2 + 12 x - 25x^2 - 15x - 60, or
5x^3 - 22x^2 - 3x - 60. Now add the remainder (7) to -60; the result will be -53.
So the poly in question is 5x^3 - 22x^2 - 3x - 53.
We have
<em>v</em> = (-7, 9) - (4, 3) = (-7 - 4, 9 - 3) = (-11, 6)
which as a linear combination of the <em>i</em> and <em>j</em> unit vectors is
<em>v</em> = -11<em>i</em> + 6<em>j</em>