Just divide the top of the fraction by the bottom, and read off the answer!
<span> divide a polynomial p(x) by (x-3). Add and subtract the multiple of (x-3) that has the same highest-power term as p(x), then simplify to get a smaller-degree polynomial r(x) plus multiple of (x-3). </span>
<span>The multiple of (x-3) that has x^4 as its leading term is x^3(x-3) = x^4 - 3x^3. So write: </span>
<span>x^4 + 7 = x^4 + 7 + x^3(x - 3) - x^3(x - 3) </span>
<span>= x^4 + 7 + x^3(x - 3) - x^4 + 3x^3 </span>
<span>= x^3(x - 3) + 3x^3 + 7 </span>
<span>That makes r(x) = 3x^3 + 7. Do the same thing to reduce r(x) by adding/subtracting 3x^2(x - 3) = 3x^3 - 9x^2: </span>
<span>= x^3(x - 3) + 3x^3 + 7 + 3x^2(x - 3) - (3x^3 - 9x^2) </span>
<span>= x^3(x - 3) + 3x^2(x - 3) + 9x^2 + 7 </span>
<span>Again to reduce 9x^2 + 7: </span>
<span>= x^3(x - 3) + 3x^2(x - 3) + 9x^2 + 7 + 9x(x - 3) - (9x^2 - 27x) </span>
<span>= x^3(x - 3) + 3x^2(x - 3) + 9x(x - 3) + 27x + 7 </span>
<span>And finally write 27x + 7 as 27(x - 3) + 88; </span>
<span>x^4 + 7 = x^3(x - 3) + 3x^2(x - 3) + 9x(x - 3) + 27(x - 3) + 88 </span>
<span>Factor out (x - 3) in all but the +88 term: </span>
<span>x^4 + 7 = (x - 3)(x^3 + 3x^2 + 9x + 27) + 88 </span>
<span>That means that: </span>
<span>(x^4 + 7) / (x - 3) = x^3 + 3x^2 + 9x + 27 with a remainder of 88</span>
Y-5 = 6x-24 ad 5 to both sides to get y alone
y=6x-19 the slope of the line is 6 and the y-intercept is -19 or (0,-19)
m = 6 or 6/1
2x - 12y = B
(-5,-8)...x = -5 and y = -8
now we sub and solve for B
2(-5) - 12(-8) = B
-10 + 96 = B
86 = B <==
