+73 6. Consider the cubic polynomial p(x) = x^3 + x^2 - 46x + 80.
(a) Using polynomial long division, write the ratio of p(x)/(x-3) in quotient-remainder form, i.e. in the form q(x) + (r)/(x-3). Evaluate p(3). How does this help you check your quotient-remainder form?
+37146
x^2+4x-34 - 22/(x-3)
x-3 | x^3+x^2-46x+80
x^3 -3x^2
_______________
4x^2-46x
4x^2-12x
_____________
-34x+80
-34x+102
__________
(remainder) -22
Basically with remainder -22/(x-3) then p(3) will equal -22
See cphill's explanation/answer here for the second part:
https://web2.0calc.com/questions/what-does-this-mean_10
+129852 Using EP's answer of R = -22
We should get the same answer by subbing 3 inito the polynomial....so...
(3)^3 + (3)^2 - 46(3) + 80 =
27 + 9 - 138 + 80 =
116 - 138 =
-22 ......Magic !!!!!
+73 Wait... I don't understand by the question: How does this help you check your quotient-remainder form?
+129852 It helps because the "r" in r / [ x - 3 ] should be the same as evaluating P(a)
So...in the case EP divided the polynomial by x - a = x - 3 got a remainder of -22
Then....we can check whether this remainder is correct by evaluating P(a) = P(3)
Note that when we evaluated P(3)....we put 3 into the polynomial and got -22
So....we can be sure that this remainder is correct....!!!!!
Does that make sense, GM???
+73 Ahh...Everything makes perfect sense now! Thanks a lot!
--Mr. SHADOW
