polynomials (1 Viewer)

[maths lover]

p of x=x^3-8x^2+9x+18 is divisible by (x-3) and (2x+1). by considering the leading term and the constant term, express the polynomial in terms of three linear factors. and hence solve p(X) is less that or equal to 0.

i know how to do the question since i got the one before it but for some reason my answer has small difference in the solving part.
thanxs any help is appreciative

 

[maths lover]

that is not the answer in the textbook. the book says x<=-2 or -1/2<=x<=3

 

[funnytomato]

that is not the answer in the textbook. the book says x<=-2 or -1/2<=x<=3

are you sure it's divisible by 2x+1?

cos P(-1/2) = -1/8 -2-9/2+18=91/8 =/= 0

 

[funnytomato]

are you sure it's divisible by 2x+1?

cos P(-1/2) = -1/8 -2-9/2+18 = 91/8 =/= 0

which textbook is it ? maybe it's a typo or something

 

[maths lover]

im really sorry but i wrote down the wrong polynomial it is p of x=2x^3-x^2-13x-6

 

[funnytomato]

im really sorry but i wrote down the wrong polynomial it is p of x=2x^3-x^2-13x-6

okay

so let the other factor be ax+b
then P(x)= 2x^3-x^2-13x-6 = (x-3)(2x+1)(ax+b)

equating coefficient of x^3 , 2=2a, a=1
... of x^0 , -6 = -3b , b=2
P(x)= 2x^3-x^2-13x-6 = (x-3)(2x+1)(x+2) , which has roots x=3, x=-1/2 and x=-2

after drawing a simple graph(a cubic with +ve leading coefficient) , for P(x) <= 0
x<= -2 or -1/2<=x<=3

 

[funnytomato]

so what was the "small difference" in your solution?

 

[maths lover]

so what was the "small difference" in your solution?

i had x<= -3/2 instead of -2

 

[maths lover]

sorry to ask, but could we say through inspection obviously a=1 and b=2.

 

[funnytomato]

p of x=x^3-8x^2+9x+18 is divisible by (x-3) and (2x+1). by considering the leading term and the constant term, express the polynomial in terms of three linear factors. and hence solve p(X) is less that or equal to 0.

i know how to do the question since i got the one before it but for some reason my answer has small difference in the solving part.
thanxs any help is appreciative

sorry to ask, but could we say through inspection obviously a=1 and b=2.

the question is explicitly asking you to "consider" the coefficients , I'd write them down to be apparent
otherwise , you could state the values of a and b by inspection
or use sum of roots since you only need the roots to graph it and then solve the inequality