Question

Check whether the polynomial g(x) is a factor of f(x) or not in each of the following: f(x) = x ^ 3 - 3x ^ 2 + 5x - 2, g(x) = x/2 + 1/3 (ii) f(x) = x ^ 3 - 3x ^ 2 + 4x - 4 , g(x) = x - 2​

Answer 1

Answer:

Total C.P=C.P+expenses=750+50=800

Profit =S.P–C.P

S.P=Profit+C.P=800+80=880

Percent profit =C.PProfit×100=80080×100=10

Loss=Percent loss=0

2) TotalC.P=C.P+expenses=4500+500=5000

Loss =S.P–C.P

S.P=Loss+C.P=1000+5000=6000

Percent loss=C.PLoss×100=Total C.P=C.P+expenses=750+50=800

Profit =S.P–C.P

S.P=Profit+C.P=800+80=880

 =50001000×100=20

Profi

Answer 2

Answer:

(i) Apply factor theorem

x+1=0

So x=−1

2x 3 +x 2 −2x−1

Replace x by −1, we get

2(−1) 3+(−1) 2 −2(−1)−1=−2+1+2−1=0

Reminder is 0 so that x+1 is a factor of 2x

3 +x 2 −2x−1

(ii) Apply factor theorem

x+2=0

So x=−2 x 3 +3x 2 +3x+1

Replace x by −2, we get(−2) 3 +3(−2) 2 +3(−2)+1=−8+12−6+1=1

Reminder is 1 so that x+2 is not a factor of x

3 +3x 2 +3x+1

(iii) Apply factor theorem x−3=0

So x=3 x 3 −4x 2 +x+6

Replace x by 3, we get(3) 3 −4(3) 2+(3)−1=27−36+3+6=0

Reminder is 0 so that x−3 is a factor of x 3 −4x 2 +x+6

hope it helps

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