Question

find a and b if (x+1) and (x-1) are the factors ax cube+ X square- 2 X+b

Answer 1

$\color{red}\huge\bold\star\underline\mathcal{Hey\:Mate}\star$

Here is your answer... ☺️☺️☺️
➡➡➡➡➡➡➡➡➡➡➡➡➡➡➡➡➡➡➡

(x-1) and (x+1) are factors of the given polynomial.

x-1 = 0. ; x+1 = 0

x = 1. ; x = -1

Put x= -1,1 to find a and b

First,put x = 1

ax³+x²-2x+b = 0

a(1)³+(1)²-2(1)+b=0

a+1-2+b=0

a+b-1 = 0

a+b = 1 --------(1)

Put x = -1

a(-1)³+(-1)²-2(-1)+b = 0

a(-1)+1+2+b = 0

-a+b+3 = 0

-a+b = -3 -------(2)

(1)+(2)

a+b = 1
-a+b=-3
-----------
2b = -2

b = -2/2

b = -1

Put b= -1 in (1)

a+(-1) = 1

a-1 = 1

a=1+1

a=2

Therefore, a = 2 and b = -1

✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔
I hope this answer is helpful to u...❤❤❤

Keep Asking... ✌️✌️✌️

✨✨✨If help u. Mark my answer as brainliest✨✨✨

$<font color="red"><marquee>❤️❤️❤️Thank You❤️❤️❤️</marquee></font>$

Answer 2

(x-1) and (x+1) are the factors

(x-1) = 0 → x=1, (x+1) = 0 → x= -1

Put x = 1

ax³+x²-2x+b

a(1)³+(1)²-2(1)+b = 0

a(1)+1-2+b = 0

a-1+b = 0

a+b = 1 -----(1)

Now, Put x = -1

a(-1)³+(-1)²-2(-1)+b = 0

a(-1)+1+2+b = 0

-a+3+b = 0

-a+b = -3 -----(2)

(1)+(2)

a+b = 1, -a+b = -3

-------------

2b = -2

b = -2/2 = -1, a+b = 1

a+(-1) = 1

a = 1+1

a = 2

Therefore, a = 2 & b = -1