Question

Show that x+1 and 2x-3 are factors of 2x³-9x²+x+12.

Answer 1

We need to check if (2x-3) is a factor of the polynomial 2x³-9x²+x+12

Fir.st equate 2x-3 to 0 and find value of x.


2x - 3 = 0
⇒ 2x = 3
⇒ x = 3/2
If x=3/2 is a root of the polynomial, then (2x-3) is a factor.

at x=3/2, value of polynomial is
2(3/2)³ - 9(3/2)² + 3/2 + 12
= 2×(27/8) - 9×(9/4) + 3/2 + 12
= 27/4 - 81/4 + 3/2 + 12
= (27 - 81 + 6 + 48)/4
= (81-81)/4
= 0
So 3/2 is a root of the polynomial. Hence (2x-3) is a factor of the polynomial.

Answer 2

X+1=0
X= -1
Put the value of X in equation

2(-1)³ - 9(-1)² +(-1) +12
=>
-2 -9 -1+12
=>
-12 + 12 =0
So it is factor of the equation

2x-3=0
Put the value of X = 3/2

Now
2(3/2)³ -9(3/2)² +3/2 +12
=>
2×27/8 - 9×9/4 +3/2 +12
=>
54/8 -81/4+3/2+12
=>
(54 -162 +12+96)/8

=>(162-162)/8 =0

So it's also factor of the equation