Answer:
The three dimensions are ( x-3)(x-1) and (x-4)
The missing dimension is x-4
Step-by-step explanation:
<u><em> Step(i):-</em></u>
Given that the polynomial
x³ -8x²+19x -12=0
put x=3
⇒ 27 -8(9)+19(3)-12 =0
84-84 =0
0=0
∴ x =3 is satisfies the given polynomial equation
one factor x-3 =0
<u><em>Step(ii):-</em></u>
By using synthetic division method
x=3 ↓ 1 -8 19 -12
<u> ↓ 0 3 -15 12</u>
<u> 1 - 5 4 0 </u>
The polynomial (x-3) ( x² -5x +4) =0
The factors of the given polynomial
x-3 =0 and x² - 5x +4 =0
x =3 and x² - 4x -x+4 =0
x =3 and x( x-4) -1(x-4) =0
( x-3) and (x-1)(x-4) =0
The three dimensions are ( x-3)(x-1) and (x-4)
<u><em>Final answer:-</em></u>
The missing dimension is x-4
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