Question

Find the quotient and the remainder when <br />$( {5}x^{3} + {3}x^{4} - {5}x^{3} + {14}x^{2} - {39}x + 11 ) \: is \: divided \: by( {x}^{2} + 4x - 2)$<br />

Answer 1

Answer is :-

QUOTIENT :-
=(3x²-12x+68)


REMAINDER :-
=(-287x+147)



For more details :-
Please refer the above photographs for the used process.



KEY POINTS TO REMEMBER :-


☸️ The division is called as LONG DIVISION PROCESS.

☸️The division is carried out in the same way as the normal division of constants is done.

☸️For Non constant terms, Try to have the form of [ax⁴+bx³+cx²+dx+e].
If not, then do as shown in the photograph by keeping the term with degree to that of the missing term.


Thanks!

Answer 2

Step-by-step explanation:

Let the line segment A(5, -6) and B(-1, -4) is divided at point P(0, y) by y-axis in ratio m:n

:. x = \frac{mx2+nx1}{m+n

and y = \frac{my2+ny1}{m+n

Here, (x, y) = (0, y); (x1, y1) = (5, -6) and (x2, y2) = (-1, -4)

So , 0 = \frac{m(-1)+n(5)}{m+n}

=> 0 = -m + 5n

=> m= 5n

=> \frac{m}{n}

= \frac{5}{1}

=> m:n = 5:1

Hence, the ratio is 5:1 and the division is internal.Now,

y = \frac{my2+ny1}{m+n}

=> y = \frac{5(-4)+1(-6)}{5+1}

=> y = \frac{-20-6}{6}

=> y = \frac{-26}{6}

=> y = \frac{-13}{3}

Hence, the coordinates of the point of division is (0, -13/3).