Question

divide using algorithm x^3+10x^2+24x by x^2 + 6x​

Answer 1

To Find :

• we need to divide x³ + 10x² + 24x by x² + 6x.

Solution :

x² + 6x ) x³ + 10x² + 24x ( x + 4

⠀⠀⠀⠀ ⠀x³ + 6x²

⠀⠀⠀⠀⠀ --⠀⠀--⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀4x² + 24x

⠀⠀⠀⠀⠀⠀⠀⠀4x² + 24x

⠀⠀⠀⠀⠀⠀⠀⠀--⠀⠀⠀--⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀0

So,

Remainder = 0

Quotient = x + 4

━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Step-by-step explanation:

$\sf \: \: \: \: \: \: \: \: \: \: \: \: {x}^{2} + 6x) \: {x}^{3} + {10x}^{2} + 24x \: (x + 4 \\ \\ \sf {x}^{3} + {6x}^{2} \\ \dfrac{ \qquad \: \: \: \: \: ( - ) \: \: \: \: \ ( - ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{ \sf \qquad \qquad \: \: {4x}^{2} + 24x} \\ \\ \sf \qquad \qquad \: {4x}^{2} + 24x \\ \dfrac{ \qquad \qquad \qquad \: \: \: \: \: ( - ) \: \: \: \: \ ( - ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{ \qquad \qquad 0}$

Here,

• Remainder = 0

• Quotient = x + 4