Question

On dividing x³ + 4 x² + 3 X + 2 by g(x),the quotient and remainder were x² - 2 and 5 x + 10 respectively.

find g(x) (Maths Class X)​

Answer 1

Step-by-step explanation:

$p(x) = g(x) \times q(x) + r(x)$

${x}^{3} + {4x}^{2} + 3x + 2 = g(x) \times ( {x}^{2} - 2) + (5x + 10)$

${x}^{3} + {4x}^{2} + 3x + 2 - (5x + 10) = g(x) \times ( {x}^{2} - 2)$

${x}^{3} + {4x}^{2} - 2x - 8 = g(x) \times ( {x}^{2} - 2)$

$\frac{ {x}^{3} + {4x}^{2} - 2x - 8 }{ {x}^{2} - 2 } = g(x)$

$x + 4 = g(x)$