Question

(iii) x³ + 13x²+32x+ 20​

Answer 1

Factorise -

x³ + 13 x² + 32x + 20

=> x³ + 12x² + x² + 20x + 12x + 20

=> x³ + 12x² + 20x + x² + 12x + 20

=> x ( x² + 12x + 20 ) + 1( x² + 12x + 20 )

=> ( x + 1 )( x² + 12x + 20 )

=> ( x + 1 )( x² + 10x + 2x + 20 )

=> ( x + 1 )( x ( x + 10 ) + 2 ( x + 10 ) )

=> ( x + 1)( x + 2)( x + 10 )

This is the final answer .

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Answer 2

$\rule{180}2$

$\mathbf{x^3+13x^2+32x+23 }$

$\sf{\longrightarrow x^3+x^2+12x^2+20x+12x+20}\\\\\sf{\longrightarrow x^2(x+1)+12x(x+1)+20(x+1)}\\\\\sf{\longrightarrow (x+1)(x^2+12x+20)}\\\\\sf{\longrightarrow (x+1)(x^2+10x+2x+20)}\\\\\sf{\longrightarrow (x+1)[x(x+10)+2(x+10)]}\\\\\boxed{\sf{\color{magenta}{\longrightarrow (x+1)(x+10)(x+2)}}}$

$\rule{180}2$