please do this question in detail

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please do this question in detail

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Try to factorise the polynomial to get the factor (x+1).

4x³ + 7x² - 3x - 6

= 4x³ + 4x² + 3x² + 3x - 6x - 6

= 4x²(x+1) + 3x(x+1) - 6(x+1)

Now take (x+1) common

(x+1)(4x²+3x-6)

So 4x³ + 7x² - 3x - 6 = (x+1)(4x²+3x-6)

By dividing 4x³ + 7x² - 3x - 6 by (x+1),

=

=

4x³ + 7x² - 3x - 6

= 4x³ + 4x² + 3x² + 3x - 6x - 6

= 4x²(x+1) + 3x(x+1) - 6(x+1)

Now take (x+1) common

(x+1)(4x²+3x-6)

So 4x³ + 7x² - 3x - 6 = (x+1)(4x²+3x-6)

By dividing 4x³ + 7x² - 3x - 6 by (x+1),

=

=