Question

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Answer 1

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Answer 2

Answer:

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[ x³ + 13x² + 32x + 20 ]    = (x+1) * (x+2) * (x+10)

Step-by-step explanation:

Let p(x) = x³ + 13x² + 32x + 20

p(-1) = (-1)³ + 13*(-1)² + 32*(-1) + 20

      = -1 + 13 - 32 + 20

      = 0

∴(x+1) is the factor  of p(x)

on dividing p(x) by (x+1)

p(x) / (x+1) = [ x³ + 13x² + 32x + 20 ] / (x+1)

                = x² + 12x + 20

∵ [ x³ + 13x² + 32x + 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)]

[ x³ + 13x² + 32x + 20 ]    = (x+1) * (x+2) * (x+10)

Hence,

[ x³ + 13x² + 32x + 20 ]    = (x+1) * (x+2) * (x+10)