Question

how is x+5 a factor of $x^{3} +2x^{2} -33x-90$

Answer 1

Answer:

Let us assume that x + 5 is a factor,

Then x = - 5 is a zero of the polynomial

p(x) = x³ + 2x² - 33x - 90

p(-5) = (-5)³ + 2(-5)² - 33(-5) - 90

= -125 + 50 + 165 - 90

= 215 - 215

= 0

Therefore x+5 is a factor of the given polynomial

Hope it helps....

Answer 2

x³ + 2x² - 33x - 90

=> x³ + 3x² - x² - 3x - 30x - 90

=> (x³+3x²) + (-x²-3x) + (-30x-90)

=> x²(x+3)-x(x+3)-30(x+3)

=> (x-3)(x²-x-30)

=> (x-3)(x²-6x+5x-30)

=> (x-3)[x(x-6)+5(x-6)]

=> (x-3)(x-6)(x+5)

I hope it will be helpful for you

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