Question

Find the quotient and remainder when

1. (x³ - 9x² +26x-24) is divided by (x-4)

2. (6x³ + x²-26x-21) is divided by (3x - 7)

3. (2x¹ - x³ +10x² + 8x-5) is divided by (x²-x+6)​

Answer 1

Answer:-

Answer:

Let f(x)=x^3 −9x^2 +26x−24

Let x=4

⇒f(4)=4 ^3 −9×4 ^2+26×4−24=64‬−144+104−24=0

One of the factor is x−4

∴x=4 is one of the root of f(x)

The division is shown

∴ the other factor is x ^2 −5x+6

x ^2−2x−3x+6

=x(x−2)−3(x−2)

=(x−2)(x−3)

∴ the factors are (x−2)(x−3)(x−4)

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