Question

(x³ - 9x² +26x-24) by (x - 4)​

Answer 1

Answer:

$\\ ( {x}^{3} - {9x}^{2} + 26x - 24) \times (x - 4) \\ x( {x}^{3} - {9x}^{2} + 26x - 24) - 4( {x}^{3} - {9x}^{2} + 26x - 24) \\ {x}^{4} - {9x}^{3} + {26x}^{2} - 24x - {4x}^{3} + 36 {x}^{2} - 104x + 96 \\ {x}^{4} - {9x}^{3} - 4 {x}^{3} + 26 {x}^{2} + 36 {x}^{2} - 24x - 104x + 96 \\ {x}^{4} - 13 {x}^{3} + 62 {x}^{2} - 128x + 96$

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Answer 2

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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