Answer :

Answer:

[tex](x + 4)( {x}^{2} - 5x + 6) \\ \\ = ( {x}^{3} - 5 {x}^{2} + 6x + 4 {x}^{2} - 20x + 24) \\ \\ = { \underline{ \underline{{x}^{3} - {x}^{2} - 14x + 24}}}[/tex]

AikoMikan

Hey there!

(x + 4) (x² - 5x + 6)

= x (x² - 5x + 6) + 4 (x² - 5x + 6)

= x³ - 5x² + 6x + 4x² - 20x + 24

= x³ - 5x² + 4x² + 6x - 20x + 24

= x³ - x² - 14x + 24 ⇨ Expanded form.

x³ - x² - 14x + 24

= (x + 4) (x² - 5x + 6) [Rational root theorem]

= (x + 4) (x² - 3x) + (-2x + 6)

= (x + 4) x (x - 3) - 2 (x - 3) [Take out the common factor]

= (x + 4) (x - 2) (x - 3) ⇨ Simplified form.

Hope it helps ya!

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