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3 years ago

What is the geometric mean of 32 and 40

Mathematics

1 answer:

Snezhnost [94]3 years ago

7 0

Geometric mean: 35.77708764

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Jay factored the 4 term polynomial : x^3 - 9x +2x^2 - 18 and decided that the complete factorization was : ( x + 2 ) (x^2-9 ). B

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Answer:

$x^3-9x+2x^2-18\left(x+2\right)\left(x+3\right)\left(x-3\right)$

Step-by-step explanation:

we are given that $x^3-9x+2x^2-18$

w are sked to step by step factorise the above polynomial

$\left(x^3+2x^2\right)+\left(-9x-18\right)$

$-9\mathrm{\:from\:}-9x-18\mathrm{:\quad }-9\left(x+2\right)$

$-9x-9\cdot \:2$

$-9\left(x+2\right)$

$\mathrm{Factor\:out\:}x^2\mathrm{\:from\:}x^3+2x^2\mathrm{:\quad }x^2\left(x+2\right)$

$-9\left(x+2\right)+x^2\left(x+2\right)$

$\left(x+2\right)\left(x^2-9\right)$

$x^2-9:\quad \left(x+3\right)\left(x-3\right)$

$x^2-9$

$\mathrm{Rewrite\:}9\mathrm{\:as\:}3^2$

$=x^2-3^2$

$\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)$

$x^2-3^2=\left(x+3\right)\left(x-3\right)$

Hence

$x^3-9x+2x^2-18=\left(x+2\right)\left(x+3\right)\left(x-3\right)$

a) The jay mistake was he did not factorise $x^3-9x+2x^2-18x^2-9 furtherb) the complete answer wil be [tex]x^3-9x+2x^2-18\left(x+2\right)\left(x+3\right)\left(x-3\right)$

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