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yulyashka [42]
3 years ago
11

G(x) = 35x^2– 48x – 27; 7x + 3 how do i solve this using long division?

Mathematics
1 answer:
Rina8888 [55]3 years ago
6 0

35<em>x</em>² = 7<em>x</em> • 5<em>x</em>, and

5<em>x</em> (7<em>x</em> + 3) = 35<em>x</em>² + 15<em>x</em>

Subtract this from the dividend to get an initial remainder of

(35<em>x</em>² - 48<em>x</em> - 27) - (35<em>x</em>² + 15<em>x</em>) = -63<em>x</em> - 27

-63<em>x</em> = 7<em>x</em> • (-9), and

-9 (7<em>x</em> + 3) = -63<em>x</em> - 27

Subtract this from the previous remainder to get a new one of

(-63<em>x</em> - 27) - (-63<em>x</em> - 27) = 0

and we're done.

Now just gather the terms in bold (and the remainder, but since it's 0 we leave it out). So we have

(35<em>x</em>² - 48<em>x</em> - 27) / (7<em>x</em> + 3) = 5<em>x</em> - (63<em>x</em> + 27) / (7<em>x</em> + 3)

(35<em>x</em>² - 48<em>x</em> - 27) / (7<em>x</em> + 3) = 5<em>x</em> - 9

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