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Maru [420]
3 years ago
8

Rewrite 2x^2+13x+26/x+4 in the form q(x)+r(x)/b(x) . Then find q(x) and r(x).

Mathematics
2 answers:
sergey [27]3 years ago
8 0

Answer:

Q(x)= 2x+5

R(x)= 6

Step-by-step explanation:

natulia [17]3 years ago
6 0
We are dividing the polynomial 2x^{2} +13x+26 by x+4

notice that 2x^{2} is x times 2x,

so if we multiply (x+4) by 2x, which gives us 2 x^{2} +8x, we can 'separate' one 2 x^{2} +8x from 2x^{2} +13x+26  to get the following simplification:

\frac{2x^{2} +13x+26}{x+4}= \frac{ 2x^{2}+8 x}{x+4} + \frac{5x+26}{x+4}=2x+ \frac{5x+26}{x+4}

similarly we notice that 5x is x times 5, so if we multiply (x+4) by 5, we get 5x+20 so we can rewrite 

\frac{5x+26}{x+4}= \frac{5x+20}{x+4}+  \frac{6}{x+4}=5+\frac{6}{x+4}

\frac{6}{x+4} can not be simplified any further since the degree of 6, is smaller than the degree of x+4

combining our work, we have:

\frac{2x^{2} +13x+26}{x+4}=2x+5+\frac{6}{x+4}

Answer:

q(x)= 2x+5
r(x)=6
b(x)=x+4


Remark: we can solve the problem by long division or the division algorithm as well.
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