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mart [117]
3 years ago
5

X2 - 28x + 96 How do you factor? I’m in Geometry but I’m doing extra credit Algebra. HALP:(

Mathematics
1 answer:
vazorg [7]3 years ago
3 0

Answer:

(x - 24)(x - 4)

Step-by-step explanation:

Given

x² - 28x + 96

Consider the factors of the constant term (+ 96) which sum to give the coefficient of the x- term (- 28)

The factors are - 24 and - 4, since

- 24 × - 4 = + 96 and - 24 - 4 = - 28, thus

x² - 28x + 96 = (x - 24)(x - 4)

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In the expansion of ( x^3 - 2/x^2 ) ^10 , find the coefficient of 1/x^5​
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Answer:

240

Step-by-step explanation:

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( {x}^{3}   - 2 {x}^{ - 2} ) {}^{10}  = x {}^{30}  +  \binom{10}{1} ( {x}^{27}     2 {x}^{ - 2} ) +  \binom{10}{2}  {x}^{24} 2x {}^{ - 4}  +  \binom{10}{3}  {x}^{21} 2x {}^{ - 6}  +  \binom{10}{4}  {x}^{18} 2x { }^{ - 8}  +  \binom{10}{5} x {}^{15} 2x {}^{ - 10}  +  \binom{10}{6} x {}^{12}2 x {}^{ - 12}  +  \binom{10}{7} x {}^{ 9} 2x {}^{ - 14}  +  \binom{10}{8} x {}^{ 6} 2x {}^{ - 16}  +  \binom{10}{9} ( {x}^{3} )2x {}^{ - 18}  + 2x {}^{ - 20}

\frac{1}{ {x}^{5} }  = x {}^{ - 5}

So what term in the series eqaul x^-5.

That term is the 10 choose 7 term.

\binom{10}{7}  {x}^{9} 2x {}^{ - 14}

Because

=  \binom{10}{7} 2x {}^{ - 14}  {x}^{9}  =  \binom{10}{7} 2 {x}^{ - 5}

So we need to compute 10 choose 7.

That equals

10!/3!(7!)= 10×9×8/6= 720/6=120.

So we get

120(2) {x}^{ - 5}

240 {x}^{ - 5}

So the coeffceint u

is 240

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