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shtirl [24]
3 years ago
9

Solve equations 5-5x=14-8x 3(2y-5)=4y-7

Mathematics
1 answer:
GaryK [48]3 years ago
5 0
5-5x=14-8x
-5x=9-8x
3x=9
x=3


3(2y-5)=4y-7
6y-15=4y-7
2y-15=-7
2y=8
y=4
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Answer:

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Step-by-step explanation:

We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a <em>binomial</em> in the form (x - a), then our remainder will be P(a).

We are dividing:

(x^2+5x+7)\div(x+k)

So, a polynomial by a binomial factor.

Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.

We want our remainder to be 3. So, P(a)=P(-k)=3.

Therefore:

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Solve for <em>k</em>. Subtract 3 from both sides:

k^2-5k+4=0

Factor:

(k-1)(k-4)=0

Zero Product Property:

k-1=0\text{ or } k-4=0

Solve:

k=1\text{ or } k=4

So, either of the two expressions:

(x^2+5x+7)\div(x+1)\text{ or } (x^2+5x+7)\div(x+4)

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