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ASHA 777 [7]
3 years ago
13

According to the rational root theorem, which is a factor of the polynomial f(x)=3x^3-5x^2-12x+20?

Mathematics
1 answer:
MakcuM [25]3 years ago
4 0

Answer:

(x-2), (x+2), (3x-5)

Step-by-step explanation:

Factors of 3: ±1, ±3

Factors of 20: ±1, ±2, ±4, ±5, ±10, ±20

Possible factors of the polynomial: ±1, ±2, ±3, ±4, ±5, ±10, ±20, .... (there's a lot more but you probably do not need to list them all)

Pick a number to divide the polynomial by (I picked 2)

(3x³-5x²-12x+20)÷(x-2) = 3x²+x-10

So (x-2) is a factor of f(x) = 3x³-5x²-12x+20

Factor 3x²+x-10 = (3x-5)(x-2) these are the other factors of f(x) = 3x³-5x²-12x+20

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An equation that correctly represent this relationship if x represents the number of pounds of fertilizer and y the number of ounces of weed killer is  0.5x + 3.5y = 70

<u>Solution:</u>

Given that, Bill spent 70 on fertilizer and weed killer for his lawn

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We have to write an equation, if x represents the number of pounds of fertilizer and y the number of ounces of weed killer.

Now,<em> total amount = amount for fertilizers + amount for weed killers.</em>

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\begin{array}{l}{\rightarrow 70=x \times 0.50+y \times 3.50} \\\\ {\rightarrow 0.5 x+3.5 y=70}\end{array}

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