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2 years ago

State the common factor of the terms in the polynomial 5x^2 + 30x^2 - 10x. Then factor the polynomial

Mathematics

1 answer:

tatuchka [14]2 years ago

6 0

Answer:

The common factor is 5x.

The factored polynomial is: $5x(7x - 2)$

Step-by-step explanation:

Factor of the numbers:

The common factor of the numbers 5, 30 and 10 is 5, as it is the greater common divisor of them, as found below:

5 - 30 - 10|5

1 - 6 - 2

Factor of the exponents:

Between $x^2, x^2$ and $x$ , the common factor is the x with the lowest exponent. So x

Common factor

Number multiplied by exponents, so 5x.

Factoring the polynomial:

$5x^2 + 30x^2 - 10x = 5x(\frac{5x^2}{5x} + \frac{30x^2}{5x} - \frac{10x}{5x}) = 5x(x + 6x - 2) = 5x(7x - 2)$

The factored polynomial is: $5x(7x - 2)$

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olga_2 [115]

So you have:
$\frac{3}{x} + 2 = \frac{2}{x} - 1
$

1) Start off by multiplying both sides by x to simplify the problem:
$\frac{3}{x} + 2 = \frac{2}{x} - 1 \\
x(\frac{3}{x} + 2) = (\frac{2}{x} - 1)x\\
3 + 2x = 2 - x
$

2) Now isolate the x by moving all terms with x onto one side and all other terms onto the other side:
$3 + 2x = 2 - x\\
3x = -1$

3) Finally, divide by 3 on both sides to find the value of x:
$3x = -1\\
x = \frac{-1}{3}$

------

Answer: x = $\frac{-1}{3}$

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