Question

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

Answer 1

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: $5x(7x - 2)$