Question

Factor 2x2 − 4x − 30 completely.

Answer 1

Answer:

$x^{2} -2x-15=(x-5)(x+3)$

Step-by-step explanation:

The given expression is

$2x^{2} -4x-30$

This is a quadratic expression, which can be equal to zero

$2x^{2} -4x-30=0$

Now, we extract the greatest common factor to obtain an easier expression to factor

$2(x^{2} -2x-15)=0\\x^{2} -2x-15=0$

To factor, first we write two binomials, the sign of the first one must be the same of the linear term and the sign of the second binomila must the product of the sign of the linear term and the constant term

$x^{2} -2x-15=(x-a)(x+b)$

Now, we have to find to number which product is 15 and which difference is 2, those numbers are 5 and 3, because 5 times 3 is 15, and 5 minus 3 is 2.

Therefore, the solution is

$x^{2} -2x-15=(x-5)(x+3)$

Answer 2

I hope this helps you