Question

Factor completely
-2x³+30x²-52x

Answer 1

To factor completely -2x³+30x²-52x, the expression can be factored as -2x(x-2)(x-13).

Step-by-step explanation:

To factor completely -2x³+30x²-52x, we can start by factoring out the greatest common factor which is -2x. This gives us -2x(x²-15x+26). The quadratic expression (x²-15x+26) can then be factored using the quadratic formula or by finding two numbers that multiply to 26 and add up to -15. The factored form of the expression is: -2x(x-2)(x-13).

Answer 2

The given expression -2x³ + 30x² - 52x can be factored completely as -2x(x - 2)(x - 13).

Step-by-step explanation:

To factor the expression -2x³ + 30x² - 52x completely, we can start by factoring out the common factor, which is -2x. This results in -2x(x² - 15x + 26). To further factor the quadratic trinomial, we need to find two numbers whose product is the product of the leading coefficient (1) and the constant term (26) and whose sum is the coefficient of the linear term (-15). These numbers are -13 and -2. Therefore, the quadratic trinomial can be factored as (x - 2)(x - 13). Putting it all together, the complete factorization is -2x(x - 2)(x - 13).

This factorization demonstrates the application of factoring techniques, including factoring out the common factor and factoring a quadratic trinomial. Factoring is a valuable skill in algebra, providing insights into the structure of polynomial expressions and facilitating the solving of equations and inequalities. The factorized form allows for a clear understanding of the roots of the polynomial and aids in further mathematical manipulations.