Rewrite the expression as a product of four linear factors: (x^(2)-5x)^(2)-2(x^(2)-5x)-24 Answer:

Question

Rewrite the expression as a product of four linear factors:  (x^(2)-5x)^(2)-2(x^(2)-5x)-24 Answer:

Bytelearn · Accepted Answer

Identify Expression: Let's identify the expression we need to factor: (x^2 - 5x)^2 - 2(x^2 - 5x) - 24. To simplify the factoring process, let's use a substitution where u = x^2 - 5x. This will allow us to rewrite the expression in terms of u, which will look like a quadratic equation. Substitute u for (x^2 - 5x): u^2 - 2u - 24.Substitute and Simplify: Now we have a quadratic equation in terms of u: u^2 - 2u - 24. We need to factor this quadratic equation. To factor u^2 - 2u - 24, we look for two numbers that multiply to -24 and add up to -2. These numbers are -6 and +4. So, we can write u^2 - 2u - 24 as (u - 6)(u + 4).Factor Quadratic Equation: Now that we have factored the quadratic in terms of u, we need to substitute back x^2 - 5x for u to get the expression in terms of x. Substitute back: (u - 6)(u + 4) becomes ((x^2 - 5x) - 6)((x^2 - 5x) + 4).Substitute Back: We now have two quadratic factors: ((x^2 - 5x) - 6) and ((x^2 - 5x) + 4). Each of these can be factored further into linear factors. First, let's factor (x^2 - 5x - 6). We look for two numbers that multiply to -6 and add up to -5. These numbers are -6 and +1. So, we can write x^2 - 5x - 6 as (x - 6)(x + 1).Factor Quadratic Factors: Next, we factor (x^2 - 5x + 4). We look for two numbers that multiply to 4 and add up to -5. These numbers are -4 and -1. So, we can write x^2 - 5x + 4 as (x - 4)(x - 1).Factor Linear Factors: Now we have all four linear factors: (x - 6), (x + 1), (x - 4), and (x - 1). The original expression (x^2 - 5x)^2 - 2(x^2 - 5x) - 24 can be rewritten as the product of these four linear factors. The final expression is: (x - 6)(x + 1)(x - 4)(x - 1).

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}-5 x\right)^{2}-2\left(x^{2}-5 x\right)-24$ $\newline$ Answer:

Full solution

More problems from Find the roots of factored polynomials

Related topics

Rewrite the expression as a product of four linear factors:\newline(x2−5x)2−2(x2−5x)−24 \left(x^{2}-5 x\right)^{2}-2\left(x^{2}-5 x\right)-24 (x2−5x)2−2(x2−5x)−24\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}-5 x\right)^{2}-2\left(x^{2}-5 x\right)-24$ $\newline$ Answer: