Factor the following expression completely. x^(4)-6x^(3)+5x^(2)-16x^(2)+96 x-80 Answer:

Question

Factor the following expression completely.  x^(4)-6x^(3)+5x^(2)-16x^(2)+96 x-80 Answer:

Bytelearn · Accepted Answer

Combine Like Terms: First, we need to combine like terms in the expression x^4 - 6x^3 + 5x^2 - 16x^2 + 96x - 80. Combining the x^2 terms: 5x^2 - 16x^2 = -11x^2. The expression now becomes x^4 - 6x^3 - 11x^2 + 96x - 80.Group and Factor: Next, we look for common factors in groups of terms. We can group the first three terms and the last two terms separately. Grouping: (x^4 - 6x^3 - 11x^2) + (96x - 80).Factor Quadratic: Now, we factor by grouping. For the first group (x^4 - 6x^3 - 11x^2), we can factor out an x^2. This gives us x^2(x^2 - 6x - 11). For the second group (96x - 80), we can factor out a 16. This gives us 16(6x - 5). The expression now becomes x^2(x^2 - 6x - 11) + 16(6x - 5).Substitute Factored Form: We now look for common factors between the two groups. There are no common factors between x^2 - 6x - 11 and 6x - 5, so we cannot factor further by grouping. We must now factor the quadratic x^2 - 6x - 11.Check for Common Factors: To factor the quadratic x^2 - 6x - 11, we look for two numbers that multiply to -11 and add to -6. The numbers -11 and 1 satisfy these conditions. We can write x^2 - 6x - 11 as (x - 11)(x + 1).Final Factored Form: Now we substitute the factored form of the quadratic back into the expression. The expression becomes x^2(x - 11)(x + 1) + 16(6x - 5).We have factored the expression as much as possible. The final factored form is x^2(x - 11)(x + 1) + 16(6x - 5). However, we need to check if there is a common factor that we might have missed.Upon re-examining the expression x^2(x - 11)(x + 1) + 16(6x - 5), we realize that there is no common factor between the two groups, and the quadratic has been factored correctly. Therefore, the expression is fully factored.

Factor the following expression completely. $\newline$ $x^{4}-6 x^{3}+5 x^{2}-16 x^{2}+96 x-80$ $\newline$ Answer:

Full solution

More problems from Operations with rational exponents

Related topics

Factor the following expression completely.\newlinex4−6x3+5x2−16x2+96x−80 x^{4}-6 x^{3}+5 x^{2}-16 x^{2}+96 x-80 x4−6x3+5x2−16x2+96x−80\newlineAnswer:

Factor the following expression completely. $\newline$ $x^{4}-6 x^{3}+5 x^{2}-16 x^{2}+96 x-80$ $\newline$ Answer: