Factor completely: (x-6)(x-9)^(2)-(5x+3)(x-9) Answer:

Recognize common factor: First, we recognize that both terms have a common factor of (x-9). We can factor (x-9) out of both terms.Factor out (x-9): The expression becomes (x-9)[(x-6)(x-9)-(5x+3)].Distribute and expand: Next, we distribute (x-9) into the second term, which gives us (x-9)[(x-6)(x-9)-5x-3].Simplify inside brackets: Now we expand the term (x-6)(x-9) to get (x-9)[x²-9x-6x+54-5x-3].Combine like terms: Simplify the expression inside the brackets to get (x-9)(x²-15x+54-5x-3).Find factors of 51: Combine like terms inside the brackets to get (x-9)(x²-20x+51).Factor quadratic expression: Now we look for factors of 51 that add up to 20. The numbers 3 and 17 fit this requirement since 3*17=51 and 3+17=20.Final completely factored form: We can now factor the quadratic expression to get (x-9)(x-3)(x-17).This is the completely factored form of the original expression.

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Factor completely:

(x-6)(x-9)^(2)-(5x+3)(x-9)
Answer:

Factor completely: $\newline$ $(x-6)(x-9)^{2}-(5 x+3)(x-9)$ $\newline$ Answer:

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Algebra 2

Sum of finite series starts from 1

Full solution

Q. Factor completely:

\newline

(x-6)(x-9)^{2}-(5 x+3)(x-9)

\newline

Answer:

Recognize common factor: First, we recognize that both terms have a common factor of $(x-9)$ . We can factor $(x-9)$ out of both terms.
Factor out $(x-9)$ : The expression becomes $(x-9)[(x-6)(x-9)-(5x+3)]$ .
Distribute and expand: Next, we distribute $(x-9)$ into the second term, which gives us $(x-9)[(x-6)(x-9)-5x-3]$ .
Simplify inside brackets: Now we expand the term $(x-6)(x-9)$ to get $(x-9)[x^2-9x-6x+54-5x-3]$ .
Combine like terms: Simplify the expression inside the brackets to get $(x-9)(x^2-15x+54-5x-3)$ .
Find factors of $51$ : Combine like terms inside the brackets to get $(x-9)(x^2-20x+51)$ .
Factor quadratic expression: Now we look for factors of $51$ that add up to $20$ . The numbers $3$ and $17$ fit this requirement since $3 \times 17=51$ and $3+17=20$ .
Final completely factored form: We can now factor the quadratic expression to get $(x-9)(x-3)(x-17)$ .
Final completely factored form: We can now factor the quadratic expression to get $(x-9)(x-3)(x-17)$ .This is the completely factored form of the original expression.