Question

Factorize the following polynomial
$(x - 5) {}^{2} - (5x - 25) - 24$
​

Answer 1

Step-by-step explanation:

${(x - 5)}^{2} - (5x - 25) - 24$

${x}^{2} - 25 - 5x + 25 - 24$

${x}^{2} - 24 - 5x$

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Answer 2

ANSWERS:

$\Large\boxed{(X-2)(X-13)}$

STEP-BY-STEP EXPLANATIONS:

To solve this problem, first you have to find the factorize and polynomial to get final answer into this question.

SOLUTIONS:

First, used perfect square formula.

$\Large\boxed{\textnormal{PERFECT SQUARE FORMULA}}}}$

$\mathsf{A-B^2=A^2-2AB+B^2}$

A=X

B=5

$\Rightarrow \displaystyle x^2-2x*5+5^2$

Solve.

$\displaystyle x^2-2x*5+5^2$

Multiply.

$\displaystyle 2\times5=10$

$\displaystyle x^2-10x+5^2$

Do exponent.

$\displaystyle 5^2=5\times5=25$

Rewrite the problem down.

$\displaystyle x^2-10x+25$

$\mathsf{x^2-10x+25-(5x-25)-24}$

$\displaystyle -(5x-25)=-5x+25$

$\mathsf{x^2-10x+25-5x+25-24}$

Solve.

Combined like terms. (Group like terms or switch sides of an equation.)

$\displaystyle x^2-10x-5x+25+25-24$

Add or subtract elements to the numbers from left to right.

$\mathsf{-10x-5x=-15x}$

$\mathsf{x^2-15x+25+25-24}$

Then, you add or subtract the numbers from left to right.

$\mathsf{25+25-24=26}$

$\longrightarrow \mathsf{ x^2-15x+26}$

Factors of x²-15x+26.

$\mathsf{\left(x^2-2x\right)+\left(-13x+26\right)}$

Factor it out by the x.

$\mathsf{x^2-2x}$

Used exponent rule.

$\Large\boxed{\textnormal{EXPONENT RULE}}$

$\mathsf{A^B^+^C=A^BA^C}$

$\mathsf{XX=X^2}$

Common term by the x.

$\mathsf{X(X-2)}$

Factor it out by the -13.

$\mathsf{-13x+26}$

Multiply.

$\mathsf{2\times13=26}$

Rewrite the whole problem down.

$\mathsf{-13x+13\times2}$

Common term of -13.

$\mathsf{-13(x-2)}$

$\mathsf{x(x-2)-13(x-2)}$

Solve.

Common term of x-2.

$\Large\Rightarrow\boxed{\mathsf{(X-2)(X-13)}}}$

Therefore, the final answer is (x-2)(x-13).