Question

a rectangle has an area of $2x^{2}-19x + 45$ square feet. which of the following represent the dimensions of the rectangle in the equivalent factored form?
a $(2x - 9)(x - 5)$
b $(2x - 5)(x + 9)$
c $(2x - 5)(x - 9)$
d $(2x + 9)(x + 5)$

Explanation:

Step1: Expandir el primer paréntesis

$$(2x - 9)(x - 5)=2x\times x-2x\times5-9\times x + 9\times5$$

Step2: Simplificar la expresión

$$2x^{2}-10x - 9x+45=2x^{2}-19x + 45$$

Step3: Expandir el segundo paréntesis

$$(2x - 5)(x + 9)=2x\times x+2x\times9-5\times x-5\times9$$

Step4: Simplificar la expresión

$$2x^{2}+18x-5x - 45=2x^{2}+13x-45$$

Step5: Expandir el tercer paréntesis

$$(2x - 5)(x - 9)=2x\times x-2x\times9-5\times x+5\times9$$

Step6: Simplificar la expresión

$$2x^{2}-18x-5x + 45=2x^{2}-23x + 45$$

Step7: Expandir el cuarto paréntesis

$$(2x + 9)(x + 5)=2x\times x+2x\times5+9\times x+9\times5$$

Step8: Simplificar la expresión

$$2x^{2}+10x+9x + 45=2x^{2}+19x + 45$$

Answer:

A. \((2x - 9)(x - 5)\)