Answered

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Select the expression that is equivalent to 2x3+11x2−21xx2+3x for x ≠ −3 or 0 .

Sagot :

MrRoyal

Answer:

[tex]\frac{(2x-3)(x+7)}{x+3}[/tex]

Step-by-step explanation:

Given

[tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex]

Required

Select equivalent expression

[tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex]

Factorize the numerator and denominator

[tex]\frac{x(2x^2+11x-21)}{x(x+3)}[/tex]

Divide by x/x

[tex]\frac{2x^2+11x-21}{x+3}[/tex]

Expand the numerator

[tex]\frac{2x^2+14x-3x-21}{x+3}[/tex]

Factorize the numerator

[tex]\frac{2x(x+7)-3(x+7)}{x+3}[/tex]

[tex]\frac{(2x-3)(x+7)}{x+3}[/tex]

Hence, the equivalent expression is:

[tex]\frac{(2x-3)(x+7)}{x+3}[/tex]

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