Pergunta

. Which expression shows a cubic binomial? 2+5x-3x^3 2x^3+xy 3x+3x^2 2xy^2
Solução

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ElvisElite · Tutor por 8 anos
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To determine which expression shows a cubic binomial, we need to understand the definitions of "cubic" and "binomial."<br /><br />- A **cubic** expression is one where the highest power of the variable is 3.<br />- A **binomial** is an expression that consists of two terms.<br /><br />Let's analyze each option:<br /><br />1. \(2 + 5x - 3x^3\)<br /> - This expression has three terms: \(2\), \(5x\), and \(-3x^3\).<br /> - The highest power of \(x\) is 3, making it cubic.<br /> - However, it is not a binomial because it has three terms.<br /><br />2. \(2x^3 + xy\)<br /> - This expression has two terms: \(2x^3\) and \(xy\).<br /> - The highest power of \(x\) is 3, making it cubic.<br /> - It is a binomial because it has two terms.<br /><br />3. \(3x + 3x^2\)<br /> - This expression has two terms: \(3x\) and \(3x^2\).<br /> - The highest power of \(x\) is 2, making it quadratic, not cubic.<br /><br />4. \(2xy^2\)<br /> - This expression has only one term: \(2xy^2\).<br /> - The highest power of \(x\) is 1 (since \(y^2\) does not affect the power of \(x\)), making it linear, not cubic.<br /><br />Therefore, the expression that shows a cubic binomial is:<br /><br />\[ 2x^3 + xy \]
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