Question

fill in the missing values below one at a time to find the quot -6x³ - 15x² - 8x - 20 is divided by -2x - 5.
answer attempt 1 out of 2
(-6x³ - 15x² - 8x - 20) ÷ (-2x - 5) =
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Explanation:

Step1: Analyze the table method for polynomial division

The table is set up such that the product of the terms in the first column and first row gives the terms of the dividend. We can see that when we multiply \(-2x\) by \(3x^2\), we get \(-6x^3\) (which matches the first term of the dividend), when we multiply \(-2x\) by \(0\) we get \(0\), and when we multiply \(-2x\) by \(4\) we get \(-8x\). Similarly, when we multiply \(-5\) by \(3x^2\) we get \(-15x^2\) (which matches the second term of the dividend), when we multiply \(-5\) by \(0\) we get \(0\), and when we multiply \(-5\) by \(4\) we get \(-20\) (which matches the last term of the dividend).

Step2: Combine the terms from the top row

The top row of the table (the quotient terms) is \(3x^2\), \(0\), and \(4\). Combining these terms, we get the quotient. The \(0\) term means there is no \(x\) term in the quotient (the linear term coefficient is \(0\)). So we combine \(3x^2 + 0x + 4\).

Answer:

\(3x^2 + 4\)