Question
If
then find the quotient from the following four option, when A is divided by B.
- x − 1
- x + 1
- 2x + 1
- 2x - 1
Hint:
The expansions of certain identities are:
![open parentheses x squared minus a squared close parentheses equals left parenthesis x plus a right parenthesis left parenthesis x minus a right parenthesis](data:image/png;base64,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)
![left parenthesis x plus a right parenthesis left parenthesis x plus b right parenthesis equals x squared plus left parenthesis a plus b right parenthesis x plus a b](data:image/png;base64,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)
We are asked to find the quotient from the given options when A is divided by B.
The correct answer is: x + 1
Step 1 of 2:
The given expressions are:
![A equals 2 x cubed plus 5 x squared plus 4 x plus 1](data:image/png;base64,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)
![B equals 2 x squared plus 3 x plus 1](data:image/png;base64,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)
When A is divided by B, we have:
![fraction numerator 2 x cubed plus 5 x squared plus 4 x plus 1 over denominator 2 x squared plus 3 x plus 1 end fraction](data:image/png;base64,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)
Step 2 of 2:
Simplify the expression
and cancel out the common factors;
![fraction numerator 2 x cubed plus 5 x squared plus 4 x plus 1 over denominator 2 x squared plus 3 x plus 1 end fraction equals fraction numerator open parentheses 2 x cubed plus 4 x squared plus 2 x close parentheses plus open parentheses x squared plus 2 x plus 1 close parentheses plus 2 x over denominator 2 x squared plus 3 x plus 1 end fraction](data:image/png;base64,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)
![equals fraction numerator 2 x open parentheses x squared plus 2 x plus 1 close parentheses plus open parentheses x squared plus 2 x plus 1 close parentheses over denominator 2 x squared plus 2 x plus x plus 1 end fraction](data:image/png;base64,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)
![equals fraction numerator left parenthesis 2 x plus 1 right parenthesis open parentheses x squared plus 2 x plus 1 close parentheses over denominator 2 x left parenthesis x plus 1 right parenthesis plus 1 left parenthesis x plus 1 right parenthesis end fraction](data:image/png;base64,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)
![equals fraction numerator left parenthesis 2 x plus 1 right parenthesis left parenthesis x plus 1 right parenthesis squared over denominator left parenthesis 2 x plus 1 right parenthesis left parenthesis x plus 1 right parenthesis end fraction](data:image/png;base64,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)
= x +1
Hence, the quotient is x + 1.
The correct answer is option b.
Here, we split the values in the initial steps to group certain terms. This was followed by using the identities to factorize them out.
Simplify means to make it simple. In mathematics, simplify is the reduction of an expression/fraction into irreducible forms.
Related Questions to study
Find the extraneous solution of ![square root of 8 x plus 9 end root equals x](data:image/png;base64,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)
Find the extraneous solution of ![square root of 8 x plus 9 end root equals x](data:image/png;base64,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)
Explain why the process of dividing by a rational number is the same as multiplying by its reciprocal.
Explain why the process of dividing by a rational number is the same as multiplying by its reciprocal.
Sketch the graph of y = 2x - 5.
Sketch the graph of y = 2x - 5.
Simplify each expressions and state the domain : ![fraction numerator x squared plus 2 x plus 1 over denominator x cubed minus 2 x squared minus 3 x end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG8AAAAqCAYAAAC9UAW/AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAApZJREFUeNrtmjFLA0EQhZcgIhIEEQliIYQgYhFsRUIQJIhYiGARRCQIFlb5A1YiWAULO0sLQUREgggiwcJCEBErsRH/gEUKCTZxlpuDFNEktztzt8l88MAY0Lc7e7ezd08pPuqoH9ADKKUE54iBdkDPMhXuUpMpcJMs6F6mwT3GcM9LEvztOdA5qIp76wtoPUJjnwTtoi/n0ObLWEAK9NWcB8Xx8zQulHxExn8C2sbGzbkr7ho0FLBTDcoE6JWwg1bM47HKFuigye/38DsfXbipkAZbM/Dd1cVT2PYnGj4XQEd/nPMaxTHYWbx1BvXd9cVbBJXw5wXQXURuTwOgR2xkKHx3RfE0t3gE0J3UiIVitVIrhkGXoJxF3zZ8RbJ4RWzP0xFoDJJYuBSx76648vzzVYmoLe9ksLopOgYNMvh2vnh6lV/hZOnz1ZOF22bQwerm4wzUx+Tb6eKN4hGgcdDLeBgNo3jlNo8jtnw7W7x+0AVovMl3p9jJcdNOIxGmb5PjkiAIgiAIgtvURc5IEARBEISAjY6f1so56FsS3Mp7KPzpmGdJcDdMxJej3ns6wa1fr+jwTsFB7z2d4Pb3jw2iv0+ZhKZMcM8r773hN17Z76BDZf9ltTE6TLuvvESwbaiS0NQJ7gpoVXnvEH1mQDe9vneYJqFNEtymVKn/QZBEcUZ5WZAwFwpHgtsEfXt+szTf/9JJErqGt4MJpkkwTUJzP/BNoA+97y0Z+G4b6iR0UKiT0BTNnK8i53z3QhKay/cKLrosk2/SJHSQ/YIjCU1JHAtI7ps6Cd0JnEnosDpya745ktCdbPacSWhK0ti0kPnmSkK3C3cS2ubDhTVcdDF84vIB2qTyLUloe2Rw4dVQFSyKlfn+BVdLdKQrYgZGAAABPXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bXJvdz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjI8L21uPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjE8L21uPjwvbXJvdz48bXJvdz48bXN1cD48bWk+eDwvbWk+PG1uPjM8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtbj4yPC9tbj48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtbj4zPC9tbj48bWk+eDwvbWk+PC9tcm93PjwvbWZyYWM+PC9tYXRoPtZ89mkAAAAASUVORK5CYII=)
Simplify each expressions and state the domain : ![fraction numerator x squared plus 2 x plus 1 over denominator x cubed minus 2 x squared minus 3 x end fraction](data:image/png;base64,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)
Reduce the following rational expressions to their lowest terms
![fraction numerator 8 x to the power of 5 minus 8 x over denominator open parentheses 3 x squared plus 3 close parentheses left parenthesis 4 x plus 4 right parenthesis end fraction](data:image/png;base64,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)
Reduce the following rational expressions to their lowest terms
![fraction numerator 8 x to the power of 5 minus 8 x over denominator open parentheses 3 x squared plus 3 close parentheses left parenthesis 4 x plus 4 right parenthesis end fraction](data:image/png;base64,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)
Describe the error student made in multiplying and simplifying![fraction numerator x plus 2 over denominator x minus 2 end fraction cross times fraction numerator x squared minus 4 over denominator x squared plus x minus 2 end fraction](data:image/png;base64,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)
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)
Describe the error student made in multiplying and simplifying![fraction numerator x plus 2 over denominator x minus 2 end fraction cross times fraction numerator x squared minus 4 over denominator x squared plus x minus 2 end fraction](data:image/png;base64,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)
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)
The LCM of the polynomials
is.
The LCM of the polynomials
is.
Write the equation in slope-intercept form of the line that passes through the points (5, 4) and (-1, 6).
The slope intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. We can draw the graph of a linear equation on the x-y coordinate plane using this form of a linear equation.
Steps for determining a line's equation from two points:
Step 1: The slope formula used to calculate the slope.
Step 2: To determine the y-intercept, use the slope and one of the points (b).
Step 3: Once you know the values for m and b, we can plug them into the slope-intercept form of a line, i.e., (y = mx + b), to obtain the line's equation.
Write the equation in slope-intercept form of the line that passes through the points (5, 4) and (-1, 6).
The slope intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. We can draw the graph of a linear equation on the x-y coordinate plane using this form of a linear equation.
Steps for determining a line's equation from two points:
Step 1: The slope formula used to calculate the slope.
Step 2: To determine the y-intercept, use the slope and one of the points (b).
Step 3: Once you know the values for m and b, we can plug them into the slope-intercept form of a line, i.e., (y = mx + b), to obtain the line's equation.