divide (x2-10x+30)/(x-5)
1.D
2.B
3.B
4.A
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Those are Lesson 3: Dividing Polynomials CE 2015
Algebra 1 B Unit 6: Rational Expressions and Functions
Assessment
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To divide the polynomial (x^2 - 10x + 30) by (x - 5), we can use long division. Here's how you can do it step by step:
Step 1: Write the dividend and divisor in long division format.
__________________
x - 5 | x^2 - 10x + 30
Step 2: Divide the first term of the dividend (x^2) by the first term of the divisor (x), which gives us x. Write this above the division line.
x
---------------
x - 5 | x^2 - 10x + 30
Step 3: Multiply the divisor (x - 5) by the quotient (x), and write the result below the dividend.
x
---------------
x - 5 | x^2 - 10x + 30
-(x^2 - 5x)
Step 4: Subtract the result obtained in step 3 from the dividend.
x
---------------
x - 5 | x^2 - 10x + 30
-(x^2 - 5x)
--------------
-5x + 30
Step 5: Bring down the next term of the dividend (-5x) and repeat steps 2 to 4 until all terms are exhausted.
x + 5
---------------
x - 5 | x^2 - 10x + 30
-(x^2 - 5x)
--------------
-5x + 30
-(-5x + 25)
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5
Step 6: The quotient is the result obtained from the division, which is x + 5. The remainder is the constant term at the bottom, which is 5.
Therefore, the result of dividing (x^2 - 10x + 30) by (x - 5) is x + 5 with a remainder of 5.
x - 5 remainder 5
------ x - 5
==== ________________
x-5 |x^2 - 10 x + 30
==== x^2 - 5 x
=====--------------
======== - 5 x + 30
=========- 5 x + 25
----------------------
=======Remainder = 5