Which of the expressions below can be factored using the difference of squares method?
1 answer:
Answer:
<em>The second choice is correct. It can be factored as:</em>
Step-by-step explanation:
<u>The Difference of Squares Method for Factoring</u>
The expression:
Is a widely used method to factor binomials that are expressed as the subtraction of two perfect squares.
The condition for a binomial to be factored by using this method is that both terms must have an exact square root and they must be subtracted.
The last two choices are not valid because they are not a subtraction but an addition.
The first choice is not valid because none of the terms is a perfect square.
The second choice is correct. It can be factored as:
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Answer:
1a. y-intercept: 12
1b. slope: -3/2
1c. equation: y = -3/2x +12
2a. y-intercept: -9
2b. slope: 2
2c. equation: y = 2x -9
Step-by-step explanation:
<h3>1.</h3>A) We observe the pattern to be <em>x-values in the table increase by 2, while y-values in the table decrease by 3</em>. We notice the first x-value is 2, so extending the table upward to x=0 would tell us the y-intercept. That is, adding 3 to the first y-value will give the y-intercept as (x, y) = (0, 12).
B) We have already observed that the "rise" (change in y) is -3 for each "run" (change in x) of 2. The slope is the ratio of these changes:
slope = m = rise/run = -3/2
C) From the above, we know that m=-3/2 and b=12. Putting these values into the equation for the line gives ...
y = -3/2x +12
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<h3>2.</h3>A) We observe the pattern to be <em>y-values increase by 2 while x-values increase by 1</em>. As before, we can find the point that would go before the first one shown in the table. It will have an x-value of 0 and a y-value of -9.
the y-intercept is -9
the slope is 2/1 = 2
the equation is y = 2x -9
