Answer:
2(x + 2)² - 5
Step-by-step explanation:
Given
2x² + 8x + 3
To obtain the required form use the method of completing the square.
The coefficient of the x² term must be 1, thus factor 2 out of 2x² + 8x
= 2(x² + 4x) + 3
add/subtract ( half the coefficient of the x- term)² to x² + 4x
= 2(x² + 2(2)x + 4 - 4) + 3
= 2(x + 2)² - 8 + 3
= 2(x + 2)² - 5
with p = 2 and q = - 5
Answer:
3 laps
Step-by-step explanation:
4/4 laps is 1 mile
3/4 laps is 3/4 of a mile
2/4 laps is 1/2 a mile (or 2/4 simplified)
1/4 laps is 1/4 milke
Answer:
1.75
Step-by-step explanation:
Answer:


Step-by-step explanation:
<u>Errors in Algebraic Operations
</u>
It's usual that students make mistakes when misunderstanding the application of algebra's basic rules. Here we have two of them
- When we change the signs of all the terms of a polynomial, the expression must be preceded by a negative sign
- When multiplying negative and positive quantities, if the number of negatives is odd, the result is negative. If the number of negatives is even, the result is positive.
- Not to confuse product of fractions with the sum of fractions. Rules are quite different
The first expression is

Let's arrange into format:

We can clearly see in all of the factors in the expression the signs were changed correctly, but the result should have been preceeded with a negative sign, because it makes 3 (odd number) negatives, resulting in a negative expression. The correct form is

Now for the second expression

Let's arrange into format

It's a clear mistake because it was asssumed a product of fractions instead of a SUM of fractions. If the result was correct, then the expression should have been
