Question 1

Why is subtracting a negative number the same as adding a positive number?

Accepted Answer

10 - 2 = 8
10 - 1 = 9
10 - 0 = 10
10 - (-1) = ?
Look at the pattern of answers. What do you think the answer should be?
It should be 11 right?
but 10 + 1 = 11
so 10 - (-1) = 10 + 1 = 11

Question 2

0:31 I thought when you multiplied a negative with a positive the product will be negative.

Accepted Answer

It's -2 squared. So (-2)(-2), which is a negative times a negative. That equals a positive 4.

Question 3

How do you square polynomial?

Accepted Answer

Step 1:  Square each term.
Step 2:  For every possible pair of terms (not using the same term twice in a pair), find twice their product.
Step 3:  Add the results of steps 1 and 2.

Example:  Square x^2 - 5x + 3.
Step 1:  (x^2)^2 = x^4, (-5x)^2 = 25x^2, and 3^2 = 9.
Step 2:  2(x^2)(-5x) = -10x^3, 2(x^2)(3) = 6x^2, and 2(-5x)(3) = -30x.
Step 3:  x^4 + 25x^2 + 9 - 10x^3 + 6x^2 - 30x = x^4 - 10x^3 + 31x^2 - 30x + 9.
So (x^2 - 5x + 3)^2 = x^4 - 10x^3 + 31x^2 - 30x + 9.

Have a blessed, wonderful day!

Question 4

I feel that you're doing this wrong.You are not considering 8 as negative 8 and that will cause problems later on.You are supposed to consider 8 as negative 8 or you might end up getting the worng answer,thus teaching us the wrong way.

Accepted Answer

Sal's technique is not wrong.  You can do it as shown in the video.
Or, it can be done as negative 8 times negative 2 = +16 in one step.
Both are correct techniques.

Question 5

What is the least number to be added to 8888 to make it a perfect square

Accepted Answer

Here's how to do that sort of problem:
Square root the number given.  Drop the decimal portion of the answer WITHOUT rounding off.  Add 1 to the result.  Square that number.  This will be the nearest perfect square AFTER the original number.  So, just take the perfect square and subtract the original number.  That will tell you what you need to add to the original number to get a perfect square.
Here it is with 8888:
√8888 = 94.28
94 + 1 = 95
95² = 9025
9025-8888 = 137
So you must add 137 to 8888 to get a perfect square.

Note however, that the nearest perfect square to 8888 is 94², which is 8836.  But since that requires a subtraction instead of an addition, I don't think that is what the problem is asking

Question 6

I'm slightly confused on what p(x) and y=p(x) means?

Accepted Answer

Have you learned about functions and function notation?  If not, I suggest you check out this link:  https://www.mathsisfun.com/sets/function.html

p(x) is function notation.  If you have an equation: ` y = x - 8` and the equation is a function, it can be changed into function notation by swapping the "y" with "p(x)": `p(x) = x - 8`.  So, y and p(x) are equal (or the same thing).  P(x) just gives you more information.  It tells you that the equation is a function called "p" and its input values are defined by the variable "x".

Hope this helps.

Question 7

Is there a time when PEMDAS doesn't apply when dealing with polynomials?

Accepted Answer

PEMDAS applies *every* time you are working with expressions.  This includes polynomial expressions.

Question 8

shouldnt -2 multipled by 2 be -4 not positive 4

Accepted Answer

Yes, it would be.  But, that is not what is happening in the video.  Sal is finding x^2 when x=-2
Remember, x^2 means x*x = (-2)(-2) = +4
Hope this helps.

Algebra (all content)

Course: Algebra (all content) > Unit 10

Evaluating polynomials

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Video transcript