Main content

### Course: Algebra (all content) > Unit 10

Lesson 1: Intro to polynomials# Evaluating polynomials

Evaluating 3x²-8x+7 when x=-2. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- how do you find real roots of a polynomial?(12 votes)
- A real root is the x-intercept of your graph. Sal found his answer at the end at timestamp1:08(1 vote)

- Why is subtracting a negative number the same as adding a positive number?(12 votes)
- 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(30 votes)

- 0:31I thought when you multiplied a negative with a positive the product will be negative.(3 votes)
- It's -2 squared. So (-2)(-2), which is a negative times a negative. That equals a positive 4.(3 votes)

- Which factorization of 6p2 + p - 5 is correct ?(2 votes)
- You can use the sum and product method :

The sum is 1 [co efficient of p]

The product is 30 [ (co efficient of p^2) * (constant term)]

Then express the expression in the form : 6p^2+6p-5p-5

Then take the common factor out and do .

6p(p+1)-5(p+1)

Then

(p+1)(6p-5) [Taking out (p+1) as a common factor](1 vote)

- How do you square polynomial?(2 votes)
- 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!(4 votes)

- 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.(2 votes)
- 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.(3 votes)

- What is the least number to be added to 8888 to make it a perfect square(2 votes)
- 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(3 votes)

- I'm slightly confused on what p(x) and y=p(x) means?(2 votes)
- 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.(3 votes)

- Is there a time when PEMDAS doesn't apply when dealing with polynomials?(2 votes)
- PEMDAS applies
**every**time you are working with expressions. This includes polynomial expressions.(2 votes)

- shouldnt -2 multipled by 2 be -4 not positive 4(2 votes)
- 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.(2 votes)

## Video transcript

Evaluate 3x squared
minus 8x plus 7 when x is equal to negative 2. So to evaluate this expression
when x is equal to negative 2, everywhere that we
see an x, we just have to substitute
it with a negative 2. So it would be 3 times,
instead of x squared, it would be 3 times negative
2 squared minus 8 times-- instead of 8 times x, 8
times negative 2 plus 7. And so what does this give us? So we have 3 times
negative 2 squared. Well, that's just positive 4. A negative times a
negative is a positive. Minus 8 times negative
2 is negative 16 plus 7. So 3 times 4 is 12. From that, you're
subtracting negative 16. Subtracting negative
16 is the same thing as adding positive 16. So it's 12 plus 16 plus 7. And so this is equal
to 12 plus 16 is 28. And then if you add
7 to 28, you get 35.