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Explain why the vertical form used in algebra to add $2 x^{2}+4 x+3$ and $5 x^{2}+3 x+6$ is similar to the vertical form used in arithmetic to add 243 and 536

$9 x^{2}+13 x+2$

Algebra

Chapter 5

Exponents and Polynomials

Section 5

Adding and Subtracting Polynomials

Polynomials

Oregon State University

Harvey Mudd College

Lectures

02:34

Explain why the vertical f…

00:51

Use vertical form to add t…

00:46

00:58

Multiply using vertical fo…

01:49

Use vertical form to subtr…

02:23

Use vertical form to multi…

01:58

02:15

01:12

Explain why the distributi…

02:17

01:13

01:06

01:29

03:14

Multiply using (a) the Dis…

01:07

00:53

01:15

Explain why $-x^{4}$ and $…

00:23

Explain why the FOIL metho…

For Exercises 25 to $32,$ …

for being asked to explain why the vertical form of having the polynomial ZX two X squared plus four X plus three plus the polynomial five X squared plus three X plus six is similar to if I was just going to add 243 plus 536 well, think but way back to when you were first learning to add, you would add each of the columns so you would say that three plus six is nine four plus tree is seven and two plus five is seven, but notice when you add each of your columns. Essentially, you're trying to figure out well, how many what is in the ones place, what's in a tense place and what's in the hundreds place. It's very similar to one. We're adding Paulino meals. Essentially, our first are in column the three plus six. We're trying to figure out how many of our constant it's left, which in this case, is positive. Nine. Our middle column is representing how many exes we have in this case for explosives. Three X is equal to positive seven x and our last column were being asked to determine what to act squares and five X squared sits well. That would also be seven x squared. So again, the reason why they're similar is due to the fact that we're adding columns, and we're trying to determine how much of each object is in each place. When we're talking about Paulie, no meals were talking about how many constants, how many ex terms, how many x squared terms versus invaluable addition. We're trying to figure out how many how much is in the ones place or in the tense. Police are in the hundreds place, so that's how they're similar.

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