3)Add: 2x^2+3x+5 ; x^2-2x+3
(^2means square)
Answers
Answer:
3x^2+x+8 is the answer
Answer:
Simplify 3x + 4x
Looking at these two terms, I see that each contains the variable x, and the variable has the same (understood) power of 1 in each term. So these are like terms, and I can combine them.
Back in grade-school arithmetic, "three apples plus four apples" got combined into "seven apples" by adding the three and the four to get seven, and bringing the "apples" along for the ride. In the same way, I will combine these two like terms by adding the numerical portion of each term, while carrying the x along for the ride:
3x + 4x
(3 + 4) x
(7) x
I showed every step above in order to highlight how the terms are being combined. I'm adding the 3 and the 4, and carrying the x along with the numerical result. My answer is:
7x
Content Continues Below
Simplify 2x2 + 3x – 4 – x2 + x + 9
It is often best to group like terms together first, and then simplify:
2x2 + 3x – 4 – x2 + x + 9
(2x2 – x2) + (3x + x) + (–4 + 9)
(2 – 1) x2 + (3 + 1) x + (5)
(1) x2 + (4) x + 5
x2 + 4x + 5
In the second line above, many students find it helpful to write in the understood coefficient of 1 in front of any variable expressions having no written coefficient, as is shown in red below:
(2x2 – x2) + (3x + x) + (–4 + 9)
(2x2 – 1x2) + (3x + 1x) + (–4 + 9)
(2 – 1) x2 + (3 + 1) x + (5)
1x2 + 4x + 5
x2 + 4x + 5
It is not required that the understood 1 be written in when simplifying expressions like this, but many students find this technique to be very helpful, at least when they're starting out. Whatever method helps you consistently complete the simplification correctly is the method you should use.
Simplify 10x3 – 14x2 + 3x – 4x3 + 4x – 6
I will start by grouping the terms according to their degree.
10x3 – 14x2 + 3x – 4x3 + 4x – 6
(10x3 – 4x3) + (–14x2) + (3x + 4x) – 6
6x3 – 14x2 + 7x – 6
Warning: When moving the terms around, remember that the terms' signs move with them. Don't mess yourself up by leaving orphaned "plus" and "minus" signs behind.
If it helps you keep things straight, rewrite the expression like this:
10x3 + (–14x2) + 3x + (–4x3) + 4x + (–6)
By turning the subtractions into additions of negatives, it is clear where the "minus" signs belong, and it's easier to move them correctly:
10x3 + (–4x3) + (–14x2) + 3x + 4x + (–6)
(10 – 4) x3 – 14x2 + (3 + 4) x – 6
...and so forth. Do what works for you.
Simplify 25 – (x + 3 – x2)
The first thing I need to do is take the negative through the parentheses:
25 – (x + 3 – x2)
25 – x – 3 + x2
Okay; these terms are not only not in descending order, they're almost completely backwards! I'll put them the right way 'round, and then simplify by combining the two constants, which are the only like terms:
x2 – x + 25 – 3
x2 – x + 22
Many students, especially when starting out, experience difficulties with the "minus" signs, including when taking them through a parenthetical like I just did above. If it helps you to keep track of what's going on, try putting the "understood" 1 in front of the parentheses (highlighted in red below), and then taking that through onto the terms within:
25 – (x + 3 – x2)
25 – 1(x + 3 – x2)
25 – 1(x) – 1(+3) – 1(–x2)
25 – 1x – 3 + 1x2
1x2 – 1x + 25 – 3
1x2 – 1x + 22
x2 – x + 22
While the first format (without the 1's being written in) is the more "standard" format, either format is mathematically valid. You should use the format that works most successfully for you. Don't be shy about inserting the understood 1 when you're starting out; don't feel bound to continue using it once you get to feeling confident without it.