Polynomials - Im stuck help ..step-bystep plz?

Question

(a) Add the Polynomials.

(b) Subtract the lower polynomial from the upper one.

x^2 + 2x -3
3x^2 - 2x - 8

Answer 1

a) (x^2 + 2x - 3) + (3x^2 - 2x - 8)
= x^2 + 2x - 3 + 3x^2 - 2x - 8
= (x^2 + 3x^2) + (2x - 2x) + (-3 - 8)
= 4x^2 - 11

b) (x^2 + 2x - 3) - (3x^2 - 2x - 8)
= x^2 + 2x - 3 - 3x^2 + 2x + 8
= -(x^2 - 3x^2) + (2x + 2x) + (-3 + 8)
= -2x^2 + 4x + 5

Answer 2

You add polynomials by grouping like terms

Example 9: Add and simplify the two polynomials 3 x 2 + 2 x + 7 and 7 x 2 -9 x - 5

Solution

Group like terms together

( 3 x 2 - 2 x + 7 ) + ( 7 x 2 -9 x - 5 }

= (3 x 2 + 7 x 2) +(- 2 x - 9 x) +(7 - 5)

and add them

= 10 x 2 - 11 x + 2



Example 10: Add , subtract and simplify:

( 5 x 4 + 2 x 3 - 8 x 2 - 10 x + 2) + ( 7 x 3 - 9 x 2 - 5 x + 3 ) - ( - x 3 + 2 x 2 - 3 x + 7 )

Solution

Remove parentheses and if a minus sign precedes a perenthesis change signs within it.

( 5 x 4 + 2 x 3 - 8 x 2 - 10 x + 2) + ( 7 x 3 - 9 x 2 - 5 x + 3 ) - ( - x 3 + 2 x 2 - 3 x + 7 ) = 5 x 4 + 2 x 3 - 8 x 2 - 10 x + 2 + 7 x 3 - 9 x 2 - 5 x + 3 + x 3 - 2 x 2 + 3 x - 7

Group like terms

(5 x 4) + (2 x 3 + 7 x 3 + x 3 ) + (- 8 x 2 - 9 x 2 - 2 x 2 ) + ( - 10 x - 5 x + 3 x ) + ( 2 + 3 - 7 )

= 5 x 4 + 10 x 3 - 19 x 2 -12 x - 2

Answer 3

To add simply add like terms: So addition gives:
x^2 + 2x -3
3x^2 - 2x - 8
-----------------
4x^2 -11

To subtract, simply change the signs of the 2nd polynomial and then add the two as above. So,
x^2 + 2x -3
-3x^2 + 2x + 8 <--- Notice all terms have their signs changed
--------------------
-2x^2 +4x +5

Couln't be any simpler, could it?

Answer 4

add line up by power of x

x**2 +2x -3
3 x**2 -2x -8 then add

4x**2 0 -11 so sum is 3x**2-11

similar for subtraction, line up elements and then subtract, whic is just reversing the signs on the bottom one and then adding

x**2 +2x -3
3 x**2 -2x -8

-2x**2 4x 5

Answer 5

a)Add the poly.
4x^2-11
b)Subt. the poly
-2x^2+4x+5

Answer 6

-2x^2 +4x +5

??? :)