Sure, let's match each pair of polynomials to their respective sums step-by-step:
1. [tex]\( 12x^2 + 3x + 6 \)[/tex] and [tex]\( -7x^2 - 4x - 2 \)[/tex]
- To find the sum, we combine the like terms:
- [tex]\( 12x^2 - 7x^2 = 5x^2 \)[/tex]
- [tex]\( 3x - 4x = -x \)[/tex]
- [tex]\( 6 - 2 = 4 \)[/tex]
- This results in [tex]\( 5x^2 - x + 4 \)[/tex]
2. [tex]\( 2x^2 - x \)[/tex] and [tex]\( -x - 2x^2 - 2 \)[/tex]
- To find the sum, we combine the like terms:
- [tex]\( 2x^2 - 2x^2 = 0 \)[/tex]
- [tex]\( -x - x = -2x \)[/tex]
- There are no constants in the first polynomial, so the constant remains [tex]\( -2 \)[/tex]
- This results in [tex]\( -2x - 2 \)[/tex]
3. [tex]\( x + x^2 + 2 \)[/tex] and [tex]\( x^2 - 2 - x \)[/tex]
- To find the sum, we combine the like terms:
- [tex]\( x^2 + x^2 = 2x^2 \)[/tex]
- [tex]\( x - x = 0 \)[/tex]
- [tex]\( 2 - 2 = 0 \)[/tex]
- This results in [tex]\( 2x^2 \)[/tex]
4. [tex]\( x^2 + x \)[/tex] and [tex]\( x^2 + 8x - 2 \)[/tex]
- To find the sum, we combine the like terms:
- [tex]\( x^2 + x^2 = 2x^2 \)[/tex]
- [tex]\( x + 8x = 9x \)[/tex]
- There are no constants in the first polynomial, so the constant remains [tex]\( -2 \)[/tex]
- This results in [tex]\( 2x^2 + 9x - 2 \)[/tex]
Matching the polynomials to their sums:
- [tex]\( 12x^2 + 3x + 6 \)[/tex] and [tex]\( -7x^2 - 4x - 2 \)[/tex] sum to [tex]\( 5x^2 - x + 4 \)[/tex]
- [tex]\( 2x^2 - x \)[/tex] and [tex]\( -x - 2x^2 - 2 \)[/tex] sum to [tex]\( -2x - 2 \)[/tex]
- [tex]\( x + x^2 + 2 \)[/tex] and [tex]\( x^2 - 2 - x \)[/tex] sum to [tex]\( 2x^2 \)[/tex]
- [tex]\( x^2 + x \)[/tex] and [tex]\( x^2 + 8x - 2 \)[/tex] sum to [tex]\( 2x^2 + 9x - 2 \)[/tex]
So the matched pairs are:
1. [tex]$12 x^2+3 x+6$[/tex] and [tex]$-7 x^2-4 x-2$[/tex] ⟶ [tex]$5 x^2-x+4$[/tex]
2. [tex]$2 x^2-x$[/tex] and [tex]$-x-2 x^2-2$[/tex] ⟶ [tex]$-2 x-2$[/tex]
3. [tex]$x+x^2+2$[/tex] and [tex]$x^2-2-x$[/tex] ⟶ [tex]$2 x^2$[/tex]
4. [tex]$x^2+x$[/tex] and [tex]$x^2+8 x-2$[/tex] ⟶ [tex]$2 x^2+9 x-2$[/tex]
