To match the given polynomials to their corresponding like items, we need to carefully examine each polynomial and find its appropriate match based on the given descriptions.
Let's break this down step-by-step:
1. Match for [tex]\( 4 x y^3 \)[/tex]:
We are to find the term that corresponds closely to [tex]\( 4 x y^3 \)[/tex]. The term that matches is [tex]\( 8 x y^3 \)[/tex] because it signifies the same variables raised to the same powers but scaled by a different coefficient. Therefore, [tex]\( 4 x y^3 \)[/tex] matches with [tex]\( 8 x y^3 \)[/tex].
→ [tex]\( a \rightarrow 4 \)[/tex]
2. Match for 14 xy:
Next, we consider the term 14 xy. The term that matches this form, but potentially with a different coefficient, is [tex]\( 6 x y \)[/tex]. Hence, 14 xy matches with [tex]\( 6 x y \)[/tex].
→ [tex]\( b \rightarrow 2 \)[/tex]
3. Match for [tex]\( 15 y^2 \)[/tex]:
For [tex]\( 15 y^2 \)[/tex], we look for the term [tex]\( -3 y^2 \)[/tex] since it has the same variable [tex]\( y \)[/tex] raised to the power 2, indicating it’s the correct match. Therefore, [tex]\( 15 y^2 \)[/tex] matches with [tex]\( -3 y^2 \)[/tex].
→ [tex]\( c \rightarrow 5 \)[/tex]
4. Match for -6:
To match -6, we examine the constants. The term here matching is 11. But after subtracting specific values, we're left with 0 which signifies that all cancel out in a balanced equation setting. Thus, -6 matches with 3.
→ [tex]\( d \rightarrow 3 \)[/tex]
5. Match for [tex]\( 5 x^2 \)[/tex]:
Finally, for [tex]\( 5 x^2 \)[/tex], the appropriate match is [tex]\( -12 x^2 \)[/tex], as it signifies the same polynomial but scaled by a different coefficient. Hence, [tex]\( 5 x^2 \)[/tex] matches with [tex]\( -12 x^2 \)[/tex].
→ [tex]\( e \rightarrow 1 \)[/tex]
Therefore, the final matches for the given polynomials are:
a. [tex]\( 4 x y^3 \)[/tex] matches with [tex]\( 8 x y^3 \)[/tex] → [tex]\( 4 \)[/tex]
b. 14 xy matches with [tex]\( 6 x y \)[/tex] → [tex]\( 2 \)[/tex]
c. [tex]\( 15 y^2 \)[/tex] matches with [tex]\( -3 y^2 \)[/tex] → [tex]\( 5 \)[/tex]
d. -6 matches with 3 → [tex]\( 3 \)[/tex]
e. [tex]\( 5 x^2 \)[/tex] matches with [tex]\( -12 x^2 \)[/tex] → [tex]\( 1 \)[/tex]
