To find the missing value in the polynomial expression given by Samuel, we need to perform the subtraction of the two polynomials step-by-step.
First, let's write down the two polynomials clearly:
[tex]\[ P_1 = 15x^2 + 11y^2 + 8x \][/tex]
[tex]\[ P_2 = 7x^2 + 5y^2 + 2x \][/tex]
We need to subtract [tex]\( P_2 \)[/tex] from [tex]\( P_1 \)[/tex]:
[tex]\[ P_1 - P_2 = (15x^2 + 11y^2 + 8x) - (7x^2 + 5y^2 + 2x) \][/tex]
We perform the subtraction term-by-term:
1. Subtract the coefficients of [tex]\( x^2 \)[/tex]:
[tex]\[ 15x^2 - 7x^2 = 8x^2 \][/tex]
2. Subtract the coefficients of [tex]\( y^2 \)[/tex]:
[tex]\[ 11y^2 - 5y^2 = 6y^2 \][/tex]
3. Subtract the coefficients of [tex]\( x \)[/tex]:
[tex]\[ 8x - 2x = 6x \][/tex]
Putting it all together, we have:
[tex]\[ P_1 - P_2 = 8x^2 + 6y^2 + 6x \][/tex]
So, the missing value in Samuel's solution is the coefficient of [tex]\( x^2 \)[/tex], which is 8.
Thus, the complete polynomial difference is:
[tex]\[ 8x^2 + 6y^2 + 6x \][/tex]
The missing value is [tex]\( 8 \)[/tex].
