Answer:
A = 8
Step-by-step explanation:
Given : Samuel found the difference of two polynomial [tex]15x^2+11y^2+8x\\\\ 7x^2+5y^2+2x\\\\ \text{as}\ Ax^2+6y^2+6x[/tex]
We have to find the value of missing coefficient A in the result so obtained.
Consider
[tex]15x^2+11y^2+8x-\left(7x^2+5y^2+2x\right)[/tex]
We first open parentheses as
[tex]-\left(7x^2+5y^2+2x\right)=-\left(7x^2\right)-\left(5y^2\right)-\left(2x\right)[/tex]
Apply plus - minus rule, [tex]+\left(-a\right)=-a[/tex]
[tex]=-7x^2-5y^2-2x[/tex]
We get,
[tex]=15x^2+11y^2+8x-7x^2-5y^2-2x[/tex]
Grouping like terms, we have,
[tex]=15x^2-7x^2+8x-2x+11y^2-5y^2[/tex]
Simplify, we get,
[tex]=8x^2+6x+6y^2[/tex]
On comparing with Given result , we have A = 8
