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Samuel found the difference of the polynomials:

[tex]\[
(15x^2 + 11y^2 + 8x) - (7x^2 + 5y^2 + 2x) = \square x^2 + 6y^2 + 6x
\][/tex]

What value is missing from his solution?
[tex]\(\square\)[/tex]

Sagot :

GinnyAnsweridn
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].
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