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Subtracting [tex][tex]$3x^2 + 4x - 5$[/tex][/tex] from [tex][tex]$7x^2 + x + 9$[/tex][/tex] results in a polynomial. After subtracting [tex][tex]$4x^2 - 3x$[/tex][/tex] from this polynomial, the difference is [tex]\boxed{\ \ \ }[/tex].

Sagot :

GinnyAnsweridn
To solve this problem, we need to follow two main subtraction steps with polynomials.

Step 1: Subtract [tex]\(3x^2 + 4x - 5\)[/tex] from [tex]\(7x^2 + x + 9\)[/tex]

Start with the first polynomial:
[tex]\[7x^2 + x + 9\][/tex]

Subtract the second polynomial:
[tex]\[3x^2 + 4x - 5\][/tex]

Combining like terms we get:
[tex]\[ (7x^2 - 3x^2) + (x - 4x) + (9 - (-5)) \][/tex]
[tex]\[ = 4x^2 - 3x + 14 \][/tex]

So, after the first subtraction, the resulting polynomial is:
[tex]\[4x^2 - 3x + 14\][/tex]

Step 2: Subtract [tex]\(4x^2 - 3x\)[/tex] from the resulting polynomial [tex]\(4x^2 - 3x + 14\)[/tex]

Take the resulting polynomial from Step 1:
[tex]\[4x^2 - 3x + 14\][/tex]

Subtract the third polynomial:
[tex]\[4x^2 - 3x\][/tex]

Combining like terms we get:
[tex]\[ (4x^2 - 4x^2) + (-3x - (-3x)) + (14 - 0) \][/tex]
[tex]\[ = 0x^2 + 0x + 14 \][/tex]
[tex]\[ = 14 \][/tex]

Thus, the final difference after subtracting [tex]\(4x^2 - 3x\)[/tex] from the resulting polynomial is:
[tex]\[14\][/tex]

So, the correct answer is:
[tex]\[14\][/tex]
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