To subtract the polynomial [tex]\( (5x^2 + 3) \)[/tex] by the polynomial [tex]\( (2x^2 + 4x - 12) \)[/tex], follow these steps:
1. First, write down the expression for the subtraction of the two polynomials:
[tex]\[
(5x^2 + 3) - (2x^2 + 4x - 12)
\][/tex]
2. Distribute the negative sign across the second polynomial:
[tex]\[
5x^2 + 3 - 2x^2 - 4x + 12
\][/tex]
3. Combine like terms by grouping the [tex]\( x^2 \)[/tex] terms together, the [tex]\( x \)[/tex] terms together, and the constant terms together:
[tex]\[
(5x^2 - 2x^2) + (-4x) + (3 + 12)
\][/tex]
4. Perform the arithmetic operations on the grouped terms:
[tex]\[
3x^2 - 4x + 15
\][/tex]
Therefore, the simplified result of the subtraction is:
[tex]\[ 3x^2 - 4x + 15 \][/tex]
Among the given options, the correct answer is:
[tex]\[ 3x^2 - 4x + 15 \][/tex]
