1) If f(x) = -3x⁴ - 2x³ + 3x²
If g(x) = 3x⁴ - 4x³ + x²
Set the equation:
f(x) + g(x) = (-3x⁴ - 2x³ + 3x²) + (3x⁴ - 4x³ + x²)
Rearrange from greatest power sign to the least:
f(x) + g(x) = -3x⁴ + 3x⁴ - 2x³ - 4x³ + 3x² + x²
Combine like terms (terms with the same amount of variables):
f(x) + g(x) = (-3x⁴ + 3x⁴) + (-2x³ - 4x³) + (3x² + x²)
f(x) + g(x) = (0) + (-6x³) + (4x²)
f(x) + g(x) = -6x³ + 4x²
B) -6x³ + 4x² is your answer.
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2) If s(x) = 2x² + 3x - 4
If t(x) = x + 4
Set the equation:
s(x) * t(x) = (2x² + 3x - 4) * (x + 4)
To solve for multiplication, choose a parenthesis. Distribute each term within that parenthesis to all terms within the other.
s(x) * t(x) = 2x²(x + 4) + 3x(x + 4) - 4(x + 4)
Simplify.
s(x) * t(x) = 2x³ + 8x² + 3x² + 12x - 4x - 16
Combine like terms.
s(x) * 5(x) = 2x³ + 11x² + 8x - 16
A) 2x³ + 11x² + 8x - 16 is your answer.
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