Match each expression with the correct solution: (8x^4 + 11x^3 - 3x^2) + (6x^3 + 5x^2 - 1) (11x^2 + 4x^3 - 6x) + (10x - 4x) (5x^2 + 9x - 2) + (12x^2 - 14) (6x^4 - 3x^3 - 8x^2) + (2... Match each expression with the correct solution: (8x^4 + 11x^3 - 3x^2) + (6x^3 + 5x^2 - 1) (11x^2 + 4x^3 - 6x) + (10x - 4x) (5x^2 + 9x - 2) + (12x^2 - 14) (6x^4 - 3x^3 - 8x^2) + (2x^4 - 7x^2 - 1) (2x^3 - 7x^2) + (10x^2 + 5x^3 - 2) (7x^3 - 6x^2 + 5) + (3x^2 - 6) Possible Solutions: 7x^3 - 3x^2 - 1 7x^3 + 11x^2 7x^3 + 3x^2 - 2 7x^3 + 4x^2 - 2x + 4 8x^4 + 12x^3 + 5x^2 - 1 8x^4 - 3x^3 - 15x^2 - 1 4x^3 + 11x^2 17x^2 + 9x - 16 17x^2 - 9x - 12 14x^2 + 9x - 10 6x^3 - 3x^2 - 9 8x^4 + 17x^3 + 2x^2 - 1
Understand the Problem
The question is a polynomial addition problem. The task is to match each polynomial expression with its correct simplified solution. Each expression involves adding two polynomials together, and the solutions are provided as possible matches.
Answer
$(8x^4+11x^3-3x^2)+(6x^3+5x^2-1) = 8x^4+17x^3+2x^2-1$ $(11x^2+4x^3-6x) + (10x-4x) = 4x^3+11x^2$ $(5x^2+9x-2)+(12x^2-14) = 17x^2+9x-16$ $(6x^4-3x^3-8x^2)+(2x^4-7x^2-1) = 8x^4-3x^3-15x^2-1$ $(2x^3-7x^2) + (10x^2+5x^3-2) = 7x^3+3x^2-2$ $(7x^3-6x^2+5) + (3x^2-6) = 7x^3-3x^2-1$
Answer for screen readers
$(8x^4+11x^3-3x^2)+(6x^3+5x^2-1) = 8x^4+17x^3+2x^2-1$ $(11x^2+4x^3-6x) + (10x-4x) = 4x^3+11x^2$ $(5x^2+9x-2)+(12x^2-14) = 17x^2+9x-16$ $(6x^4-3x^3-8x^2)+(2x^4-7x^2-1) = 8x^4-3x^3-15x^2-1$ $(2x^3-7x^2) + (10x^2+5x^3-2) = 7x^3+3x^2-2$ $(7x^3-6x^2+5) + (3x^2-6) = 7x^3-3x^2-1$
Steps to Solve
- Simplify $(8x^4+11x^3-3x^2)+(6x^3+5x^2-1)$
Combine like terms: $8x^4 + (11x^3 + 6x^3) + (-3x^2 + 5x^2) - 1 = 8x^4 + 17x^3 + 2x^2 - 1$
- Simplify $(11x^2+4x^3-6x) + (10x-4x)$
Simplify the second term: $10x - 4x = 6x$ Combine like terms: $4x^3 + 11x^2 + (-6x + 6x) = 4x^3 + 11x^2$
- Simplify $(5x^2+9x-2)+(12x^2-14)$
Combine like terms: $(5x^2 + 12x^2) + 9x + (-2 - 14) = 17x^2 + 9x - 16$
- Simplify $(6x^4-3x^3-8x^2)+(2x^4-7x^2-1)$
Combine like terms: $(6x^4 + 2x^4) - 3x^3 + (-8x^2 - 7x^2) - 1 = 8x^4 - 3x^3 - 15x^2 - 1$
- Simplify $(2x^3-7x^2) + (10x^2+5x^3-2)$
Combine like terms: $(2x^3 + 5x^3) + (-7x^2 + 10x^2) - 2 = 7x^3 + 3x^2 - 2$
- Simplify $(7x^3-6x^2+5) + (3x^2-6)$
Combine like terms: $7x^3 + (-6x^2 + 3x^2) + (5 - 6) = 7x^3 - 3x^2 - 1$
$(8x^4+11x^3-3x^2)+(6x^3+5x^2-1) = 8x^4+17x^3+2x^2-1$ $(11x^2+4x^3-6x) + (10x-4x) = 4x^3+11x^2$ $(5x^2+9x-2)+(12x^2-14) = 17x^2+9x-16$ $(6x^4-3x^3-8x^2)+(2x^4-7x^2-1) = 8x^4-3x^3-15x^2-1$ $(2x^3-7x^2) + (10x^2+5x^3-2) = 7x^3+3x^2-2$ $(7x^3-6x^2+5) + (3x^2-6) = 7x^3-3x^2-1$
More Information
Polynomial addition involves combining like terms, where like terms have the same variable raised to the same power.
Tips
A common mistake when adding polynomials is to only add the coefficients, forgetting to include the variable part (e.g., adding $5x^2$ and $3x$ to get $8x^3$ instead of recognizing they cannot be combined). Another common mistake is not paying attention to the signs of the terms. Be careful when adding terms with negative coefficients.
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