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Add the polynomials: (– 10x4 + 7a – 5) + ( – 12æ³ – 7æ² + 4)

Add the polynomials: (– 10x4 + 7a – 5) + ( – 12æ³ – 7æ² + 4)

Elementary Algebra
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter6: Polynomials
Section6.1: Add And Subtract Polynomials
Problem 6.18TI: Subtract: (x25x8) from (6x2+9x1) .
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**Add the polynomials:** \[ (-10x^4 + 7x^3 - 5) + (-12x^3 - 7x^2 + 4) \] This problem involves the addition of two polynomials. To solve this, combine like terms by adding the coefficients of terms with the same degree. 1. **Identify Like Terms:** - \( x^4 \): \(-10x^4 \) - \( x^3 \): \(7x^3 + (-12x^3)\) - \( x^2 \): \(-7x^2\) - Constant terms: \(-5 + 4\) 2. **Combine Like Terms:** - \( -10x^4 \) stays the same as there are no other \( x^4 \) terms. - \( 7x^3 + (-12x^3) = -5x^3 \) - \(-7x^2 \) - \(-5 + 4 = -1\) 3. **Write the Simplified Polynomial:** - \(-10x^4 - 5x^3 - 7x^2 - 1\) The simplified expression is: \[ -10x^4 - 5x^3 - 7x^2 - 1 \]
Transcribed Image Text:**Add the polynomials:** \[ (-10x^4 + 7x^3 - 5) + (-12x^3 - 7x^2 + 4) \] This problem involves the addition of two polynomials. To solve this, combine like terms by adding the coefficients of terms with the same degree. 1. **Identify Like Terms:** - \( x^4 \): \(-10x^4 \) - \( x^3 \): \(7x^3 + (-12x^3)\) - \( x^2 \): \(-7x^2\) - Constant terms: \(-5 + 4\) 2. **Combine Like Terms:** - \( -10x^4 \) stays the same as there are no other \( x^4 \) terms. - \( 7x^3 + (-12x^3) = -5x^3 \) - \(-7x^2 \) - \(-5 + 4 = -1\) 3. **Write the Simplified Polynomial:** - \(-10x^4 - 5x^3 - 7x^2 - 1\) The simplified expression is: \[ -10x^4 - 5x^3 - 7x^2 - 1 \]
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