QuestionJuly 15, 2025

Add (12x^4+4x^2-5x+8) to (7x^3-2x^2+6x-3)

Add (12x^4+4x^2-5x+8) to (7x^3-2x^2+6x-3)
Add (12x^4+4x^2-5x+8) to (7x^3-2x^2+6x-3)

Solution
4.7(193 votes)

Answer

12x^4 + 7x^3 + 2x^2 + x + 5 Explanation 1. Align Like Terms Arrange the polynomials vertically, aligning like terms. 2. Add Coefficients of Like Terms Add coefficients for each power of x separately: - 12x^4 (no like term) remains 12x^4. - 0x^3 + 7x^3 = 7x^3. - 4x^2 - 2x^2 = 2x^2. - -5x + 6x = 1x. - 8 - 3 = 5.

Explanation

1. Align Like Terms<br /> Arrange the polynomials vertically, aligning like terms.<br /><br />2. Add Coefficients of Like Terms<br /> Add coefficients for each power of $x$ separately:<br />- $12x^4$ (no like term) remains $12x^4$.<br />- $0x^3 + 7x^3 = 7x^3$.<br />- $4x^2 - 2x^2 = 2x^2$.<br />- $-5x + 6x = 1x$.<br />- $8 - 3 = 5$.
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