PSAT Math : How to subtract polynomials

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : Polynomial Operations

\(\displaystyle (x^4+7x^2-5x+4)-(-4x^4+5x^3-x^2+3)\)

Possible Answers:

\(\displaystyle -3x^4+5x^3+6x^2-5x+7\)

\(\displaystyle x^4-5x^3+11x^2-5x+1\)

\(\displaystyle 5x^4-5x^3+8x^2-5x+1\)

\(\displaystyle x^4+7x^2-10x+1\)

\(\displaystyle 5x^4+5x^3+6x^2-5x+7\)

Correct answer:

\(\displaystyle 5x^4-5x^3+8x^2-5x+1\)

Explanation:

Step 1: Distribute the negative to the second polynomial:

\(\displaystyle (x^4+7x^2-5x+4)-(-4x^4+5x^3-x^2+3)\)

\(\displaystyle x^4+7x^2-5x+4+4x^2-5x^3+x^2-3\)

Step 2: Combine like terms:

\(\displaystyle x^4+4x^4-5x^3+7x^2+x^2-5x+4-3\)

\(\displaystyle 5x^4-5x^3+8x^2-5x+1\)

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