HiSET: Math : Polynomials

Study concepts, example questions & explanations for HiSET: Math

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Example Questions

Example Question #1 : Algebraic Concepts

Add these two expressions together: \(\displaystyle 20x^2-14x+23\) and \(\displaystyle -27x^2+30x-41\).

Possible Answers:

\(\displaystyle -47x^2+44x-64\)

\(\displaystyle 7x^2-16x+18\)

\(\displaystyle -7x^2+16x+18\)

\(\displaystyle -7x^2+16x-18\)

Correct answer:

\(\displaystyle -7x^2+16x-18\)

Explanation:

Step 1: Add the terms based on their similarities...

\(\displaystyle 20x^2\) and \(\displaystyle -27x^2\) becomes \(\displaystyle -7x^2\).

\(\displaystyle -14x\) and \(\displaystyle 30x\) becomes \(\displaystyle 16x\).

\(\displaystyle 23\) and \(\displaystyle -41\) becomes \(\displaystyle -18\)

Step 2: Combine all the terms after "becomes" in step 1...

We add and get: \(\displaystyle -7x^2+16x-18\).

Example Question #2 : Algebraic Concepts

Subtract \(\displaystyle 2x^4+12x^3-12x+14\) and \(\displaystyle -3x^4+2x^3-6x^2+7x\).

Possible Answers:

\(\displaystyle 5x^4+10x^3-6x^2-19x+14\)

\(\displaystyle -5x^4-10x^3+6x^2+19x-14\)

\(\displaystyle 5x^4+10x^3-6x^2-19x-14\)

\(\displaystyle 5x^4-10x^3+6x^2+19x-14\)

Correct answer:

\(\displaystyle 5x^4+10x^3-6x^2-19x+14\)

Explanation:

Step 1: Subtract these terms by separating by exponents...

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

\(\displaystyle 12x^3-2x^3=10x^3\)

\(\displaystyle -6x^2\)

\(\displaystyle -12x-(7x)=-12x-7x=-19x\)

\(\displaystyle +14\)

Step 2: Add all the simplified terms together...

\(\displaystyle 5x^4+10x^3-6x^2-19x+14\)

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