Question

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Answer 1

Given

• 2 - 3x²
• 2x - x³
• 1 - 3x + x²

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To do

• Add the given polynomials.

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Solution

Bring all the polynomials into one expression.

⇒ (2 - 3x²) + (2x - x³) + (1 - 3x + x²)

⇒ 2 - 3x² + 2x - x³ + 1 - 3x + x²

Now, let's simplify the following expression, step-by-step

2 - 3x² + 2x - x³ + 1 - 3x + x²

Step 1: Combine like terms.

⇒ 2 - 3x² + 2x - x³ + 1 - 3x + x²

⇒ 2 + 1 - 3x² + x² + 2x - 3x - x³

⇒ 3 - 2x² - x - x³

∴ After adding the given polynomials we get '3 - 2x² - x - x³'

∴ (2 - 3x²) + (2x - x³) + (1 - 3x + x²) = 3 - 2x² - x - x³

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Additional Information

• An algebraic expression is a mathematical sentence which consists of both variables and constants.
• An algebraic expression doesn't consist of an equal to sign.
• We can't find the value of the variables in an algebraic expression
• Variables may vary in their values. We use small English alphabets to represent them. For example ⇒ x, y, z, p
• Constants have a fixed value.

• An algebraic equation is a mathematical sentence which consists of variables, constants and an equal to sign.
• We can find the value of the variables present in an algebraic expression.
• A linear equation is a type of equation that consists of variables and constants. The highest power of the variable is '1'.
• We use the quadratic formula to solve a quadratic equation.
• Quadratic Formula ⇒ $\dfrac{-b\± \sqrt{b^{2}-4ac}}{2a}$

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