Polynomials Math Example 3

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Example 3

medium
Multiply (2x+3)(x2−x+4)(2x + 3)(x^2 - x + 4).

Solution

  1. 1
    Step 1: Distribute 2x2x across (x2−x+4)(x^2 - x + 4): 2x⋅x2+2x⋅(−x)+2x⋅4=2x3−2x2+8x2x \cdot x^2 + 2x \cdot (-x) + 2x \cdot 4 = 2x^3 - 2x^2 + 8x.
  2. 2
    Step 2: Distribute 33 across (x2−x+4)(x^2 - x + 4): 3⋅x2+3⋅(−x)+3⋅4=3x2−3x+123 \cdot x^2 + 3 \cdot (-x) + 3 \cdot 4 = 3x^2 - 3x + 12.
  3. 3
    Step 3: Combine like terms: 2x3+(−2x2+3x2)+(8x−3x)+12=2x3+x2+5x+122x^3 + (-2x^2 + 3x^2) + (8x - 3x) + 12 = 2x^3 + x^2 + 5x + 12.

Answer

2x3+x2+5x+122x^3 + x^2 + 5x + 12
To multiply a binomial by a trinomial, distribute each term of the binomial across every term of the trinomial, then combine like terms. The degree of the product equals the sum of the degrees of the factors.

About Polynomials

An expression built by adding terms that consist of constants multiplied by variables raised to non-negative integer powers.

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More Polynomials Examples

Example 1 easy

What is the degree of the polynomial [formula]?

Example 2 medium

Add the polynomials [formula] and [formula].

Example 4 easy

Classify [formula] by degree and number of terms.

Example 5 medium

Subtract [formula] from [formula].

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