Question

What would happen if we multiply P(x) = x² - 2x and R(x) = 2x + 1?

a) Division
b) Addition
c) Subtraction
d) Multiplication

Answer 1

Multiplying the polynomials P(x) = x² - 2x and R(x) = 2x + 1 using the distributive property results in 2x³ - 3x² - 2x.

Step-by-step explanation:

When we multiply P(x) = x² - 2x and R(x) = 2x + 1, we perform a multiplication of two polynomials. To multiply these two expressions, we need to use the distributive property, also known as the FOIL method (First, Outer, Inner, Last), to combine each term from the first polynomial with each term from the second polynomial.

The result of multiplying these polynomials will be:

• x² multiplied by 2x, which gives 2x³,
• x² multiplied by 1, which gives x²,
• -2x multiplied by 2x, which gives -4x²,
• -2x multiplied by 1, which gives -2x.

Now, we combine like terms:

1. 2x³ (no like term to combine with),
2. x² - 4x² gives -3x²,
3. -2x (no like term to combine with).

So the final result after multiplying P(x) by R(x) is 2x³ - 3x² - 2x.