Home > Algebra > Multiplication of Polynomials by Binomials

How do you expand and simplify #f(x) = (x-1)(x+3)(x-5)#?

Answer 1

=#x^3 -3x^2 -13x+15#

Multiply two of the brackets together first, then multiply that answer by the third bracket. You can use any order. Trying to multiply them all at the same time is very complicated.

#(x-1)(x+3)(x-5)# =#(x-1)(x^2 -5x+3x-15) " collect like terms"# =#(x-1))(x^2-2x -15)# =#x^3 -2x^2 -15x-x^2 +2x+15 " collect like terms"# =#x^3 -3x^2 -13x+15#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Hazel Anglin

To expand and simplify the expression ( f(x) = (x-1)(x+3)(x-5) ), you can use the distributive property to multiply the terms together. First, multiply the binomials ( (x-1) ) and ( (x+3) ), then multiply the result by ( (x-5) ). After expanding, you can combine like terms to simplify the expression.

( f(x) = (x-1)(x+3)(x-5) ) ( f(x) = (x^2 - x + 3x - 3)(x-5) ) ( f(x) = (x^2 + 2x - 3)(x-5) ) ( f(x) = x^3 - 5x^2 + 2x^2 - 10x - 3x + 15 ) ( f(x) = x^3 - 3x^2 - 13x + 15 )

Therefore, the expanded and simplified form of ( f(x) = (x-1)(x+3)(x-5) ) is ( f(x) = x^3 - 3x^2 - 13x + 15 ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.