Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial? Create a sample problem that has a binomial which IS a factor of the polynomial being divided, and another problem that has a binomial which is NOT a factor of the polynomial being divided.

Question

Mathematics

Ezra Bright

11 February, 20:07

Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial? Create a sample problem that has a binomial which IS a factor of the polynomial being divided, and another problem that has a binomial which is NOT a factor of the polynomial being divided.

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Heidy Irwin · Answer 1

The divisor is a factor if you get the remainder zero after division.

Just as you know that 4 is a factor of 16 because 16/4 has zero remainder.

For example,

(2x-1) (x+2) (3x+7) / (x+2)

= (6x^3+23x^2+15x-14) / (x+2)

we know that the remainder is zero, because we constructed it that way. To make that a fraction where the divisor is NOT a factor, just change any of the coefficients. Then the divisor will no longer go in evenly.