True or false, the product of two polynomials will be a polynomial regardless of the signs of the leading coefficients of the polynomials. (If false correct the underlining words, regardless of the...

True or false, the product of two polynomials will be a polynomial regardless of the signs of the leading coefficients of the polynomials. (If false correct the underlining words, regardless of the signs) 

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ishpiro | College Teacher | (Level 1) Educator

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True: the product of two polynomials will be a polynomial regardless of the signs of the leading coefficients of the polynomials.

When two polynomials are multiplied, each term of the first polynomial is multiplied by each term of the second polynomial. The multiplication of each pair of terms is performed using the rules of exponents, for example:

`(2x^2)(-3x^3) = -6x^5`

Here, the coefficients are multiplied and the exponents of the powers with the same base are added, according to the rules of exponents.

The result is always a polynomial, regardless what the coefficients might be of any of the terms, including the leading coefficients.

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