The product will be 2x³ - 11x² + 16x - 3.
How to multiply two polynomials?
In order to multiply two polynomials, we have to multiply every term of one polynomial with every term of other polynomial.
So according to asked question,
(x − 3)(2x² − 5x + 1)
= x(2x² − 5x + 1)-3(2x² − 5x + 1) using Multiplicative Distribution Law
=x*2x² −x*5x + x*1 -3*2x²−(-3)*5x +(-3)1 using Multiplicative Distribution Law
=2x³-5x²+x-6x²+15x-3
=2x³-5x²-6x²+x+15x-3 (reodering and gathering like terms)
=2x³-11x²+16x-3
Therefore the product will be (x − 3)(2x² − 5x + 1)=2x³-11x²+16x-3
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