The product of two polynomials is 3x^3 - x^2 | vedclass

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(B) Let the given product be $P(x) = 3x^3 - x^2 - 3x + 1$ and one polynomial be $A(x) = 3x^2 + 2x - 1$.To find the other polynomial $B(x)$,we divide $

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$x-1$

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(B) Let the given product be $P(x) = 3x^3 - x^2 - 3x + 1$ and one polynomial be $A(x) = 3x^2 + 2x - 1$.To find the other polynomial $B(x)$,we divide $P(x)$ by $A(x)$:$B(x) = \frac{3x^3 - x^2 - 3x + 1}{3x^2 + 2x - 1}$Performing polynomial long division:$1$. Divide $3x^3$ by $3x^2$ to get $x$.$2$. Multiply $x$ by $(3x^2 + 2x - 1)$ to get $3x^3 + 2x^2 - x$.$3$. Subtract this from $P(x)$: $(3x^3 - x^2 - 3x + 1) - (3x^3 + 2x^2 - x) = -3x^2 - 2x + 1$.$4$. Divide $-3x^2$ by $3x^2$ to get $-1$.$5$. Multiply $-1$ by $(3x^2 + 2x - 1)$ to get $-3x^2 - 2x + 1$.$6$. Subtracting this gives a remainder of $0$.Thus,the other polynomial is $x - 1$.

The product of two polynomials is $3x^3 - x^2 - 3x + 1$ and one of the polynomials is $3x^2 + 2x - 1$. Find the other polynomial.

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