Question

Could you help me with how to multiply polynomials(5x - 1)(2x^2 -3x + 4)

Answer 1

`(5x\: -\: 1)(2x^2\: -3x\: +\: 4)=10x^3-17x^2+23x-4`

Explanation:

We have the following multiplication of polynomials:

`\mleft(5x-1\mright)\mleft(2x^2-3x+4\mright)`

When multiplying two polynomials we must bear in mind that all the terms of the first polynomial must be multiplied by all the terms of the second polynomial, like this:

`\begin{gathered} \mleft(5x-1\mright)\mleft(2x^2-3x+4\mright)=5x\cdot2x^2+5x\cdot-3x+5x\cdot4+(-1)\cdot2x^2+(-1)\cdot-3x+(-1)\cdot4 \\ (5x\: -\: 1)(2x^2\: -3x\: +\: 4)=10x^3-15x^2+20x-2x^2+3x-4 \\ (5x\: -\: 1)(2x^2\: -3x\: +\: 4)=10x^3-17x^2+23x-4 \end{gathered}`