Question

How can I rewrite y = .07x(x - 4)(x - 6)(x - 10)² in standard form? Please show steps, thank you!

Answer 1

`y=(0.07x)\cdot(x-4)\cdot(x-6)\cdot(x-10)^2`

The standard form of a polynomial is given by the order of the terms making sure that the term with the highest degree is placed first.

start expanding the square term

`y=(0.07x)\cdot(x-4)\cdot(x-6)\cdot(x^2-20x+100)`

then, multiply the first two terms

`y=(0.07x^2-0.28x)\cdot(x-6)\cdot(x^2-20x+100)`

continue multiplying the next two terms

`y=(0.07x^3-0.42x^2-0.28x^2+1.68x)\cdot(x^2-20x+100)`

simplify and organize the terms

`y=(0.07x^3-0.7x^2+1.68x)\cdot(x^2-20x+100)`

solve the final product

`\begin{gathered} y=0.07x^3\cdot(x^2-20x+100)-0.7x^2\cdot(x^2-20x+100)+1.68x\cdot(x^2-20x+100) \\ y=0.07x^5-1.4x^4+7x^3-0.7x^4+14x^3-70x^2+1.68x^3-33.6x^2-168x \end{gathered}`

group alike terms

`y=0.07x^5-2.1x^4+22.68x^3-103.6x^2+168x`