Question

Answer 1

1) \(2x^2-8x=0\)

\(\Rightarrow2x\left(x-4\right)=0\)\(\Rightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)

2) \(\Rightarrow3\left(x-7\right)\left(x+2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=7\\x=-2\end{matrix}\right.\)

3) \(\Rightarrow x\left(x-3\right)+5\left(x-3\right)=0\)

\(\Rightarrow\left(x-3\right)\left(x+5\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-5\end{matrix}\right.\)

Answer 2

1. 2x² - 8x = 0

<=> 2x(x - 4) = 0

<=> \(\left[{}\begin{matrix}2x=0\\x-4=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)

2. 3x(x - 7) - 6(7 - x) = 0

<=> 3x(x - 7) + 6(x - 7) = 0

<=> (3x + 6)(x - 7) = 0

<=> \(\left[{}\begin{matrix}3x+6=0\\x-7=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=2\\x=7\end{matrix}\right.\)

c. x² + 2x - 15 = 0

<=> x² + 5x - 3x - 15 = 0

<=> x(x + 5) - 3(x + 5) = 0

<=> (x - 3)(x + 5) = 0

<=> \(\left[{}\begin{matrix}x-3=0\\x+5=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=3\\x=-5\end{matrix}\right.\)