Question

Describe the zero product property and explain how tu use it to solve (2x + 10) (x - 7) = 0

Answer 1

Answer:

See below

Step-by-step explanation:

Basically, when you have a product to two factors set equal to 0, you can use the Zero Product Property and make two separate equations, both set equal to 0, to find the roots for each factor:

$2x+10=0\\2x=-10\\x=-5$

$x-7=0\\x=7$

Notice that by plugging these roots back into the equation, either factor will be 0, making the whole expression 0:

$(2x+10)(x-7)=0\\(2(7)+10)(7-7)=0\\(24)(0)=0\\0=0$

$(2x+10)(x-7)=0\\(2(-5)+10)(-5-7)=0\\(0)(-12)=0\\0=0$