Use the zero product rule to solve the following equations for xx. (x−5)(x+3)=0\left(x-5\right)\left(x+3\right)=0

x = 5 x=5 x = 5 or x = − 3 x=-3 x = − 3

Use the zero product rule to solve the following equations for x x . ( x − 5 ) ( x + 3 ) = 0 \left(x-5\right)\left(x+3\right)=0

This problem is asking us to solve the following equation for x using the zero product rule. Now remember the zero product rule simply says that any number multiplied by zero is going to equal zero. So if I plug in a value for x into this equation that turns our first factor into zero, then the whole thing is going to equal zero. And same thing for our second factor, if I plug a value into x into this equation that turns this factor into zero, then the whole thing is going to equal zero. So to solve this problem, we're going to take each of our factors, x minus five and x plus three, and set them equal to zero and solve for x. So for our first factor we'll add five to both sides and we get x equals five as one of our solutions. And for our second factor we're subtract three from both sides and we get x equals negative three as our second solution. And we could always take these solutions and plug them back into our original equation four x to check that they are correct.

Use the zero product rule to solve the following equations for x x . ( x − 5 ) ( x + 3 ) = 0 \left(x-5\right)\left(x+3\right)=0

x = 5 x=5 x = 5 or x = − 3 x=-3 x = − 3

x = − 5 x=-5 x = − 5 or x = − 3 x=-3 x = − 3

x = 5 x=5 x = 5 or x = 3 x=3 x = 3

x = − 5 x=-5 x = − 5 or x = 3 x=3 x = 3

7. Factoring

Quadratic Equations & Applications

Intermediate Algebra

7. Factoring

Quadratic Equations & Applications

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Multiple Choice

Use the zero product rule to solve the following equations for $x$ .
$(x - 5) (x + 3) = 0$

$x=-5$ or $x=-3$

$x=5$ or $x=3$

$x=-5$ or $x=3$

$x=5$ or $x=-3$

Verified step by step guidance

Identify the given equation: $\left(x-5\right)\left(x+3\right) = 0$.

Recall the zero product rule, which states that if the product of two factors is zero, then at least one of the factors must be zero. So, set each factor equal to zero: $x - 5 = 0$ and $x + 3 = 0$.

Solve the first equation $x - 5 = 0$ by adding 5 to both sides to isolate $x$: $x = 5$.

Solve the second equation $x + 3 = 0$ by subtracting 3 from both sides to isolate $x$: $x = -3$.

Conclude that the solutions to the equation are $x = 5$ or $x = -3$.

4:41m

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