How do you solve by factoring and using the principle of zero products #x^2 + 7x + 6 = 0#?

Question

How do you solve by factoring and using the principle of zero products  #x^2 + 7x + 6 = 0#?

Eva Abramson · Accepted Answer

#x=-6" or "x=-1# #"using the a-c method"# #"the factors of + 6 which sum to + 7 are + 6 and + 1"# #rArr(x+6)(x+1)=0# #"equate each factor to zero and solve for x"# #x+6=0rArrx=-6# #x+1=0rArrx=-1#

Eli Assouline · Answer

undefined To solve the quadratic equation $x^2 + 7x + 6 = 0$ by factoring and using the principle of zero products, we first factor the quadratic expression:

$x^2 + 7x + 6 = 0$

$(x + 6)(x + 1) = 0$

Now, we use the principle of zero products, which states that if the product of two factors is zero, then at least one of the factors must be zero:

$x + 6 = 0$ or $x + 1 = 0$

Solving each equation for $x$, we get:

For $x + 6 = 0$:
$x = -6$

For $x + 1 = 0$:
$x = -1$

So, the solutions to the equation are $x = -6$ and $x = -1$.

Kennedy Adams · Answer

undefined To solve the quadratic equation $x^2 + 7x + 6 = 0$ by factoring and using the principle of zero products, follow these steps:

1. Write down the quadratic equation: $x^2 + 7x + 6 = 0$.

2. Factor the quadratic expression into two binomial factors. You're looking for two numbers that multiply to give you $6$ and add up to $7$. In this case, those numbers are $6$ and $1$.

$x^2 + 7x + 6 = (x + 6)(x + 1) = 0$.

3. Apply the principle of zero products, which states that if the product of two factors equals zero, then at least one of the factors must be zero.

$x + 6 = 0$ or $x + 1 = 0$.

4. Solve each equation for $x$:

For $x + 6 = 0$:
   $$x = -6.$$

For $x + 1 = 0$:
   $$x = -1.$$

5. Therefore, the solutions to the quadratic equation $x^2 + 7x + 6 = 0$ are $x = -6$ and $x = -1$.