The process of solving by factoring is all about breaking down an equation into its individual factors, equating each one to zero, and then solving for the variable. This technique is often seen in the world of quadratic equations, but it's not limited to them - it can be used for any polynomial equation. The principle it depends on is the zero product property, which states that if the product of a and b equals zero, then either a or b must equal zero.
| Topic | Problem | Solution |
|---|---|---|
| None | $4 b^{2}+8 b+7=4$ | The given equation is a quadratic equation in the form of \(ax^2 + bx + c = 0\). We can solve this … |
| None | Question find out the value of $x: x^{\wedge} 2-1… | A questão está pedindo para resolver a equação \(x^2 - 1 = 0\). Esta é uma equação quadrática simpl… |
| None | $x^{2}-6 x+5=0$ | We are given the quadratic equation \(x^{2}-6 x+5=0\). |
| None | Solve for $x$. \[ 5 x^{2}-3=14 x \] If there is m… | Rearrange the equation to the form of \(ax^2 + bx + c = 0\), which gives us \(5x^2 - 14x - 3 = 0\). |
| None | $3 x^{2}-108=0$ | We are given the quadratic equation \(3x^{2} - 108 = 0\). |
| None | Solve the equation by the square root property. I… | Given the equation \(5x^{2}=55\). |
| None | Two numbers multiply to be 20 and add to be 12 . … | Set up the equations as \(x*y=20\) and \(x+y=12\). |
| None | A ball is thrown from an initial height of 4 feet… | Given the equation for the height of the ball is \(h=4+29t-16t^2\), we need to find the time \(t\) … |
| None | An astronaut on the moon throws a baseball upward… | We are given the height of the ball as a function of time, \(s = -2.7t^2 + 40t + 6.5\), where \(s\)… |
| None | Solve $x^{2}=25$, where $x$ is a real number. Sim… | The given equation is a simple quadratic equation, $x^{2}=25$, where $x$ is a real number. |
| None | a) $x^{2}-5 x+6=0$ | Esta é uma equação quadrática na forma de \(ax^{2}+bx+c=0\). As raízes da equação podem ser encontr… |
| None | $x^{2}-25=0$ | Given the quadratic equation \(x^{2}-25=0\). |
| None | $-3$. Something's Fishy The Survivors are quickly… | Rewrite the equation in factored form: \(N = -2x(x - 28)\) |
| None | a) $4 x^{2}+3 x=0$ | Factor out an x from the equation: \(x(4x + 3) = 0\) |
| None | $x^{2}-5 x-6=0$ | Given the quadratic equation: \(x^2 - 5x - 6 = 0\) |
| None | $1 x^{2}+6 x+9=0$ | Given the quadratic equation: \(x^2 + 6x + 9 = 0\) |
| None | $x^{2}-16=0$ | Solve the quadratic equation \(x^2 - 16 = 0\) by factoring. |
| None | a $x^{2}-10 x+25=0$ | Given the quadratic equation: \(x^{2}-10x+25=0\) |
| None | a) $x^{2}-2=2 x-4$ | Rewrite the equation in the standard form: \(x^2 - 2x - 2 = 0\) |
| None | Exercise 12 1. In the diagram, the graphs of $y=x… | a) To solve the equation $x^2 - 2x - 3 = -2$, we can rewrite it as $x^2 - 2x - 1 = 0$ |
| None | a) $-3 t^{2}+t=0$ | Solve the equation: \(-3t^2 + t = 0\) |
| None | Solve the equation for $x$ : \[ x^{2}+17 x+60=0 \] | Given the quadratic equation: \(x^2 + 17x + 60 = 0\) |
| None | Solve \( x^{2}=81 \), where \( x \) is a real num… | \( x^2 = 81 \) |
| None | \( x^{2}+x-20=0 \) | \( (x-4)(x+5)=0 \) |
| None | (3) \( 4 x^{2}-36=0 \) | \( 4x^{2} - 36 = 0 \) |
| None | find out the value of \( x: x^{\wedge} 2-1=0 \) | \( x^{2} - 1 = 0 \) |
| None | find out the value of \( x: x^{\wedge} 2-1=n d \)… | To solve the quadratic equation x^2-1=0: |