Similarly, if the polynomial is of a quadratic expression, we can use the quadratic equation to find the roots/factor of a given expression. can sometimes be factorised into two brackets in the form of ((x + a)(x + b)) where (a) and (b) can be any term, positive. Apart from these methods, we can factorise the polynomials by the use of general algebraic identities. This multiplication and simplification demonstrates why, to factor a quadratic, well need to start by finding the two numbers (being the p and the q above) that add up to equal b, where. In the above, (p + q) b and pq c from x2 + bx + c. Guess and Check Example: what are the factors of 2x2 + 7x + 3 No common factors. We can multiply the binomials like this: ( x + p) ( x + q) x2 + p x + q x + pq. But no need to worry, we include more complex examples in the next section. We simply must determine the values of r1 r1 and r2 r2. Factoring relies on the fact that if ab 0, then a 0 or b 0. In these cases, solving quadratic equations by factoring is a bit simpler because we know factored form, y (x-r1) (x-r2) y (xr1)(xr2), will also have no coefficients in front of x x. We can use the zero-product property to solve quadratic equations in which we first have to factor out the greatest common factor (GCF), and for equations that have special factoring formulas as well, such as the difference of squares, both of which we will see later in this section. For example, 2x 2 is a quadratic expression as the power of x is 2. The factors are 2x and 3x 1, We can now also find the roots (where it equals zero): 2x is 0 when x 0 3x 1 is zero when x 1 3 And this is the graph (see how it is zero at x0 and x 1 3 ): But it is not always that easy. There are three primary methods for solving quadratic equations: Factoring, Completing the Square, and the Quadratic Formula. Now its your turn to solve a few equations on your own. For example, equations such as 2+x - 6=0 is in standard form. The complete solution of the equation would go as follows: x 2 3 x 10 0 ( x + 2) ( x 5) 0 Factor. An equation containing a second-degree polynomial is called a quadratic equation.
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