b-squared plus 5b plus 1 is an expression: not an equation or inequality. There is, therefore, nothing that can be solved.
Second, the expression does not have real factors. It makes no sense to use product (factor) and sum to find complex factors. Using the quadratic formula or completing the squares are far simpler.
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(3x+4)(3x-4)=0 x=±4/3
The zero product property is used to solve equations using factoring. Ex x2 + 5x = 4 .... 1st rearrange to = 0 x2 - 3x- 4 = 0 .... now factor left side (x-4)(x+1) = 0 .... now make 2 separate equations and solve x-4 = 0 so x = 4 .... x+1 = 0 so x = -1
To factor the polynomial x^3 - 2x^2 - 3x, we first need to find its roots. We can do this by using synthetic division or factoring by grouping. Once we find a root, we can then factor out the corresponding linear factor and apply the remaining steps of long division or factoring by grouping to obtain the remaining quadratic factor.
Yes, however not all quadratic equations can easily be solved by factoring, sometimes you can factor and sometimes it is easier to use the quadratic formula. Example: x2 + 4x + 4 This can be easily factored to (x + 2)(x +2) Therefore the answer is -2 by setting x +2 = 0 and solving for x This can be done using the quadratic equation and you would get the same results, however, it was much faster to factor instead.
A quick outline of the module. Topics to by taught/ but no explainations, examples,etc. Example... It may state that students will be learning how to solve quadatic equations by graphing, factoring, completing the square, and using the quadratic formula.