Answer:
3(x-5)(x-2)
Step-by-step explanation:
First you can take 3 as a common factor:
[tex]3(x^{2} -7x+10)[/tex]
Then you can take two ways:
Use the resolver ecuation to get the roots, or think in two numbers that the sum is -7 and the product is 10.
The only two integers that we can choice are -5 and -2
(-5)*(-2)=10
-5+(-2)=-7
Then you can write the ecuation as a product of its roots:
3 * (x-5) * ( x-2)
And its the same expresion as:
3x^2-21x+30
To be sure you are doing well, solve the product of your solution and you will have the same expresion.
Answer:
3*(x-5)*(x-2)
Step-by-step explanation:
To factorize 3*x^2 - 21*x + 30 we can find the roots with the quadratic formula:
[tex] x = \frac{-b \pm \sqrt{b^2 - 4(a)}(c)}{2(a)} [/tex]
[tex] x = \frac{21 \pm \sqrt{(-21)^2 - 4(3)(30)}}{2(3)} [/tex]
[tex] x = \frac{21 \pm 9}{6} [/tex]
[tex] x_1 = \frac{21 + 9}{6} [/tex]
[tex] x_1 = 5 [/tex]
[tex] x_2 = \frac{21 - 9}{6} [/tex]
[tex] x_2 = 2 [/tex]
The factorized form is [tex] a*(x - x_1)*(x - x_2)[/tex], that is, 3*(x-5)*(x-2)
