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algol [13]
2 years ago
12

Complete the factorization of 3x ^ 2 - 10x + 8 3x^ 2 -10x+8=(x- Box x-4)

Mathematics
1 answer:
aniked [119]2 years ago
5 0

Answer:

3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})

Step-by-step explanation:

The general form of a quadratic polynomial is given by:

ax^2+bx+c    (1)

You have the following polynomial:

3x^2-10x+8    (2)

In order to complete the factorization you can use the quadratic formula, to obtain the roost of the polynomial. The quadratic formula is given by:

x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}    (3)

By comparing the equation (1) with the equation (2) you obtain:

a = 3

b = -10

c = 8

Then, you replace these values in the equation (3):

x_{1,2}=\frac{-(-10)\pm \sqrt{(-10)^2-4(3)(8)}}{2(3)}\\\\x_{1,2}=\frac{10\pm2}{6}\\\\x_1=2\\\\x_2=\frac{4}{3}

Then, the factorization of the polynomial is:

3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})

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