Factor completely.3, x, squared, minus, 10, x, plus, 73x 2 −10x+7
Question
Factor completely.3, x, squared, minus, 10, x, plus, 73x 2 −10x+7
Solution
The expression you provided seems to have a typo. It should probably be "3x^2 - 10x + 7". Let's factor this quadratic equation.
The quadratic equation is in the form ax^2 + bx + c. Here, a = 3, b = -10, and c = 7.
We need to find two numbers that multiply to (a*c) = 21 and add up to b = -10.
Those two numbers are -7 and -3 because -7*-3 = 21 and -7 + -3 = -10.
So, we can write -10x as -7x - 3x. Now, the equation becomes:
3x^2 - 7x - 3x + 7
Now, we can factor by grouping:
x(3x - 7) - 1(3x - 7)
Now, you can see that (3x - 7) is a common factor. So, this can be factored out, giving the final factored form of the equation:
(3x - 7)(x - 1)
So, the expression 3x^2 - 10x + 7 factors to (3x - 7)(x - 1).
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