Find factors of the quadratic expression: 3v^(2)-6v+3 (?v+?)(v+?)

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Find factors of the quadratic expression: 3v^(2)-6v+3   (?v+?)(v+?)

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Identify Numbers for Factoring: We are given the quadratic expression 3v^2 - 6v + 3 and we need to factor it into the form (av + b)(cv + d). First, we look for two numbers that multiply to give the product of the coefficient of v^2 (which is 3) and the constant term (which is also 3), and add up to give the coefficient of v (which is -6). The product of the coefficient of v^2 and the constant term is 3 * 3 = 9. We need two numbers that multiply to 9 and add up to -6. The numbers that satisfy these conditions are -3 and -3, since (-3) * (-3) = 9 and (-3) + (-3) = -6.Factor Out Common Factor: Now we can write the quadratic expression as a product of two binomials using the numbers we found. The factored form will be (av + b)(cv + d), where a, b, c, and d are the numbers we are looking for. Since the original quadratic has a leading coefficient of 3, we can factor out a common factor of 3 from the expression to make it easier to find the binomials. We can write 3v^2 - 6v + 3 as 3(v^2 - 2v + 1).Factor Quadratic Expression: Next, we factor the quadratic expression inside the parentheses, v^2 - 2v + 1. We already know that the numbers -3 and -3 work for the product and sum, but since we factored out a 3, we need to adjust these numbers. The correct numbers that multiply to 1 (the constant term in the parentheses) and add up to -2 (the coefficient of v in the parentheses) are -1 and -1, since (-1) * (-1) = 1 and (-1) + (-1) = -2. So, the factored form inside the parentheses is (v - 1)(v - 1) or (v - 1)^2.Combine Factored Forms: Finally, we combine the factored form inside the parentheses with the common factor we factored out earlier. The factored form of the original quadratic expression 3v^2 - 6v + 3 is 3(v - 1)^2.

Find factors of the quadratic expression: $3v^{2}-6v+3$ $\newline$ $(?v+?)(v+?)$

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Find factors of the quadratic expression: $3v^{2}-6v+3$ $\newline$ $(?v+?)(v+?)$