Factor completely. 4x^(2)-28 x+40=

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Factor completely.  4x^(2)-28 x+40=

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Identify quadratic trinomial form: Identify the quadratic trinomial and its form. The given expression is 4x^2 - 28x + 40. This is a quadratic trinomial of the form ax^2 + bx + c.Find two numbers for multiplication and addition: Find two numbers that multiply to ac (the product of the coefficient of x^2 and the constant term) and add up to b (the coefficient of x). For the given expression, a = 4, b = -28, and c = 40. We need to find two numbers that multiply to 4 * 40 = 160 and add up to -28.Find the two numbers: Find the two numbers. The two numbers that multiply to 160 and add up to -28 are -20 and -8. Check: (-20) * (-8) = 160 and (-20) + (-8) = -28.Rewrite middle term using two numbers: Rewrite the middle term using the two numbers found in Step 3. Rewrite -28x as -20x - 8x. The expression now looks like this: 4x^2 - 20x - 8x + 40.Factor by grouping: Factor by grouping. Group the terms into two pairs: (4x^2 - 20x) and (-8x + 40). Factor out the greatest common factor from each pair. From the first pair, factor out 4x: 4x(x - 5). From the second pair, factor out -8: -8(x - 5). The expression now looks like this: 4x(x - 5) - 8(x - 5).Factor out common binomial factor: Factor out the common binomial factor. The common binomial factor is (x - 5). Factor this out to get: (x - 5)(4x - 8).Simplify second factor: Simplify the second factor if possible. The second factor 4x - 8 can be further factored by taking out the common factor of 4. This gives us: 4(x - 2).Write final factored form: Write the final factored form of the expression. The final factored form of the expression is (x - 5)(4)(x - 2).

Factor completely. $\newline$ $4x^{2}-28x+40=$

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Factor completely.\newline4x2−28x+40=4x^{2}-28x+40=4x2−28x+40=

Factor completely. $\newline$ $4x^{2}-28x+40=$