Factor completely. 100-140 x+49x^(2)= +=^(-x)

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Factor completely.  100-140 x+49x^(2)=  +=^(-x)

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Recognize Polynomial Type: Recognize the type of polynomial and determine the factoring strategy. The given polynomial is a quadratic in the form of ax^2 + bx + c. We can attempt to factor it as a product of two binomials if it is factorable. The coefficients suggest that it might be a perfect square trinomial because 100 and 49 are perfect squares, and 140 is twice the product of the square roots of 100 and 49.Write Perfect Squares: Write down the perfect squares of the coefficients of the quadratic polynomial. The square root of 100 is 10, and the square root of 49 is 7. The middle term coefficient, -140, is twice the product of 10 and 7, which is 2 * 10 * 7 = 140. This suggests that the polynomial might be a perfect square trinomial.Check Perfect Square Trinomial: Write the polynomial in the form of (ax + b)^2 to see if it matches the given polynomial. The perfect square trinomial would be (10 - 7x)^2 because (10)^2 = 100 and (7x)^2 = 49x^2 and the middle term would be 2 * 10 * 7x = 140x, but we have -140x in the polynomial, so it should be (10 - 7x)^2.Expand to Verify: Expand (10 - 7x)^2 to verify if it equals the given polynomial. (10 - 7x)^2 = (10 - 7x)(10 - 7x) = 100 - 70x - 70x + 49x^2 = 100 - 140x + 49x^2. This matches the given polynomial exactly.Write Final Factored Form: Write the final factored form of the polynomial. The factored form of the polynomial 100 - 140x + 49x^2 is (10 - 7x)^2.

Factor completely. $\newline$ $100-140 x+49 x^{2}=$

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Factor completely.\newline100−140x+49x2= 100-140 x+49 x^{2}= 100−140x+49x2=

Factor completely. $\newline$ $100-140 x+49 x^{2}=$