Identify Coefficients: Identify the coefficients of the quadratic expression.The quadratic expression is z2+10z+21. In the standard form of a quadratic expression, ax2+bx+c, the coefficient a is the coefficient of z2, which is 1. The coefficient b is the coefficient of z, which is 10. The coefficient c is the constant term, which is 21.
Find Multiplying Numbers: Find two numbers that multiply to c (21) and add up to b (10). We need to find two numbers that multiply to 21 and add up to 10. The numbers 3 and 7 satisfy these conditions because 3×7=21 and 3+7=10.
Write Factored Form: Write the factored form using the two numbers found.The factored form of the quadratic expression is (z+3)(z+7), because when we expand this, we get z2+3z+7z+21, which simplifies to z2+10z+21.
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