Write a polynomial of least degree with roots 7, −7, and −2. Write your answer using the variable x and in standard form with a leading coefficient of 1.
Q. Write a polynomial of least degree with roots 7, −7, and −2. Write your answer using the variable x and in standard form with a leading coefficient of 1.
Identify factors for roots: Identify the linear factors for each root: for root 7, the factor is (x−7); for root −7, the factor is (x+7); for root −2, the factor is (x+2).
Multiply factors for polynomial: Multiply these factors to get the polynomial: (x−7)(x+7)(x+2).
Simplify first two factors: Simplify the first two factors: (x−7)(x+7)=x2−49.
Multiply simplified factors: Now multiply (x2−49) by (x+2): (x2−49)(x+2)=x3+2x2−49x−98.
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