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26 August, 00:01

Find $t$ if the expansion of the product of $x^3 - 4x^2 + 2x - 5$ and $x^2 + tx - 7$ has no $x^2$ term.

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  1. 26 August, 00:21
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    The expansion of the product of the given polynomials can be determined through the distributive property of multiplication.

    (x³ - 4x² + 2x - 5) (x² + tx - 7)

    This goes with the first term of the first expression first up until every term of the first expression is multiplied to the terms of the second expression.

    x⁵ + tx⁴ - 7x³ - 4x⁴ - 4tx³ + 28x² + 2x³ + 2tx² - 14x - 5x² - 5tx + 35

    The terms with x² are 28x², 2tx², and - 5x². The sum of the numerical coefficients should be zero.

    28 + 2t - 5 = 0

    The value of t from the equation is - 11.5.
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