Factor completely: r^(8)-5r^(4)u^(3)-14u^(6) Answer:

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Factor completely:  r^(8)-5r^(4)u^(3)-14u^(6) Answer:

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Identify Common Factor: Identify the common factor in the polynomial. The polynomial r^(8)-5r^(4)u^(3)-14u^(6) has a common factor of r^(4) in the first two terms, but not in the third term. However, we can look for a different type of factorization, which is factoring by grouping or looking for a pattern that resembles a known factorable form.Recognize Quadratic Form: Recognize the polynomial as a quadratic in form. The polynomial can be seen as a quadratic in terms of r^(4), where r^(4) is the variable and u^(3) is a constant. The polynomial then takes the form of (r^(4))^2 - 5r^(4)u^(3) - 14u^(6), which resembles a quadratic equation ax^2 + bx + c.Factor as Quadratic: Factor the polynomial as if it were a quadratic. We will use the factoring technique for quadratics to factor the polynomial. We need to find two numbers that multiply to give -14u^(6) (the constant term) and add to give -5u^(3) (the coefficient of the middle term). These two numbers are -7u^(3) and -2u^(3).Write as Binomials: Write the polynomial as a product of two binomials. The polynomial can now be written as (r^(4) - 7u^(3))(r^(4) + 2u^(3)). This is the factorization of the polynomial into two binomials.Check Factorization: Check the factorization by expanding the binomials. To ensure that the factorization is correct, we can multiply the two binomials to see if we get the original polynomial: (r^(4) - 7u^(3))(r^(4) + 2u^(3)) = r^(8) + 2r^(4)u^(3) - 7r^(4)u^(3) - 14u^(6) = r^(8) - 5r^(4)u^(3) - 14u^(6). The expanded form matches the original polynomial, confirming that the factorization is correct.

Factor completely: $\newline$ $r^{8}-5 r^{4} u^{3}-14 u^{6}$ $\newline$ Answer:

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Factor completely:\newliner8−5r4u3−14u6 r^{8}-5 r^{4} u^{3}-14 u^{6} r8−5r4u3−14u6\newlineAnswer:

Factor completely: $\newline$ $r^{8}-5 r^{4} u^{3}-14 u^{6}$ $\newline$ Answer: