Multiply polynomial $5 x^{4} - 2 x^{2} - 10 x^{2}$ by $2 x + 5$ .

Answer

$(5 x^{4} - 2 x^{2} - 10 x^{2}) \cdot (2 x + 5) = 10 x^{5} + 25 x^{4} - 24 x^{3} - 60 x^{2}$

Explanation

Step 1: First we have to write polynomials in descending order.

P (x) Q (x) = 5 x^{4} - 12 x^{2} = 2 x + 5

In this example we are multiplying two binomials so FOIL method can be used.

(5 x^{4} - 12 x^{2}) \cdot (2 x + 5) = FIRST 5 x^{4} \cdot 2 x + OUTER 5 x^{4} \cdot 5 + INNER (- 12 x^{2}) \cdot 2 x + LAST (- 12 x^{2}) \cdot 5 = = 10 x^{5} + 25 x^{4} + (- 24 x^{3}) + (- 60 x^{2}) = = 10 x^{5} + 25 x^{4} + (- 24 x^{3}) + (- 60 x^{2}) = = 10 x^{5} + 25 x^{4} - 24 x^{3} - 60 x^{2};

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Multiply polynomial 5x4−2x2−10x2 by 2x+5.

(5x4−2x2−10x2)⋅(2x+5)=10x5+25x4−24x3−60x2

Multiply polynomial $5 x^{4} - 2 x^{2} - 10 x^{2}$ by $2 x + 5$ .

$(5 x^{4} - 2 x^{2} - 10 x^{2}) \cdot (2 x + 5) = 10 x^{5} + 25 x^{4} - 24 x^{3} - 60 x^{2}$