Problem

Find the product of the functions f(x)=3x+2 and g(x)=2x−5

Answer

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Answer

Combining like terms, we get h(x)=6x2−11x−10.

Steps

Step 1 ：The product of two functions f(x) and g(x) is given by h(x)=f(x)⋅g(x).

Step 2 ：Substitute f(x)=3x+2 and g(x)=2x−5 into the above formula, we get h(x)=(3x+2)⋅(2x−5).

Step 3 ：Using the distributive property of multiplication over addition, we expand the above expression: h(x)=3x⋅2x−3x⋅5+2⋅2x−2⋅5.

Step 4 ：This simplifies to h(x)=6x2−15x+4x−10.

Step 5 ：Combining like terms, we get h(x)=6x2−11x−10.

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