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What number is multiplied by 2 in left parentheses to get 8 in original expression? That is j, the coefficient for x^2. Follow the same pattern to find k, the middle coefficient.

j= x^2 coefficient
k= x coefficient


= 8x^3 – 125

= (2x−5)(4x^2+10x+25)


ANSWER: j= 4; k= 10

Hope this helps! :)
calculista

Answer:

[tex]j=4[/tex]

[tex]k=10[/tex]

Step-by-step explanation:

we have that

[tex]8x^{3}-125=(2x-5)(jx^{2} +kx+25)[/tex]

Applying the distributive property to the right side

[tex](2x-5)(jx^{2} +kx+25)=2jx^{3}+2kx^{2} +50x-5jx^{2}-5kx-125[/tex]

Combine like terms

[tex]=2jx^{3}+(2k-5j)x^{2} +(50-5k)x-125[/tex]

Compare with [tex]8x^{3}-125[/tex]

so

[tex]2j=8[/tex] -------> [tex]j=4[/tex]

[tex](2k-5j)=0[/tex] ------> substitute the value of j and solve for k

[tex]2k=5(4)[/tex] ------> [tex]k=10[/tex]

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