How do you use polynomial synthetic division to divide $(18x^2-15x-25)div(x-5/3)$ and write the polynomial in the form $p(x)=d(x)q(x)+r(x)$ ?

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Answer 1 · 2017-12-30T10:43:13

The answer is $=(x-5/3)(18x+15)+0$

$color(white)(aaaa)$ $5/3$ $color(white)(aaaa)$ $|$ $18$ $color(white)(aaaa)$ $-15$ $color(white)(aaaa)$ $-25$

$color(white)(aaaa)$ $color(white)(aaaaaa)$ $|$ $color(white)(aaaaaaaa)$ $30$ $color(white)(aaaaaa)$ $25$

$color(white)(aaaa)$ $color(white)(aaaaaa)$ $|$ $18$ $color(white)(aaaaaa)$ $15$ $color(white)(aaaaaaa)$ $0$

Therefore,

$18x^2-15x-25=(x-5/3)(18x+15)+0$

The quotient is $=18x+15$ and the remainder is $=0$

How do you use polynomial synthetic division to divide (18x^2-15x-25)div(x-5/3)(18x^2-15x-25)div(x-5/3) and write the polynomial in the form p(x)=d(x)q(x)+r(x)p(x)=d(x)q(x)+r(x)?