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

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

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Answer 1 · 2017-12-30T10:43:13

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

Explanation:

Perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $\frac{5}{3}$ $5/3$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $18$ $18$ $a a a a$ $color(white)(aaaa)$ $- 15$ $-15$ $a a a a$ $color(white)(aaaa)$ $- 25$ $-25$

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

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

Therefore,

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

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

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

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Explanation:

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How do you use polynomial synthetic division to divide (18x2−15x−25)÷(x−53)(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)?

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Explanation:

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