Question

Divide 2x^3-7x^2+5x-9 by 2x-3

Answer 1

$\huge{\mathfrak{\dag{\underline{\red{A{\green{n{\orange{s{\blue{w{\pink{e{\purple{r}}}}}}}}}}}}}}}$

p(x) = 2x³ - 7x² + 5x - 9

g(x) = 2x - 3

q(x) = x² - 2x - ½

r(x) = -²½

Answer 2

The quotient of the polynomial division is $\bf \red{{x}^{2} - 2x - \frac{1}{2} }$.

The remainder is $\bf \frac{ - 21}{2}$ or -10.5

Given:

• $2 {x}^{3} - 7 {x}^{2} + 5x - 9$ and
• $2x - 3$

To find:

• Divide the greater degree polynomial with the smaller degree polynomial.

Solution:

Perform long division.

$2x - 3 \: ) \: 2 {x}^{3} - 7 {x}^{2} + 5x - 9 \: ( {x}^{2} - 2x - \frac{1}{2} \\ 2 {x}^{3} - 3 {x}^{2} \: \: \: \: \: \: \: \\( - ) \: \: \: \: ( + ) \: \: \: \: \: \: \: \: \: \: \\ - - - - - - \: \: \: \: \: \: \\ - 4 {x}^{2} + 5x \\ - 4 {x}^{2} + 6x \\ ( + ) \: \: \: ( - ) \\ - - - - - - \\ - x - 9 \\ - x + \frac{3}{2} \\ ( + ) \: \: \: ( - ) \\ - - - - - - \\ - \frac{21}{2} \\ - - - - - -$

Thus,

The quotient of the polynomial division is $\bf {x}^{2} - 2x - \frac{1}{2}$.

The remainder is $\bf \frac{ - 21}{2}$.

Learn more:

1) (2m³+m²+m+9)÷(2m-1 divide and write the quotient and the remainder

https://brainly.in/question/7314664

2) Divide (x5 -y 5 ) by (x-y) using the method of long division.

https://brainly.in/question/19370514

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