Question

Show that (x – y) is a factor of the polynomial x^3 – 2x^2y – 5xy^2 + 6y^3

Answer 1

Answer:

$p(x) = {x}^{3} - 2 {x}^{2} y - 5x {y}^{2} + 6 {y}^{3} \\ put \: \: x = y \\ p(y) = {y}^{3} - 2 {y}^{2} .y - 5y. {y}^{2} + 6 {y}^{3} \\ = {y}^{3} - 2 {y}^{3} - 5 {y}^{3} + 6 {y}^{3} \\ = - {y}^{3} + {y}^{3} \\ = 0$

Hence x - y is a factor of polynomial

Answer 2

Answer:

Answer:

\begin{gathered}p(x) = {x}^{3} - 2 {x}^{2} y - 5x {y}^{2} + 6 {y}^{3} \\ put \: \: x = y \\ p(y) = {y}^{3} - 2 {y}^{2} .y - 5y. {y}^{2} + 6 {y}^{3} \\ = {y}^{3} - 2 {y}^{3} - 5 {y}^{3} + 6 {y}^{3} \\ = - {y}^{3} + {y}^{3} \\ = 0 \\ \end{gathered}

p(x)=x

3

−2x

2

y−5xy

2

+6y

3

putx=y

p(y)=y

3

−2y

2

.y−5y.y

2

+6y

3

=y

3

−2y

3

−5y

3

+6y

3

=−y

3

+y

3

=0

Hence x - y is a factor of polynomial

Step-by-step explanation:

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