Question

show that 3x+5 is a factor of 3x^3-16x^2-5x+50​

Answer 1

$\color {red} </p><p>\Large \underline {\underline {Question \: :}}$

Show that 3x + 5 is a factor of 3x³ - 16x² - 5x + 50.

$\color {red} </p><p>\Large \underline {\underline {Answer \: :}}$

$3x + 5 = 0$

$3x = - 5$

$x = - \frac{5}{3}$

Put the value of x in 3x³ - 16x² - 5x + 50.

$p(x) = 3x {}^{3} - 16 {x}^{2} - 5x + 50$

$p( - \frac{5}{3} ) = 3( - \frac{5}{3} ) {}^{3} - 16 {( - \frac{5}{3} )}^{2} - 5( - \frac{5}{3} ) + 50$

$p( - \frac{5}{3} ) = 3 \times - \frac{125}{27} - 16 \times \frac{25}{9} - 5 \times - \frac{5}{3} + 50$

$p( - \frac{5}{3} ) = - \frac{125}{9} - \frac{400}{9} + \frac{25}{3} + 50$

$p( - \frac{5}{3} ) = - \frac{175}{3} + \frac{25}{3} + 50$

$p( - \frac{5}{3} ) = - 50 + 50$

$p( - \frac{5}{3} ) = 0$

Hence, the value of p(-5/3) = 0

$\implies$ So, we can say that 3x + 5 is a factor of 3x³ - 16x² - 5x + 50.

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Answer 2

Answer:

$\large\bold\red {Refer~ to ~above~ attachment}$

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