Question

Don't spam...Step by step explaination needed...​

Answer 1

Answer:

$\:$

(c) 3

Step-by-step explanation:

Given polynomial :

f(x) = 2x³–5x² + 5x

Let the number to be subtracted be n

(x is already in equation so, n is better)

since, 2x – 3 factor given

→

$f ( \frac{3}{2} ) = 0$

So,

$2x {}^{3} - 5x {}^{2} + 5 {x}^{2} - n$

$2x {}^{3} - 5x {}^{2} + 5x - n = 0 \\ \\ 2( \frac{3}{2} ) {}^{3} - 5( \frac{3}{2} ) {}^{2} + 5( \frac{3}{2} ) - n = 0 \\ \\ 2 \times \frac{27}{8} - 5 \times \frac{9}{4} + 5 \times \frac{3}{2} - n \: = 0 \\ \\ \frac{27}{4} - \frac{45}{4} + \frac{15}{2} - \frac{n}{1} = 0 \\ \\ 27 - 45 + 30 - 4n = 0 \\ \\ 12 - 4n \: = 0 \\ \\n = \frac{ - 12}{ - 4} \\ \\ n = > 3$

Answer 2

Answer:

$\:$

(c) 3

Step-by-step explanation:

Given polynomial :

f(x) = 2x³–5x² + 5x

Let the number to be subtracted be n

(x is already in equation so, n is better)

since, 2x – 3 factor given

→

$f ( \frac{3}{2} ) = 0$

So,

$2x {}^{3} - 5x {}^{2} + 5 {x}^{2} - n$

$2x {}^{3} - 5x {}^{2} + 5x - n = 0 \\ \\ 2( \frac{3}{2} ) {}^{3} - 5( \frac{3}{2} ) {}^{2} + 5( \frac{3}{2} ) - n = 0 \\ \\ 2 \times \frac{27}{8} - 5 \times \frac{9}{4} + 5 \times \frac{3}{2} - n \: = 0 \\ \\ \frac{27}{4} - \frac{45}{4} + \frac{15}{2} - \frac{n}{1} = 0 \\ \\ 27 - 45 + 30 - 4n = 0 \\ \\ 12 - 4n \: = 0 \\ \\n = \frac{ - 12}{ - 4} \\ \\ n = > 3$