Question

can you help me with this it's synthetic substitution or direct substitution ​

Answer 1

$\huge\boxed{\sf \green{ Given : }}$

• $\red{\sf \: The \: Value \: Of \: x \: in \: 1st \: Eqn \: is \: 3 }$

• $\orange{ \sf \: The \: Value \: Of \: x \: in \: 1st \: Eqn \: is \: 2}$

$\red {\underline{ \sf \: Let's \: Solve \: For \: Eqn \: 1 : }}$

• $\sf \: f(x) = {2x}^{3} - {5x}^{2} - x$

• $\sf \: f(3) = {2(3)}^{3} - {5(3)}^{2} - 3$

• $\sf \: f(3) = 2(27) - 5(6) - 3$

• $\sf \: f(3) = 54 - 30 - 3$

• $\sf \: f(3) = 24 - 3$

• $\red{ \sf \: f(3) = 21}$

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$\orange {\underline{ \sf \: Let's \: Solve \: For \: Eqn \: 2}}$

• $\sf \: f(x) = {4x}^{3} + 3x - 5$

• $\sf \: f(2) = - 4 {(2)}^{3} + 3(2) - 5$

• $\sf \: f(2) = - 4(8) + 6 - 5$

• $\sf \: f(2) = - 32 + 6 - 5$

• $\sf \: f(2) = - 26 - 5$

• $\orange{ \sf f(2) = - 31}$

____________________________

[Eqn 3]

f(x) = x³ + 3x² + 6x - 11 when x = 5

• f(x) = x³ + 3x² + 6x - 11

• f(5) = (5)³ + 3*(5)²+6*(5)-11

• f(5) = 125 + 3*(25) + 30 - 11

• f(5) = 125 + 75 + 30 - 11

• f(5) = 200 + 30 - 11

• f(5) = 230 - 11

• f(5) = 219

____________________________

[Eqn 4]

f(x)=x³ - x² + 12x - 15 when x = 1

• f( x ) = x³ - x² + 12x - 15

• f( 1 ) = ( 1 )³ - ( 1 )² + 12( 1 ) - 15

• f( 1 ) = 1 - 1 + 12 - 15

• f( 1 ) = 0 + 12 - 15

• f( 1 ) = -3

____________________________

[Eqn 5]

f(x) = 2x³ + 6x² + 4x + 8 when x = 2

• f( x ) = 2x³ + 6x² + 4x + 8

• f( 2 ) = 2( 2 )³ + 6( 2 )² + 4( 2 ) +8

• f( 2 ) = 2( 8 ) + 6( 4 ) + 8 + 8

• f( 2 ) = 16 + 24 + 16

• f( 2 ) = 40 + 16

• f( 2 ) = 56

$\boxed{\sf \purple{ Hope \: It's \: Helpful!}}$

Answer 2

Evaluating the polynomial using direct substitution method will give the following :

f(x) = 2x³ - 5x² - x when x = 3

f(3) = 6

f(x) = -4x³ + 3x - 5 when x = 2

f(2) = -31

Substitution

Substitution simply means to put in place of another.  Therefore,

f(x) = 2x³ - 5x² - x when x = 3

f(3) = 2(3)³ - 5(3)² - 3

f(3) = 2(27) - 5(9) - 3

f(3) = 54 - 45 - 3

f(3) = 6

f(x) = -4x³ + 3x - 5 when x = 2

f(2) = -4(2)³ + 3(2) - 5

f(2) = -4(8) + 6 - 5

f(2) = -32 + 6 - 5

f(2) = -32 + 1

f(2) = -31

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