Find the value of 4 x Superscript 5 Baseline minus 9 x Superscript 4 Baseline plus 5 x cubed minus 2 x squared for​ (a) xequals1 and for​ (b) xequalsnegative 2.

Answer 1

To find the value of the expression \(4x^5 - 9x^4 + 5x^3 - 2x^2\) for the given values of \(x\), we will evaluate the expression for \(x = 1\) and \(x = -2\).

(a) For \(x = 1\):

Substituting \(x = 1\):

\[ 4(1)^5 - 9(1)^4 + 5(1)^3 - 2(1)^2 = 4(1) - 9(1) + 5(1) - 2(1) \]

Calculating step by step:

\[ = 4 - 9 + 5 - 2 \]

Now, combine the values:

\[ = (4 - 9) + (5 - 2) \] \[ = -5 + 3 \] \[ = -2 \]

So, for \(x = 1\), the value is \(-2\).

(b) For \(x = -2\):

Substituting \(x = -2\):

\[ 4(-2)^5 - 9(-2)^4 + 5(-2)^3 - 2(-2)^2 \]

Calculating each term:

1. \(4(-2)^5 = 4 \cdot (-32) = -128\)
2. \(-9(-2)^4 = -9 \cdot 16 = -144\)
3. \(5(-2)^3 = 5 \cdot (-8) = -40\)
4. \(-2(-2)^2 = -2 \cdot 4 = -8\)

Now combine these values:

\[ -128 - 144 - 40 - 8 \]

Calculating step by step:

\[ = -128 - 144 = -272 \] \[ = -272 - 40 = -312 \] \[ = -312 - 8 = -320 \]

So, for \(x = -2\), the value is \(-320\).

Summary of Results:

• For \(x = 1\), the value is \(-2\).
• For \(x = -2\), the value is \(-320\).