Question

what is ((3x^4 + 2x^2 - 6)) subtracted from ((4x^4 + 2x^3 - 6))?
a (x^4)
b (x^3)
c (x^4 + x^3 - 3)
d (7x^4 + x^2 - 9)
e (x^4 + 6x^2 - 9)

Explanation:

Step1: Write the subtraction expression

We need to subtract \((3x^4 + 2x^2 - 6)\) from \((4x^4 + 2x^3 - 6)\), so the expression is \((4x^4 + 2x^3 - 6)-(3x^4 + 2x^2 - 6)\).

Step2: Distribute the negative sign

Using the distributive property \(a-(b + c - d)=a - b - c + d\), we get \(4x^4 + 2x^3 - 6-3x^4 - 2x^2 + 6\).

Step3: Combine like terms

• For the \(x^4\) terms: \(4x^4-3x^4 = x^4\)
• For the \(x^3\) term: \(2x^3\) (no other \(x^3\) terms to combine with)
• For the \(x^2\) term: \(- 2x^2\) (no other \(x^2\) terms to combine with)
• For the constant terms: \(-6 + 6=0\)

Putting it all together, we have \(x^4+2x^3 - 2x^2\)? Wait, no, wait, maybe I misread the original problem. Wait, the original problem: let's check again. Wait, the first polynomial is \(3x^4+2x^2 - 6\) and the second is \(4x^4 + 2x^3-6\). So when we subtract the first from the second: \((4x^4 + 2x^3-6)-(3x^4 + 2x^2 - 6)\)

Simplify term by term:

\(4x^4-3x^4=x^4\)

\(2x^3\) (no \(x^3\) in the first polynomial)

\(0x^2-2x^2=-2x^2\)? Wait, no, the first polynomial has \(2x^2\), so when we subtract, it's \(-2x^2\)

Constants: \(-6 - (-6)=-6 + 6 = 0\)

Wait, but the options: Let's check the options again. Wait, maybe there's a typo in my reading. Wait, maybe the first polynomial is \(3x^4+2x^3 - 6\)? Wait, no, the user's image: "What is \((3x^4 + 2x^2 - 6)\) subtracted from \((4x^4 + 2x^3 - 6)\)?"

Wait, maybe I made a mistake. Wait, let's re-express:

\((4x^4 + 2x^3 - 6)-(3x^4 + 2x^2 - 6)\)

= \(4x^4 + 2x^3 - 6-3x^4 - 2x^2 + 6\)

= \((4x^4-3x^4)+2x^3-2x^2+(-6 + 6)\)

= \(x^4+2x^3-2x^2\)

Wait, but the options: Let's check the options. The options are:

A. \(x^4\)

B. \(x^3\)

C. \(x^4 + x^3-3\)

D. \(7x^4 + x^2-9\)

E. \(x^4 + 6x^2-9\)

Wait, this is confusing. Maybe I misread the exponents. Wait, maybe the first polynomial is \(3x^4+2x^3 - 6\) instead of \(3x^4+2x^2 - 6\)? Let's assume that maybe it's a typo (maybe \(2x^3\) instead of \(2x^2\)). Let's try that.

If the first polynomial is \(3x^4 + 2x^3 - 6\), then:

\((4x^4 + 2x^3 - 6)-(3x^4 + 2x^3 - 6)\)

= \(4x^4 + 2x^3 - 6-3x^4 - 2x^3 + 6\)

= \((4x^4-3x^4)+(2x^3-2x^3)+(-6 + 6)\)

= \(x^4\)

Ah, that matches option A. So probably there was a typo in the exponent ( \(2x^3\) instead of \(2x^2\) in the first polynomial). So proceeding with that correction (since otherwise the answer isn't in the options):

Step1: Write the subtraction expression (correcting the first polynomial's \(x^2\) to \(x^3\) as a likely typo)

\((4x^4 + 2x^3 - 6)-(3x^4 + 2x^3 - 6)\)

Step2: Distribute the negative sign

\(4x^4 + 2x^3 - 6-3x^4 - 2x^3 + 6\)

Step3: Combine like terms

• \(x^4\) terms: \(4x^4-3x^4 = x^4\)
• \(x^3\) terms: \(2x^3-2x^3 = 0\)
• Constant terms: \(-6 + 6 = 0\)

So the result is \(x^4\)

Answer:

A. \(x^4\)