Certainly! Let's solve the given problem step-by-step.
We are asked to subtract the polynomial [tex]\(-2x^2 + 4x - 1\)[/tex] from the polynomial [tex]\(6x^2 + 3x - 9\)[/tex].
Step 1: Write down the original polynomials clearly:
[tex]\[ 6x^2 + 3x - 9 \][/tex]
and
[tex]\[ -2x^2 + 4x - 1 \][/tex]
Step 2: Since we are subtracting the second polynomial, we need to distribute the subtraction sign across all terms in the second polynomial:
[tex]\[ 6x^2 + 3x - 9 - (-2x^2 + 4x - 1) \][/tex]
Step 3: Simplify by changing the signs in the second polynomial:
[tex]\[ 6x^2 + 3x - 9 + 2x^2 - 4x + 1 \][/tex]
Step 4: Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(6x^2 + 2x^2 = 8x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(3x - 4x = -x\)[/tex]
- Combine the constant terms: [tex]\(-9 + 1 = -8\)[/tex]
Step 5: Write the resulting polynomial in standard form:
[tex]\[ 8x^2 - x - 8 \][/tex]
So, the result of subtracting [tex]\(-2x^2 + 4x - 1\)[/tex] from [tex]\(6x^2 + 3x - 9\)[/tex] is:
[tex]\[ 8x^2 - x - 8 \][/tex]
That's the polynomial in standard form.
