Question

subtract the polynomials: \\((9x^2 - 5x + 1) - (4x^2 + 2x - 6) = \\) type your answer... \\(x^2 - \\) type your answer... \\(x + \\) type your answer...

Explanation:

Step1: Distribute the negative sign

We have \((9x^2 - 5x + 1) - (4x^2 + 2x - 6)\). Distribute the negative sign to the second polynomial: \(9x^2 - 5x + 1 - 4x^2 - 2x + 6\).

Step2: Combine like terms for \(x^2\) terms

Combine \(9x^2\) and \(-4x^2\): \(9x^2 - 4x^2 = 5x^2\).

Step3: Combine like terms for \(x\) terms

Combine \(-5x\) and \(-2x\): \(-5x - 2x = -7x\).

Step4: Combine constant terms

Combine \(1\) and \(6\): \(1 + 6 = 7\).
So the result is \(5x^2 - 7x + 7\). Now, comparing with the given form \(x^2 - \square x + \square\) (wait, actually the first term should be \(5x^2\), maybe a typo in the problem's given form? But following the calculation:
For the coefficient of \(x\): we have \(-7x\), so the box for the \(x\) coefficient is \(7\) (since it's \( - \square x\), so \(\square = 7\)). For the constant term, it's \(7\). And the coefficient of \(x^2\) is \(5\).

Answer:

For the \(x^2\) coefficient: \(5\)
For the \(x\) coefficient (the box after \(-\)): \(7\)
For the constant term (the last box): \(7\)
(So the polynomial is \(5x^2 - 7x + 7\))