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

To subtract the polynomials, we first distribute the negative sign to the second polynomial: \((9x^2 - 5x + 1) - (4x^2 + 2x - 6) = 9x^2 - 5x + 1 - 4x^2 - 2x + 6\)

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

Combine the \(x^2\) terms: \(9x^2 - 4x^2 = 5x^2\)

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

Combine the \(x\) terms: \(-5x - 2x = -7x\), but since the form is \( \_x^2 - \_x + \_ \), we can think of it as \(5x^2 - 7x + \_ \) (because subtracting a negative coefficient is like adding its positive, but here we combine to get the coefficient for the subtracted \(x\) term)

Step4: Combine constant terms

Combine the constant terms: \(1 + 6 = 7\)

Answer:

5 \(x^2\) - 7 \(x\) + 7 (So the first box is 5, the second box is 7, the third box is 7)