Question

complete this assessment to review what youve learned. it will not count toward your grade. fill in the blanks to complete the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference. (2 points) complete the polynomial subtraction equation. $9x^2 + \boxed{11}x + 13 - 2x^2 + 12x + \boxed{7} = \boxed{7x^2} + 5x + 2$ (note: the original images incorrect parts are represented with placeholders for clarity, focusing on the polynomial subtraction context.)

Explanation:

Step1: Subtract \(x^2\) terms

We have \(9x^2 - 2x^2\). Using the rule of subtracting like terms (coefficients are subtracted), we get \((9 - 2)x^2 = 7x^2\).

Step2: Subtract \(x\) terms

Let the coefficient of \(x\) in the first polynomial be \(a\) and in the second be \(12\). The result of subtracting \(x\) terms is \(5x\), so we have \(ax - 12x = 5x\). Solving for \(a\): \(ax=5x + 12x=17x\), so \(a = 17\).

Step3: Subtract constant terms

Let the constant term in the second polynomial be \(b\) and in the first be \(13\). The result of subtracting constant terms is \(2\), so we have \(13 - b = 2\). Solving for \(b\): \(b=13 - 2 = 11\).

So the correct polynomial subtraction is:
\(9x^2 + 17x + 13-(2x^2 + 12x + 11)=7x^2 + 5x + 2\)

Answer:

The correct blanks are: \(9x^2 + \boldsymbol{17}x + 13-(2x^2 + 12x + \boldsymbol{11}) = 7x^2 + 5x + 2\)