Fill in the blanks to complete the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference.

Question

9x^2 + ___x + 13
-2x^2 + 12x + ___
___x^2 + 5x + 2

Answer 1

To complete the polynomial equation, we need to perform the subtraction of the second polynomial from the first polynomial.

Given:

1. First polynomial: \( 9x^2 + bx + 13 \)
2. Second polynomial: \( -2x^2 + 12x + c \)
3. Resulting polynomial after subtraction: \( dx^2 + 5x + 2 \)

The subtraction can be expressed as follows:

\[ (9x^2 + bx + 13) - (-2x^2 + 12x + c) = dx^2 + 5x + 2 \]

Simplifying the left side gives:

\[ 9x^2 + bx + 13 + 2x^2 - 12x - c = dx^2 + 5x + 2 \] \[ (9 + 2)x^2 + (b - 12)x + (13 - c) = dx^2 + 5x + 2 \]

Now, we can equate the coefficients for each corresponding power of \(x\):

1. For \(x^2\): \[ 9 + 2 = d \Rightarrow d = 11 \]

2. For \(x\): \[ b - 12 = 5 \Rightarrow b = 17 \]

3. For the constant term: \[ 13 - c = 2 \Rightarrow c = 11 \]

Putting all the values together, we have:

• \(b = 17\)
• \(c = 11\)
• \(d = 11\)

So, the completed polynomial equation with the blanks filled in is:

\[ 9x^2 + 17x + 13

• 2x^2 + 12x + 11 = 11x^2 + 5x + 2 \]