Question

question 1
type the correct answer in each box.
consider these quadratic expressions:
a. $-3x^2 + 11x - 3$
b. $11x^2 - x + 10$
c. $4x^2 + 27x - 28$
d. $-3x^2 + 11x + 31$

for each polynomial operation, write the letter that corresponds to the resulting expression from the list.
$(5x^2 + 2x + 1) + (6x^2 - 3x + 9)$ is equivalent to expression $square$.
$(-3x^2 + 6x - 12) + (5x + 9)$ is equivalent to expression $square$;
$(8x + 16) - (3x^2 - 3x - 15)$ is equivalent to expression $square$;
$(5x^2 + 23x - 7) - (x^2 - 4x + 21)$ is equivalent to expression $square$;

Explanation:

for First Operation: \((5x^2 + 2x + 1) + (6x^2 - 3x + 9)\)

Step1: Combine like terms for \(x^2\)

\(5x^2+6x^2 = 11x^2\)

Step2: Combine like terms for \(x\)

\(2x-3x=-x\)

Step3: Combine constant terms

\(1 + 9=10\)

Step4: Form the resulting expression

The resulting expression is \(11x^2 - x + 10\), which corresponds to option B.

for Second Operation: \((-3x^2 + 6x - 12)+(5x + 9)\)

Step1: Combine like terms for \(x^2\)

\(-3x^2\) (no other \(x^2\) term)

Step2: Combine like terms for \(x\)

\(6x + 5x=11x\)

Step3: Combine constant terms

\(-12 + 9=-3\) Wait, no, wait, let's re - check. Wait, the original expression: \((-3x^2+6x - 12)+(5x + 9)\)
\(=-3x^2+(6x + 5x)+(-12 + 9)=-3x^2+11x-3\), which corresponds to option A.

for Third Operation: \((8x + 16)-(3x^2 - 3x - 15)\)

Step1: Distribute the negative sign

\(8x + 16-3x^2+3x + 15\)

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

\(-3x^2\)

Step3: Combine like terms for \(x\)

\(8x+3x = 11x\)

Step4: Combine constant terms

\(16 + 15=31\)
The resulting expression is \(-3x^2+11x + 31\), which corresponds to option D.

for Fourth Operation: \((5x^2+23x - 7)-(x^2 - 4x + 21)\)

Step1: Distribute the negative sign

\(5x^2+23x - 7-x^2 + 4x-21\)

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

\(5x^2-x^2 = 4x^2\)

Step3: Combine like terms for \(x\)

\(23x + 4x=27x\)

Step4: Combine constant terms

\(-7-21=-28\)
The resulting expression is \(4x^2+27x - 28\), which corresponds to option C.

Answer:

First box: B
Second box: A
Third box: D
Fourth box: C