2.
Simplify the polynomial.
–3f^2 + 4f – 3 + 8f^2 + 7f + 1
5f^2 – 11f + 2
11f^2 + 11f + 2
5f^2 + 11f – 2
–5f^2 + 11f – 2
3. (2x2 + 6x + 1) + (–7x2 + 2x – 3)
5x2 – 4x – 2
–5x2 + 8x – 2
5x2 – 8x + 2
–9x2 – 8x + 2
4. (3x2 – 7x – 4) – (6x2 – 6x + 1)
–3x2 – x –5
–3x2 –13x + 5
9x2 – x + 5
3x2 – 13x – 5
6. The area of room A is (5x^2– 7x – 6) ft^2. Room B has an area of (8x^2 + 6x – 1) ft^2. If room A is the larger room, how much greater is the area of room A than the area of room B?
–3x^2 – x – 7
13x^2 – 13x – 7
–3x^2 – 13x – 5
3x^2 – x – 5
My answers:
2. 5f^2 + 11f + 2
3. 5x2 – 8x + 2
4. –3x2 – x –5
6. -3x^2-13x-5
#2 should be 5f^2 + 11f – 2
#3 ok
#4 should be –3x2 –13x + 5
#6 ok
Evaluate 5x2-4 when x =3.
what is 4f + 11f equal
Here are the answers I would give:
2. Here's the simplified polynomial: 5f^2 + 11f + 2. Just like magic, all the terms simplified and joined together for a polynomial party!
3. Ta-da! The simplified polynomial is 5x^2 - 8x + 2. It's like coming out of a maze and finding a treasure - simple and exciting!
4. The simplified polynomial is -3x^2 - x - 5. It's like solving a puzzle - subtracting the terms and piecing it all together!
6. Wait for it... the area of room A is greater than the area of room B by -3x^2 - 13x - 5 square feet. That's the difference in the grandeurs of the two rooms - room A struts its stuff with more space!
To simplify the given polynomials, follow these steps:
2. To simplify –3f^2 + 4f – 3 + 8f^2 + 7f + 1:
Combine the like terms by adding or subtracting the coefficients of the same degree of the variable.
Combine the coefficients for the squared term: -3f^2 + 8f^2 = 5f^2.
Combine the coefficients for the first-degree term: 4f + 7f = 11f.
Combine the constant terms: -3 + 1 = -2.
The simplified polynomial is 5f^2 + 11f – 2.
3. To simplify (2x^2 + 6x + 1) + (-7x^2 + 2x – 3):
Combine the like terms by adding or subtracting the coefficients of the same degree of the variable.
Combine the coefficients for the squared term: 2x^2 + (-7x^2) = -5x^2.
Combine the coefficients for the first-degree term: 6x + 2x = 8x.
Combine the constant terms: 1 + (-3) = -2.
The simplified polynomial is -5x^2 + 8x – 2.
4. To simplify (3x^2 – 7x – 4) – (6x^2 – 6x + 1):
Distribute the negative sign to the terms inside the parentheses:
(3x^2 – 7x – 4) – (6x^2 – 6x + 1) becomes 3x^2 – 7x – 4 – 6x^2 + 6x - 1.
Combine the like terms by adding or subtracting the coefficients of the same degree of the variable.
Combine the coefficients for the squared term: 3x^2 + (-6x^2) = -3x^2.
Combine the coefficients for the first-degree term: -7x + 6x = -x.
Combine the constant terms: -4 - 1 = -5.
The simplified polynomial is -3x^2 – x – 5.
6. To find out how much greater the area of room A is than the area of room B:
Subtract the expression for the area of room B from the expression for the area of room A.
(5x^2 – 7x – 6) - (8x^2 + 6x – 1) becomes 5x^2 – 7x – 6 - 8x^2 - 6x + 1.
Combine the like terms by adding or subtracting the coefficients of the same degree of the variable.
Combine the coefficients for the squared term: 5x^2 + (-8x^2) = -3x^2.
Combine the coefficients for the first-degree term: -7x + (-6x) = -13x.
Combine the constant terms: -6 + 1 = -5.
The difference in area, the greater area of room A compared to room B, is -3x^2 – 13x – 5.