1. How can this product be simplified?
5x^2(2x – 3)
5x^2 + 2x – 3
10x^3 – 15x^2
–5x^2
7x^3 – 15x^2
2. What is the GCF of the terms of 8c^3 + 12c^2 + 10c ?
2
4
2c
4c
3. How can the polynomial 6d^4 + 9d^3 – 12d^2 be factored?
3d^2(2d^2 + 3d – 4)
3d^2(3d^2 + 6d – 9)
3d(d^3 + 3d^2 – 4)
6d^2(d2 + 3d^3 - 6
4. There is a circular garden in the middle of a square yard. The radius of the circle is 4x. The side length of the yard is 20x. What is the area of the part of the yard that is not covered by the circle?
4x(5)
8x^(5 – Pie sysmbol)
16x(25 + Pie Symbol)
16x2(25 – Pie Symbol )
5. What is the simplified form of –3z^2(z + 2) – 4(z2 + 1)?
–7x^2 + 1
–3z^3 – 4z^2 – 6z – 4
–3z^3 – 2z^2 – 4
–3z^3 – 10z^2 – 4
Answers:
1.)B
2.)C
3.)A
4.)D
5.)D
Thank You
im sorry i didn't see the bottom part i take that back
i didn't check number 4 but the others should be right
Thank You.
To simplify the product 5x^2(2x - 3), you need to distribute the 5x^2 to each term inside the parentheses.
Step 1: Distribute the 5x^2 to the first term inside the parentheses:
5x^2 * 2x = 10x^3
Step 2: Distribute the 5x^2 to the second term inside the parentheses:
5x^2 * (-3) = -15x^2
The simplified expression becomes 10x^3 - 15x^2, which is option B.
To find the greatest common factor (GCF) of the terms 8c^3, 12c^2, and 10c, you need to look for the common factors that can divide all three terms evenly.
Step 1: Write down the prime factorization of each term:
8c^3 = 2^3 * c^3
12c^2 = 2^2 * 3 * c^2
10c = 2 * 5 * c
Step 2: Identify the common factors:
The common factors are 2 and c.
Step 3: Find the GCF:
Multiply the common factors together: GCF = 2 * c = 2c, which is option C.
To factor the polynomial 6d^4 + 9d^3 - 12d^2, you need to find the largest common factor and then use grouping or factoring by grouping method.
Step 1: Find the largest common factor of all terms:
All terms have a common factor of 3d^2.
Step 2: Factor out the common factor:
3d^2(2d^2 + 3d - 4)
Step 3: Check for further factoring:
The expression 2d^2 + 3d - 4 cannot be factored further.
The factored form of the polynomial is 3d^2(2d^2 + 3d - 4), which is option A.
To find the area of the part of the yard that is not covered by the circle, you need to subtract the area of the circle from the area of the square yard.
Step 1: Find the area of the square yard:
The side length of the yard is 20x, so the area of the square yard is (20x)^2 = 400x^2.
Step 2: Find the area of the circle:
The radius of the circle is 4x, so the area of the circle is π(4x)^2 = 16πx^2.
Step 3: Calculate the area not covered by the circle:
Area not covered = Area of square yard - Area of circle
Area not covered = 400x^2 - 16πx^2
The simplified form of the area not covered by the circle is 16x^2(25 - π), which is option D.
To simplify the expression –3z^2(z + 2) - 4(z^2 + 1), you need to distribute the coefficients to each term inside the parentheses and then combine like terms.
Step 1: Distribute -3z^2 to each term in the first parentheses:
-3z^2 * z = -3z^3
-3z^2 * 2 = -6z^2
Step 2: Distribute -4 to each term in the second parentheses:
-4 * z^2 = -4z^2
-4 * 1 = -4
Step 3: Combine like terms:
-3z^3 - 6z^2 - 4z^2 - 4
Step 4: Simplify further:
-3z^3 - 10z^2 - 4
The simplified form of the expression is -3z^3 - 10z^2 - 4, which is option D.