MATH SOLVE

9 months ago

Q:
# PLEASE HELP WILL GET BRAINIEST 1. Simplify and write in standard form. Then, classify the polynomial by degree and number of terms [5x³ + 3x² - 7x + 10] + [3x³ - x² + 4x - 1] 2. Simplify and write in standard form. Then, classify the polynomial by degree and number of terms. [9w - 4w² + 10] + [8w² + 7 + 5w] 3. Simplify the product. -3x [x² + 3x - 1]4. Find the GCF of the polynomial, then factor. 8v⁶ + 2v⁵ - 10v⁹ 5. Simplify the product of the binomial [5t + 4]² 6. A rectangle has dimensions 3x 1 and 2x + 5. Write an expression for the area of the rectangle as a product and in standard form. 7. Factor m² + 9m - 228. Factor 5t² - t -18 9. Factor 25x² - 9 10. Factor 9t² + 12t + 4

Accepted Solution

A:

Answers :Answers. Step-by-step explanation:Question 1. 1. First we will open the brackets and bring together the terms with same degrees in decreasing order of their power.[tex]5x^3+3x^2-7x+10+3x^3-x^2+4x-1\\[/tex][tex]5x^3+3x^3+3x^2-x^2-7x+4x+10-1\\[/tex]2. Then we will simplify the terms with same degrees.[tex]8x^3+2x^2-3x+9[/tex]3. Now we see that the highest power in the polynomial. which is 3 in our case. Hence , Degree of the polynomial is 3.4. The total number of terms in the polynomial is 3 as we can see in the simplified form below [tex]8x^3+2x^2-3x+9[/tex]Question 2. In this question also we will follow the same process as we have done in the previous problem.Open the brackets and rearrange them as per their degrees . The highest power in the polynomial will be our Degree of the polynomial. Let us see how : [tex]9w-4w^2+10+8w^2+7+5w\\-4w^2+8w^2+9w+5w+10+7\\4w^2+14w+17\\[/tex]Hence the Degree of the polynomial is 2 and the number of terms in polynomial is 3. Question 3 : In this we have to find the product. In order to find the product we will use the distributive law and multiply -3x with each term inside the bracket. [tex](-3x * x^2)+ (-3x*3x) + (-3x*-1)\\-3x^3-9x^2+3x\\\\[/tex]by using the law [tex]x^m*x^n = x^(m+n)[/tex]Question 4 : Here we ave to find the HCF of the polynomial . In order to the same we will simplify each term of the polynomial into its reduced form and then extract the common among them. [tex]8v^6+2v^5-10v^9\\2*4*v^5*v + 2*v^5 -2*5*v^5*v^4\\2v^5*4v + 2v^5*1-2v^5*5v^4\\[/tex]Hence we see that [tex]2v^5[/tex] is common in them , hence this is our HCFQuestion 5 : We have to find the product of the binomial. In order to do that we will multiply the polynomial to itself using distributive law and then rearrange the terms with same power and then simplify them. The detailed solution is provided below.[tex][5t+4]^2\\[5t+4]*[5t+4]\\5t*5t+5t*4+4*5t+4*4\\25t^2+20t+20t+16\\25t^2+40t+16\\[/tex]