PLS HELP ME!!
I really need the answers to these few questions I need toturn them in ASAP.
Simplify each polynomial. Write each in standard form.
HINT: Watch for the operation! Add? Subtract? Or Multiply?
8. 4m(2m+9m^2-6)
12. (x-1)^2
13. (4y+2)^2
Factor each polynomial.
HINT: Change from x^2+bx+c to (x+p)(x+q) where p and q are the factors of c that add to b.
19. p^2-20p+100
20. r^2+6r-40
21. x^2-13x-30
22. d^2-18d+45
8 , 12 and 13
Multiply members one by one and edit expression.
20.
r² + 6 r - 40 =
( r² - 4 r ) + 10 r - 40 =
( r² - 4 r ) + ( 10 r - 40 ) =
r ( r - 4 ) + 10 ( r - 4 ) =
( r - 4 ) ( r + 10 )
21.
x² - 13 x - 30 =
( x² + 2 x ) - 15 x - 30 =
( x² + 2 x ) - ( 15 x + 30 ) =
22.
d² - 18 d + 45 =
( d² - 3 d ) - 15 d + 45 =
( d² - 3 d ) - ( 15 d - 45 ) =
Do the following steps.
19.
p² - 20 p + 100 =
p² - 2 ∙ p ∙ 10 +10² =
( p - 10 )²
8. To simplify the polynomial 4m(2m+9m^2-6), distribute the 4m to each term inside the parentheses:
4m * 2m + 4m * 9m^2 - 4m * 6
This gives us: 8m^2 + 36m^3 - 24m
So, the simplified form of the polynomial is 36m^3 + 8m^2 - 24m.
12. To simplify the polynomial (x-1)^2, we need to expand it using the square of a binomial formula:
(x-1)^2 = x^2 - 2x(1) + (1)^2
Simplifying further, we get: x^2 - 2x + 1
Therefore, the simplified polynomial in standard form is x^2 - 2x + 1.
13. Similar to question 12, we will expand (4y+2)^2 using the square of a binomial formula:
(4y+2)^2 = (4y)^2 + 2(4y)(2) + (2)^2
Simplifying further, we get: 16y^2 + 16y + 4
Thus, the simplified form of the polynomial in standard form is 16y^2 + 16y + 4.
19. To factor the polynomial p^2 - 20p + 100, we need to find two numbers that multiply to 100, and when added, give us -20 (the coefficient of the middle term). In this case, the numbers are -10 and -10:
p^2 - 20p + 100 = (p - 10)(p - 10) = (p - 10)^2
So, the factors of the polynomial are (p - 10)(p - 10) or (p - 10)^2.
20. To factor the polynomial r^2 + 6r - 40, we need to find two numbers that multiply to -40 and add up to 6. Those numbers are 10 and -4:
r^2 + 6r - 40 = (r + 10)(r - 4)
The factors of the polynomial are (r + 10)(r - 4).
21. To factor the polynomial x^2 - 13x - 30, we need to find two numbers that multiply to -30 and add up to -13. Those numbers are -15 and 2:
x^2 - 13x - 30 = (x - 15)(x + 2)
The factors of the polynomial are (x - 15)(x + 2).
22. To factor the polynomial d^2 - 18d + 45, we need to find two numbers that multiply to 45 and add up to -18. Those numbers are -15 and -3:
d^2 - 18d + 45 = (d - 15)(d - 3)
The factors of the polynomial are (d - 15)(d - 3).
Sure, I'd be happy to help you with these questions!
For question 8, we need to simplify the polynomial expression 4m(2m+9m^2-6). To do this, we need to distribute the 4m to each term inside the parentheses. This means we multiply 4m by each term individually.
Starting with 2m, we get 4m * 2m = 8m^2.
Moving on to the next term, we have 4m * 9m^2 = 36m^3.
Finally, we multiply 4m by -6, which gives us -24m.
Combining these terms, we get 8m^2 + 36m^3 - 24m. To write this in standard form, we arrange the terms in descending order of exponents:
36m^3 + 8m^2 - 24m.
For question 12, we are asked to simplify the polynomial expression (x-1)^2. To do this, we use the distributive property and multiply each term inside the parentheses by itself.
Expanding the expression, we get (x-1)^2 = (x-1)(x-1) = x^2 - x - x + 1.
Combining like terms, we have x^2 - 2x + 1, which is already in standard form.
For question 13, we have the polynomial expression (4y+2)^2. Using the same process as before, we multiply each term inside the parentheses by itself.
Expanding the expression, we get (4y+2)^2 = (4y+2)(4y+2) = 16y^2 + 4y + 4y + 1.
Combining like terms, we have 16y^2 + 8y + 1, which is already in standard form.
Moving on to factoring the given polynomials, we use the hint provided to find the factors that add up to the coefficient of the middle term and multiply to the constant term.
For question 19, we have the polynomial p^2 - 20p + 100. We need to find two numbers that multiply to 100 and add up to -20. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Among these, the pair that satisfies the condition is -10 and -10.
Thus, we can factor the polynomial as follows: (p - 10)(p - 10), or (p - 10)^2.
For question 20, we have the polynomial r^2 + 6r - 40. The factors of -40 that add up to 6 are -4 and 10.
Thus, we can factor the polynomial as follows: (r - 4)(r + 10).
Similarly, for question 21, we have the polynomial x^2 - 13x - 30. The factors of -30 that add up to -13 are -15 and 2.
Thus, we can factor the polynomial as follows: (x - 15)(x + 2).
Lastly, for question 22, we have the polynomial d^2 - 18d + 45. The factors of 45 that add up to -18 are -3 and -15.
Thus, we can factor the polynomial as follows: (d - 3)(d - 15).
Remember to always double-check your factoring by multiplying the factors to ensure they expand back to the original polynomial.
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
However, I will start you out with one problem.
20. -4, 10