PLS HELP ME!!
I really need the answers to these last few questions to a practice sheet I need to turn 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)
9. q(11+8q-2q^2 )
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.
21. x^2-13x-30
22. d^2-18d+45
8. 4m(2m+9m^2-6)
Distribute Parenthesis -> 4m · 2m + 4m · 9m^2 + 4m(-6)
Multiply -> 4 · 2mm + 4 · 9m^2m - 4 · 6m
Simplify -> 36m^3 + 8m^2 - 24m
9. q(11+8q-2q^2 )
Distribute Parenthesis -> q · 11 + q · 8 + q(-2q^2)
Multiply -> 11q · + 8qq - 2q^2q
Simplify -> -2q^3 +8q^2 + 11q
12. (x-1)^2
This is a perfect square so you can just use the formula:
(a-b)^2 = a^2 -2ab + b^2 (a = x and b = 1)
(x-1)^2 = x^2 - 2(x)(1) + 1^2
Simplify: x^2 - 2x + 1
13. (4y+2)^2
This is also a perfect square formula!
See if you can solve this one using the formula I gave you.
21. x^2-13x-30
break the expression into groups -> (x^2 + 2x) + (-15x -30)
Factor out x from x^2 +2x -> x(x+2)
Factor out -15 from (-15x - 30) -> -15(x + 2)
Combine terms -> x(x + 2) - 15(x + 2)
factor out (x + 2) -> (x+2) (x-15)
22. d^2-18d+45
Break the expression into groups -> (d^2 - 3d) + (-15d + 45)
Factor out d from (d^2 - 3d) -> d(d - 3)
Factor out -15 from (-15d + 45) -> -15(d - 3)
Combine terms -> d(d - 3) - 15(d - 3)
Factor out common term d -3 -> (d - 3) (d - 15)
Hope this helps! Sorry if its not the way you're "supposed" to do it, but it's the only way I remember how to simplify these.
I'm sorry, but I cannot directly provide you with the answers to your questions. However, I can guide you through the process of finding the answers yourself.
Let's start with question 8: Simplify the polynomial 4m(2m+9m^2-6).
To simplify this expression, you need to distribute 4m to each term inside the parentheses.
4m(2m+9m^2-6) = 4m * 2m + 4m * 9m^2 - 4m * 6
Multiplying the terms, we get:
= 8m^2 + 36m^3 - 24m
Now, let's move on to question 9: Simplify the polynomial q(11+8q-2q^2).
Similarly to the previous question, distribute the q to each term inside the parentheses:
q(11+8q-2q^2) = q * 11 + q * 8q - q * 2q^2
Multiplying the terms, we get:
= 11q + 8q^2 - 2q^3
For question 12: Simplify the expression (x-1)^2.
To simplify this expression, you need to square each term inside the parentheses:
(x-1)^2 = (x-1)(x-1)
To simplify further, you can use the FOIL method (First, Outer, Inner, Last):
(x-1)(x-1) = x*x + x*(-1) + (-1)*x + (-1)*(-1)
= x^2 - x - x + 1
Combining like terms, we get:
= x^2 - 2x + 1
Lastly, let's move on to question 13: Simplify the expression (4y+2)^2.
Follow the same process as question 12:
(4y+2)^2 = (4y+2)(4y+2)
Using the FOIL method:
(4y+2)(4y+2) = (4y)*(4y) + (4y)*(2) + (2)*(4y) + (2)*(2)
= 16y^2 + 8y + 8y + 4
Combining like terms, we get:
= 16y^2 + 16y + 4
Now, let's move on to factoring.
For question 21: Factor the polynomial x^2-13x-30.
To factor this polynomial, we need to find two numbers that multiply to give -30 and add to give -13 (since the coefficient of x^2 is 1).
The factors of -30 are: (-1, 30), (-2, 15), (-3, 10), (-5, 6).
Out of these pairs, (-3, 10) is the pair that adds up to -13. Therefore, we can factor the expression as:
x^2 - 13x - 30 = (x - 3)(x + 10)
And finally, for question 22: Factor the polynomial d^2-18d+45.
Similarly, we need to find two numbers that multiply to give 45 and add to give -18.
The factors of 45 are: (-1, -45), (-3, -15), (-5, -9), (1, 45), (3, 15), (5, 9).
Out of these pairs, (-3, -15) is the pair that adds up to -18. Therefore, we can factor the expression as:
d^2 - 18d + 45 = (d - 3)(d - 15)
Remember to always check your factoring by using distributive property to see if you obtain the original expression.
I hope this explanation helps you with your practice sheet!