Question

i need help woth these sample questions. will you show me step-by-step how to do each of them?
1: x^2 + 15x + 44
2: n^2 - 15n + 56
3: x^2 - 4x - 12
4: the area of a rectangular rug is given by the trinomonial r^2 - 6r - 55.What are the possible demensions of the rug?What are the length and the idth of the rug?
5: x^2 + 2xy - 99y^2
6: 9y^2 + 27y + 14
7; 2x^2 + 3x - 9
8: the area of knitted blanket is 10x^2 - 11x - 6.What are the possible demensions of the blanket?
9: 25x^2 35x - 30
10: x2 - 22x + 12r
11: x^2 - 25
12: 64c^2 - 9
13: 144y^2 - 196
14: 9z^8 + 81z^2 - 7^2 - 63
15: v= 4

Answer 1

v=4y^3 + 15y^2 + 9y

Answer 2

1: x^2 + 15x + 44

Is this an exercise in factoring?

Fidn all the factorizations of 44

1 * 44
2 * 22
4 * 11

Everything is positive, so which of those factorizations, if any, when added together, gives 15?

1 + 44 = 45 Nope
2 + 22 = 24 Nope
4 + 11 = 15 -- We have a winner!

(x+4)(x+11) Done.

Answer 3

that was right and i understad a little more now thank you, can you help me with the others? @tkhunny

Answer 4

You can show me the next one. Go!

Answer 5

n^2 - 15n + 56 @tkhunny

Answer 6

Here is may be the fastest method (the Diagonal Sum Method) to solve these type of equations, when a = 1. First, recall the Rule of signs.
When a and c have different signs, the roots have different signs
When a and c have same sign, the roots have same sign
- When a and b have different signs, both roots are positive
- When a and b have same sign, both roots are negative.
1. Solve: x^2 + 15x + 44 = 0. Solving results in finding 2 numbers knowing their sum (-b) and their product (c). Both roots are negative (Rule of signs). Compose factor pairs of c = 44. Proceeding: (-1, -44)(-2, -22)(-4, -11). The last sum is -4 - 11 = -15 = -b. Then the 2 real roots are -4 and -11.
Write in factoring form: (x + 4)(x + 11) = 0
2. Solve x^2 - 15x + 56 = 0. Both roots are positive. Compose factor pairs of c = 56. Proceeding: (1, 56)(2, 28)(7, 8). This last sum is 7 + 8 = 15 = -b. Then, the 2 real roots are 7 and 8. Factoring form: (x -7)(x - 8) = 0
3. Solve: x^2 - 4x - 12 = 0, Roots have different signs. Compose factor pairs of c = -12. Proceeding: (-1, 12)(-2, 6). This last sum is 4 = -b. Then the 2 real roots are: -2 and 6.

Answer 7

5. x^2 + 2xy - 99y^2 . To factor, find 2 numbers b1 and b2 that satisfy: b1*b2 = -99y^2, and (b1 + b2) = 2. Compose factor pairs of -99y^2. Proceeding" ...(-9, + 11). They are b1 = -9 and b2 = 11. Replace in the equation the term 2yx by the 2 terms 11y and -9y then factor.
Finally: (x - 9y)(x + 11y)
6. 9y^2 + 27y + 14.Proceed with the same method. b1*b2 = 126; (b1 + b2) = 27. b1 = 6; b2 = 21.
(3y + 2)(3y + 7)
7. 2x^2 + 3x -9 = (2x - 3)(x + 3). b1*b2 = -18;(b1 + b2) = 3; b1 = -3, b2 = 6.
8. 10x^2 - 11x - 6 = (5x + 2)(2x - 3)

Answer 8

@myininaya

Answer 9

10x^2 - 11x - 6 = (5x + 2)(2x - 3). Possible dimensions of the blanket:
x = 2 -> Dimensions: 12 x 1
x = 3 -> id 17 x 3
x = 4 -> id 22 x 5....

Answer 10

4. Area of the rug:
r^2 - 6r - 55 = (r + 5)(r - 11). Possible dimensions:
r = 6 -> Dimension 1 x 12
r = r -> id 2 x 13
r = 8 -> id 3 x 14 ......