Answer:
a = 7 and b = - 18
Step-by-step explanation:
If (x - 1) is a factor of f(x) then x = 1 is a root and f(1) = 0, thus
f(1) = 1³ + 10(1)² + a + b = 0 and
1 + 10 + a + b = 0 ⇒ a + b = - 11 → (1)
Similarly if
(x + 2) is a factor then x = - 2 is a root and f(- 2) = 0
f(- 2) = (- 2)³ + 10(- 2)² - 2a + b = 0, thus
- 8 + 40 - 2a + b = 0 ⇒ - 2a + b = - 32 → (2)
Solve (1) and (2) simultaneously
Subtract (1) from (2)
- 3a = - 21 ( divide both sides by 3)
a = 7
Substitute a = 7 in (1)
7 + b = - 11 ⇒ b = - 11 - 7 = - 18
The required polynomial is
f(x) = x³ + 10x² + 7x - 18
48 divisors: 1; 2; 3; 4; 6; 8; 12; 16; 24; 48;
Answer:
Step-by-step explanation:
Width =w
Length = w + 6
Perimeter of rectangular room = 54 m
2*(length +width ) = 54
2*(w +6 + w) = 54
2*(<u>w +w</u> + 6) = 54 {Combine like terms}
2*(2w + 6) = 54
Use distributive property
2*2w + 2*6 = 54
4w + 12 = 54
Subtract 12 form both side
4w = 54 - 12
4w = 42
Divide both sides by 4
w = 42/4
w = 10.5 m
Length = 10.5 + 6 = 16.5 m
Length = 16.5 m
Width = 10.5 m
If it involves an Arc, the inscribed angle is 1/2 of the measure of the are across from it. If the figure inscribed in a quadrilateral, opposite angles are supplementary (when added together equals 180 degrees) This is all I know :)
Answer:
6
Step-by-step explanation:
