Can someone please help
2 answers:
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Answer:
GCF = 5
Step-by-step explanation:
Given:
The numbers are given as:
10, 30 and 45
A factor of a number is a number by which the given number is evenly divisible.
Example: 2 is a factor of 4 as . So, 4 is evenly divisible by 2 and hence 2 is a factor of 4.
Now, factors of 10 = 1, 2, <u>5</u>, 10.
Factors of 30 = 1, 2, 3, <u>5</u>, 6, 10, 15, 30.
Factors of 45 = 1, 3, <u>5</u>, 9, 15, 45.
So, the greatest common factor in all the three numbers is 5.
Hence, the greatest common factor of 10, 30 and 45 is 5.
Answer:
see explanation
Step-by-step explanation:
(9)
Expand and simplify right side and compare coefficients of like terms on left side.
(x - 2)(x² + ax + b) + c
= x³ + ax² + bx - 2x² - 2ax - 2b + c
= x³ + x²(a - 2) + x(b - 2a) - 2b + c
compare with
x³ + 2x² - 3x + 4
x² terms
a - 2 = 2 ( add 2 to both sides )
a = 4
x terms
b - 2a = - 3 ← substitute a = 4
b - 8 = - 3 ( add 8 to both sides )
b = 5
constant terms
- 2b + c = 4 ← substitute b = 5
- 10 + c = 4 ( add 10 to both sides )
c = 14
Thus a = 4, b = 5 and c = 14
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(10)
Since both functions cross the x- axis at - 2 then (- 2, 0) satisfies both, that is
f(- 2) = + a(- 2)³ + b(- 2)² + 36(- 2) + 144 = 0, that is
- 16 - 8a + 4b - 72 + 144 = 0
- 8a + 4b + 56 = 0
- 8a + 4b = - 56 → (1)
and
g(- 2) = + (a + 3)(- 2)³ - 23(- 2)² + (b + 10)(- 2) + 40 = 0, that is
- 16 - 8(a + 3) - 92 - 2(b + 10) + 40 = 0
- 16 - 8a - 24 - 92 - 2b - 20 + 40 = 0
- 8a - 2b - 112 = 0
- 8a - 2b = 112 → (2)
Subtract (1) from (2) term by term
- 6b = 168 ( divide both sides by - 6 )
b = - 28
Substitute b = - 28 into (2)
- 8a + 56 = 112 ( subtract 56 from both sides )
- 8a = 56 ( divide both sides by - 8 )
a = - 7
Thus a = - 7 and b = - 28