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Answer:
1) -5x² + 13x + 6
2) B(x) =(4x + 1 )(2x + 3)
A(x) = (5x +2)(3-x)
Step-by-step explanation:
1) Expand the equation by using distributive property. Then simplify by combining the like terms.
A(x) = (3 -x)2² - (x -3)(7x+ 4) - 18 + 2x²
= (3 - x)4 - [x*7x + x*4 - 3*7x - 3*4] - 18 + 2x²
= 3*4 - x*4 - [7x² + 4x - 21x - 12] - 18 + 2x²
= 12 - 4x - 7x² - 4x + 21x + 12 - 18 + 2x²
= 2x² - 7x² -4x - 4x + 21x + 12 + 12 - 18
= -5x² + 13x + 6
B(x) = (3x + 2)² - (x - 1)²
Identities:
(a + b)² = a² + 2ab + b² ; Here a =3x & b = 2
(m -n)² = m² - 2mn + n² ; Here m = x & n = 1
2) B(x) = (3x)² + 2*3x*2 + 2² - [x² - 2*x*1 + 1]
= 9x² + 12x + 4 - [x² - 2x + 1]
= 9x² + 12x + 4 - x²+ 2x - 1
= 9x² - x² + 12x + 2x + 4 - 1
= 8x² + 14x +3
Product = 8*3 = 24
Sum = 14
Factors = 2 , 12 {2*12 = 24 & 2 +12= 14}
= 8x² + 2x + 12x + 3 {Rewrite the middle term}
= 2x(4x + 1) + 3(4x + 1)
= (4x + 1 )(2x + 3)
A(x) = - 5x² + 13x + 6
= -5x² + 15x -2x + 6
= 5x(-x +3) +2 (-x + 3)
= (5x +2)(3-x)
4) B(x) - 3 = 8x² + 14x + 3 - 3
= 8x² + 14x
= 2x *4x + 2x *7
=2x(4x + 7)
Hence proved.
B(x) = 3
8x² + 14x + 3 = 3
8x² + 14x + 3 - 3 = 0
8x² + 14x = 0
2x(4x + 7) = 0
2x = 0 or 4x + 7 = 0
x = 0 or 4x = -7
[tex]\sf x = \dfrac{-7}{4}[/tex]
x = 0 or [tex]\sf \dfrac{-7}{4}[/tex]