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Answer:
[tex]A = 2[/tex]
[tex]B = -1[/tex]
[tex]C = -9[/tex]
Step-by-step explanation:
Given
[tex]2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C[/tex]
Required
Find A, B and C
Rearrange the expression
[tex]2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C[/tex]
[tex]2x\² + 15x + 19 = Ax\² + 8Ax + Bx + 16A + 4B + C[/tex]
To do this, we simply compare the expressions on both sides of the equation.
So, we have:
[tex]Ax\² = 2x\²[/tex] --- (1)
[tex]8Ax + Bx = 15x[/tex] --- (2)
[tex]16A + 4B + C = 19[/tex] --- (3)
Divide both sides by x² in (1)
[tex]Ax\² = 2x\²[/tex]
[tex]A = 2[/tex]
Divide both sides by x in (2)
[tex]8Ax + Bx = 15x[/tex]
[tex]8A + B = 15[/tex]
Substitute 2 for A.
[tex]8*2 + B = 15[/tex]
[tex]16+ B = 15[/tex]
Make B the subject
[tex]B = 15 - 16[/tex]
[tex]B = -1[/tex]
Substitute 2 for A and -1 for B in (3)
[tex]16A + 4B + C = 19[/tex]
[tex]16*2 + 4*-1 + C = 19[/tex]
[tex]32 - 4 + C = 19[/tex]
[tex]28 + C = 19[/tex]
Make C the subject
[tex]C = 19 - 28[/tex]
[tex]C = -9[/tex]
Answer:
it D
Step-by-step explanation:
I just used elimination like a small brain
like so
when a = 1, b = 0, c = 3, d = -3
x^3 + 8x – 3 = Ax^3 + 5Ax + Bx^2 + 5B + Cx + D