To determine To calculate: The partial decomposition of the function 6x+8x2+4x+4.

Question

To determine  To calculate: The partial decomposition of the function 6x+8x2+4x+4.

Ched1950 · Accepted Answer

Calculation: Consider the provided expression, Here, f(x)=6x+8 and g(x)=x2+4x+4 Factorize g(x): g(x)=x2+4x+4 =x2+2x+2x+4 =x(x+2)+2(x+2) =(x+2)2 So, the expression can be written as, 6x+8x2+4x+4=6x+8(x+2)2 Here, in g (x), there is one linear factor with square power. So, the expression can be decomposed as: 6x+8(x+2)2=Ax+2+B(x+2)2…………(1) Here, Least Common Divisor (x+2)2 Multiply both sides of (1) by the Least Common Divisor to clear fractions: (x+2)2[6x+8(x+2)2]=(x+2)2[Ax+2+B(x+2)2] Simplify to obtain: 6x+8=A(x+2)+B 6x+8=Ax+2A+B 6x+8=(A)x+(2A+B) Compare the coefficients of x and constant terms: A=6 nd2A+B=nd2A+B=8 Substitute 6 for A in equation 2A + B = 8 and simplify for B: 2(6)+B=8 12+b=8 B=−4 Substitute the obtained values of A and B in equation (1): 6x+8(x+2)2=6x+2+−4(x+2)2 Therefore, the partial fraction decomposition for 6x+8(x+2)2s6x+2+−4(x+2)2s6x+2+−4(x+2)2

To determine To calculate: The partial decomposition of the functi

Answered question

Answer & Explanation

New Questions in Pre-Algebra