Question

6.2 grouping: problem 7
(1 point)
the polynomial ( 48 x ^ { 3 } + 30 x ^ { 2 } + 40 x + 25 ) can be factored into the product of two polynomials, ( a cdot b ) where the degree of ( a ) is greater than the degree of ( b ). find ( a ) and ( b ).

( a = )
( b = )
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Explanation:

Step1: Group the polynomial

Group the polynomial \(48x^{3}+30x^{2}+40x + 25\) as \((48x^{3}+30x^{2})+(40x + 25)\).
Factor out the greatest common factor from each group:
For the first group \(48x^{3}+30x^{2}=6x^{2}(8x + 5)\).
For the second group \(40x + 25 = 5(8x+5)\).

Step2: Factor by grouping

Now, the polynomial becomes \(6x^{2}(8x + 5)+5(8x + 5)\).
Factor out the common binomial factor \((8x + 5)\), we get \((6x^{2}+5)(8x + 5)\).

Since the degree of \(A\) is greater than the degree of \(B\) (degree of \(6x^{2}+5\) is \(2\) and degree of \(8x + 5\) is \(1\))

Answer:

\(A=6x^{2}+5\), \(B = 8x+5\)