Factor the polynomial [tex]6b^2 - 17b + 10[/tex].

6 b 2 − 17 b + 10 Δ = b 2 − 4 a c = ( − 17 ) 2 − 4 ∗ 6 ∗ 10 = 289 − 240 = 49 x 1 ​ = 2 a − b − Δ ​ ​ = 2 ∗ 6 17 − 49 ​ ​ = 12 17 − 7 ​ = 12 10 ​ = 6 5 ​ x 2 ​ = 2 a − b + Δ ​ ​ = 2 ∗ 6 17 + 49 ​ ​ = 12 17 + 7 ​ = 12 24 ​ = 2 A n s w er : x = 6 5 ​ or x = 2

Answered by Lilith | 2024-06-10

The polynomial 6 b 2 − 17 b + 10 can be factored as ( 2 b − 5 ) ( 3 b − 2 ) . This is achieved by using the method of factoring by grouping after identifying the appropriate factors of the product of the leading coefficient and the constant term. The final, factored form provides a clearer understanding of the polynomial's roots.
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Answered by Lilith | 2024-12-20