Factor the expression \(8y^2 - 22y - 21\).
Answer (2)
8 y 2 − 22 y − 21 = 0 a = 8 , b = − 22 , c = − 21 Δ = b 2 − 4 a c = ( − 22 ) 2 − 4 ∗ 8 ∗ ( − 21 ) = 484 + 672 = 1156 y 1 = 2 a − b − Δ = 2 ∗ 8 22 − 1156 = 16 22 − 34 = 16 − 12 = − 4 3 y 2 = 2 a − b + Δ = 2 ∗ 8 22 + 1156 = 16 22 + 34 = 16 56 = 2 7 = 3 2 1
To factor the expression 8 y 2 − 22 y − 21 , we find that the factored form is ( 4 y + 3 ) ( 2 y − 7 ) . This is achieved by identifying two numbers that add to -22 and multiply to -168, which leads us to split the middle term and factor by grouping. Ultimately, the expression factors neatly into two binomials.
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