How do you factor $3 h^{2} + 19 h + 20$ $3h^2 + 19h + 20$ ?

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How do you factor $3 h^{2} + 19 h + 20$ $3h^2 + 19h + 20$ ?

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Answer 1 · 2015-06-02T06:31:15

$f (h) = 3 h^{2} + 19 h + 20$ $f(h) = 3h^2+19h+20$

Let's use AC Method, with a twist...

$A = 3$ $A=3$ , $B = 19$ $B=19$ , $C = 20$ $C=20$

Look for a factorization of $A C = 3 \cdot 20 = 60$ $AC=3*20=60$ into a pair of factors whose sum is $B = 19$ $B=19$ .

The pair $B 1 = 4$ $B1=4$ , $B 2 = 15$ $B2=15$ works.

Then for each of the combinations $A$ $A$ , $B 1$ $B1$ and $A$ $A$ , $B 2$ $B2$ , divide by the $HCF$ $"HCF"$ (highest common factor) to get the coefficients of a factor of $f (h)$ $f(h)$ ...

$(A, B 1) = (3, 4)$ $(A, B1) = (3, 4)$ $(HCF 1)$ $("HCF 1")$ $\to$ $rarr$ $(3, 4)$ $(3, 4)$ $\to$ $rarr$ $(3 h + 4)$ $(3h+4)$
$(A, B 2) = (3, 15)$ $(A, B2) = (3, 15)$ $(HCF 3)$ $("HCF 3")$ $\to$ $rarr$ $(1, 5)$ $(1, 5)$ $\to$ $rarr$ $(h + 5)$ $(h+5)$

So $f (h) = 3 h^{2} + 19 h + 20 = (3 h + 4) (h + 5)$ $f(h) = 3h^2+19h+20 = (3h+4)(h+5)$

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How do you factor $3 h^{2} + 19 h + 20$ $3h^2 + 19h + 20$ ?

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