7. Factoring

Factoring Trinomials of the Form x² + bx + c

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Multiple Choice

Factor the following trinomials completely.
$y^{2} - 7 y + 12$

$(y + 3) (y - 4)$

$(y - 3) (y - 4)$

$(y + 7) (y - 1)$

$(y - 1) (y - 12)$

Verified step by step guidance

Identify the trinomial to factor: $y^2 - 7y + 12$.

Look for two numbers that multiply to the constant term \$12$ and add up to the coefficient of the middle term, which is $-7$.

List the factor pairs of \$12$: $(1, 12)$, $(2, 6)$, and $(3, 4)$. Since the middle term is negative, consider pairs where both numbers are negative.

Check which pair of negative numbers adds to $-7$: $-3$ and $-4$ multiply to \$12$ and add to $-7$.

Write the factored form using these numbers: $(y - 3)(y - 4)$.

Master Factoring Trinomials of the Form x² + bx + c with a bite sized video explanation from Patrick Ford

Factor the following trinomials completely.y2−7y+12y^2-7y+12