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

( y − 3 ) ( y − 4 ) \left(y-3\right)\left(y-4\right) ( y − 3 ) ( y − 4 )

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

Since this polynomial has a leading term of just y squared, we're going to use the method that we learned recently to factor it where we ask ourselves what are two numbers that multiply to our c value and add to our b value. So let's start by listing some factor pairs for 12. We have one and twelve, as well as two and six, and three and four. Now do any of these sum to seven? Yes. Three plus four equal seven. But we're not looking for seven, we're actually looking for negative seven. So instead, we're gonna use the factor pairs of negative three and negative four, which still multiply to positive 12 but also sum to negative seven. So that means I can factor this polynomial as y minus three times y minus four. And this here is our final answer.

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

( y − 3 ) ( y − 4 ) \left(y-3\right)\left(y-4\right) ( y − 3 ) ( y − 4 )

( y + 3 ) ( y − 4 ) \left(y+3\right)\left(y-4\right) ( y + 3 ) ( y − 4 )

( y + 7 ) ( y − 1 ) \left(y+7\right)\left(y-1\right) ( y + 7 ) ( y − 1 )

( y − 1 ) ( y − 12 ) \left(y-1\right)\left(y-12\right) ( y − 1 ) ( y − 12 )

7. Factoring

Factoring Trinomials of the Form x² + bx + c

Beginning & Intermediate Algebra

7. Factoring

Factoring Trinomials of the Form x² + bx + c

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Multiple Choice

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

$\left(y+3\right)\left(y-4\right)$

$\left(y-3\right)\left(y-4\right)$

$\left(y+7\right)\left(y-1\right)$

$\left(y-1\right)\left(y-12\right)$

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 (-7).

List the factor pairs of 12: (1, 12), (2, 6), (3, 4). Determine which pair sums to -7 when both numbers are negative, since the middle term is negative.

Write the factors as binomials using the numbers found: $(y - a)(y - b)$, where $a$ and $b$ are the numbers from the previous step.

Verify by expanding the binomials using the FOIL method to ensure the product equals the original trinomial.

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