Question

when factoring the trinomial $4x^2 - 15x + 9$, which pair of factors of $36(a * c)$ sums to $-15(b)$? -4 and -9; -12 and -3; 12 and 3; 6 and 6

Explanation:

Step1: Recall the product and sum

We need two numbers that multiply to \(36\) (since \(a = 4\), \(c=9\), \(a\times c=4\times9 = 36\)) and add up to \(- 15\).

Step2: Analyze the sign and factors

Since the product is positive (\(36\)) and the sum is negative (\(-15\)), both numbers must be negative (because negative times negative is positive and negative plus negative is negative).
Let's check the pairs:

• For \(-4\) and \(-9\): \((-4)\times(-9)=36\), \((-4)+(-9)=-13

eq - 15\)

• For \(-12\) and \(-3\): \((-12)\times(-3) = 36\), \((-12)+(-3)=-15\)
• For \(12\) and \(3\): \(12\times3 = 36\), \(12 + 3=15

eq-15\)

• For \(6\) and \(6\): \(6\times6=36\), \(6 + 6 = 12

eq-15\)

Answer:

B. -12 and -3