Factor 15x^2 - 8x - 16
(5x+4)(3x-4)
To factor the polynomial 15x^2 - 8x - 16, we need to find two binomials that, when multiplied, give us back the original polynomial.
Step 1: Multiply the coefficient of the leading term (15) with the constant term (-16). In this case, 15 * (-16) = -240.
Step 2: Determine the factors of the result obtained in Step 1 (-240) that will add up to the coefficient of the middle term (-8).
The factors of -240 that add up to -8 are -20 and +12.
Step 3: Rewrite the middle term (-8x) using these two factors.
15x^2 - 20x + 12x - 16
Step 4: Group the terms into two pairs.
(15x^2 - 20x) + (12x - 16)
Step 5: Factor out the greatest common factor (GCF) from each pair.
5x(3x - 4) + 4(3x - 4)
Step 6: Notice that we have a common binomial factor, (3x - 4), in both terms.
(5x + 4)(3x - 4)
Thus, the factored form of the polynomial 15x^2 - 8x - 16 is (5x + 4)(3x - 4).