A: This quadratic expression can be factored by finding the correct pair of binomial factors.
B: (5x + 8)
B: (3x - 2)
perfect square trinomial:
(a + b)² = a² + 2ab + b²
or (a - b)² = a² - 2ab + b²
this needs coefficient on x² and the constant to be perfect squares
difference of squares:
a² - b² = (a+b)(a-b)
so for 15x² + 14x - 16 we can't use either.
it's clearly not a difference of squares
16 is a perfect square but 15 is not
for A: This quadratic expression can be factored by finding the correct pair of binomial factors.
to factor this we need to find a certain number.
we get number by multiply the coefficient on x² by constant term.
in 15x² + 14x - 16, we multiply 15 by -16 to get -240
now we have to find two numbers that
multiply to get -240 and add to get 14
these two numbers are 24 and -10 because 24 * -10 = -240 and 24 + (-10) = 14
break down +14x with those two numbers we found
15x² + 14x - 16 = 15x² + 24x - 10x - 16
factor by group: (15x² + 24x) - (10x - 16)
for 15x² + 24x, we factor out 3x
for (10x - 16), we factor out -2
= 3x(5x + 8) - 2(5x + 8)
factor out (5x + 8)
= (3x - 2)(5x + 8)
so the factors are
B: (5x + 8)
B: (3x - 2)
