factor the expression
4xsquared+35x+24
my answer: (4x+3)(x-8)
4x2 +35x+24=
24 = 2x12
24 = 4x6
24 = 8x3*****
(4x+3)(X+8)
4X2 + 3X + 32X +24
+ 4XSQ. + 35X + 24
Pork?
To factor the expression 4x^2 + 35x + 24, we need to find two binomials that, when multiplied, give us the original expression.
First, we look for two numbers that multiply to give us the constant term, 24, and add up to give us the coefficient of the middle term, 35.
The factors of 24 are:
1 x 24 = 24
2 x 12 = 24
3 x 8 = 24
4 x 6 = 24
Now we check if any of these combinations add up to 35. The only pair that does is 3 and 8. Therefore, we can rewrite the middle term, 35x, as the sum of these two numbers: 3x + 32x.
Now we can group the terms:
4x^2 + 35x + 24
= 4x^2 + 3x + 32x + 24
= (4x^2 + 3x) + (32x + 24)
Next, we factor out the greatest common factor (GCF) from each group:
= x(4x + 3) + 8(4x + 3)
Now we see that both groups have a common factor, which is the binomial (4x + 3). We can then factor out this binomial:
= (4x + 3)(x + 8)
Therefore, the factored form of the expression 4x^2 + 35x + 24 is (4x + 3)(x + 8).