USE THE AC METHOD FACTORING 9+^2+5+-4 CAN SOME ONE SHOW ME THE STEP TO SOLVING THIS PROBLEM
9x^2 + 5x - 4
the AC method
Multiply the 9 times -4
You have -36
think of factors that will multiple to equal -36 but add to equal the middle number 5.
36 times -1 no
9 times -4 yes
Sometimes it takes awhile to find the right numbers.
Once you do, you write them and -4x + 9x
You replace the middle term with them.
9x^2 -4x + 9x - 4
Next, you factor by grouping
(9x^2 -4x) + (9x - 4)
Take out the common factor in each group.
x(9x-4) + 1(9x-4)
see the (9x-4)... you write that down once and get your other factor from what is left over (x+1)
FINAL ANSWER: (9x-4)(x+1)
Multiply those factors to check to be sure you are correct.
To factor the quadratic expression using the AC method, let's start with the given expression: 9x^2 + 5x - 4.
Step 1: Identify the coefficients A, B, and C.
In this case, A = 9, B = 5, and C = -4.
Step 2: Multiply A and C.
Multiply the coefficient of x^2 (A) with the constant term (C): A * C = 9 * (-4) = -36.
Step 3: Find factors of the product AC that add up to B.
We need to determine two numbers that multiply to -36 and add up to 5. Let's list the factor pairs of -36: -1 and 36, -2 and 18, -3 and 12, -4 and 9, -6 and 6. By evaluating these factor pairs, we find that -4 and 9 satisfy the condition (-4 + 9 = 5).
Step 4: Rewrite the middle term using the identified factors.
Rewrite the middle term (Bx) using the two factors from step 3. In this case, replace 5x with -4x + 9x. So the expression becomes: 9x^2 - 4x + 9x - 4.
Step 5: Group the terms.
Group the expression by pairs: (9x^2 - 4x) + (9x - 4).
Step 6: Factor by grouping.
Factor out the greatest common factor (GCF) from each pair. In the first pair, factor out x: x(9x - 4). In the second pair, factor out 1: 1(9x - 4).
Step 7: Factor out the common binomial.
Notice that we now have a common binomial, (9x - 4), in both terms. Factor out this binomial: (x + 1)(9x - 4).
Therefore, using the AC method, the factored form of the expression 9x^2 + 5x - 4 is (x + 1)(9x - 4).