Factorize the algebraic expression 3x2 + 7x − 12x − 34 − 2x2 + 10

Question

ScanSolve AI Tutor · Accepted Answer

Here is a step-by-step guide on how to factorize the algebraic expression $3x^2 + 7x - 12x - 34 - 2x^2 + 10$ :

Combine like terms*.
Identify and group terms that have the same variable and exponent.
$(3x^2 - 2x^2) + (7x - 12x) + (-34 + 10)$
Simplify the expression*.
Perform the addition and subtraction for each group of like terms.
$(3-2)x^2 + (7-12)x + (-34+10)$ $1x^2 - 5x - 24$
The simplified expression is $x^2 - 5x - 24$ .
Identify two numbers that multiply to the constant term and add to the coefficient of the middle term*.
For the quadratic trinomial $x^2 - 5x - 24$ , we need two numbers that:
- Multiply to $-24$ (the constant term).
- Add up to $-5$ (the coefficient of the $x$ term). Let's consider factors of $-24$ : $1 \times (-24) = -24$ , $1 + (-24) = -23$ $2 \times (-12) = -24$ , $2 + (-12) = -10$ $3 \times (-8) = -24$ , $3 + (-8) = -5$ The two numbers are 3 and $-8$ .
Write the expression in factored form*.
Using the two numbers found in Step 3, the trinomial $x^2 - 5x - 24$ can be factored as $(x + \text{first number})(x + \text{second number})$ .
$(x + 3)(x - 8)$

Factorize the algebraic expression 3x2 + 7x - 12x - 34 - 2x2 + 10