How do I factorize the algebraic expression 3x2 + 7x − 12x − 34 − 2x2 + 10?

Question

ScanSolve AI Tutor · Accepted Answer

Here's a step-by-step guide for Alice to factorize the algebraic expression:

3.5.1 Provide Alice with a step-by-step guide on how to factorize the algebraic expression.
The expression is $3x^2 + 7x - 12x - 34 - 2x^2 + 10$ .

Simplify the expression by combining all like terms.
Combine the $x^2$ terms, the $x$ terms, and the constant terms.
$(3x^2 - 2x^2) + (7x - 12x) + (-34 + 10)$ $x^2 - 5x - 24$
Identify two numbers that multiply to the constant term (which is $-24$ ) and add up to the coefficient of the middle term (which is $-5$ ).
The two numbers are 3 and $-8$ , because $3 \times (-8) = -24$ and $3 + (-8) = -5$ .
Write the simplified trinomial as a product of two binomials using these two numbers.
$(x + 3)(x - 8)$

How do I factorize the algebraic expression 3x2 + 7x - 12x - 34 - 2x2 + 10?

Answer

Step-by-step solution

Simplify the expression by combining all like terms.

Identify two numbers that multiply to the constant term (which is $-24$ ) and add up to the coefficient of the middle term (which is $-5$ ).

Write the simplified trinomial as a product of two binomials using these two numbers.

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