Doubt in factoring a trinomial

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Discussion Overview

The discussion revolves around factoring the trinomial expression $3x^2 + 11x + 10$. Participants explore different methods and approaches to factor the expression correctly, focusing on the mathematical reasoning behind their steps.

Discussion Character

  • Mathematical reasoning
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses confusion about their initial attempt to factor the expression, suggesting a separation into $3x^2 + 10x + x + 10$.
  • Another participant proposes a method by multiplying the first coefficient and the last term to find factors of 30 that sum to 11, concluding that the factorization is $(3x + 5)(x + 2)$.
  • A similar approach is reiterated by another participant, emphasizing the multiplication of the first coefficient by the last to arrive at the same factorization.
  • One participant provides an alternative factoring method by rearranging the terms and grouping them, leading to the same factorization of $(3x + 5)(x + 2)$.

Areas of Agreement / Disagreement

Participants generally agree on the factorization of the trinomial as $(3x + 5)(x + 2)$, but there is no explicit consensus on the initial confusion expressed by the first participant regarding their method.

Contextual Notes

The discussion does not address potential limitations in the initial approach or assumptions made during the factoring process. There are also no unresolved mathematical steps noted.

mathlearn
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Hey (Wave) (Party),

Problem

Factor $3x^2+11x+10$

Workings

This expression can be separated into,

$3x^2+10x+x+10$

Where have i done wrong ? (Thinking)

Many Thanks :)
 
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What I would do here is observe that:

$$3\cdot10=30$$

$$6\cdot5=30$$

$$6+5=11$$

Hence:

$$3x^2+11x+10=(3x+5)(x+2)$$
 
MarkFL said:
What I would do here is observe that:

$$3\cdot10=30$$

$$6\cdot5=30$$

$$6+5=11$$

Hence:

$$3x^2+11x+10=(3x+5)(x+2)$$

Did you multiply the expression by 3 (Happy) to get 30.
 
mathlearn said:
Did you multiply the expression by 3 (Happy) to get 30.

I multiplied the first coefficient by the last to get 30, and then looked for two factors of this product whose sum is 11, which are 6 and 5.

Here's a tutorial I wrote on the subject:

http://mathhelpboards.com/math-notes-49/factoring-quadratics-3396.html
 
Alternatively,

$$\begin{align*}3x^2+11x+10&=3x^2+5x+6x+10 \\
&=x(3x+5)+2(3x+5) \\
&=(3x+5)(x+2)\end{align*}$$
 

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