Q. 358 - Intermediate Algebra

Question

Factor Trinomials of the Form $x^2+bx+c$
In the following exercises, factor each trinomial of the form $x^2+bx+c$.

$x^2-3x-10$

Step-by-Step Solution

Answer

The binomial factors of $x^2-3x-10$ is $(x-5)(x+2)$

Step 1. Given

The trinomial $x^2-3x-10$

To factor the given trinomial

Step 2. Write as binomials with first term as x

Write two sets of parentheses and put $x$ as the first term.

$x^2-3x-10=(x )(x )$

Step 3. Find two numbers that multiply to c and add to b

Find two numbers that multiply to give $-10$ and add to $-3$.

Factors of $-10$	Addition of factors
$1,-10$	$-9$
$2,-5$	$-3$

Step 4. Use numbers as last number of factors.

So the factor that multiply to give $-10$ and add to $-3$ is $-5,2$.

So the factor is $(x-5)(x+2)$

Step 5. Check the answer

The factors are $(x-5)(x+2)$

Multiply the factors 

$(x-5)(x+2)=x^2+2x-5x-10$

                     $=x^2-3x-10$

Hence the multiplication of factors gives the trinomial.