Question

trinomial factoring
factor the following expressions using trinomial \abc\ factoring.

1. ( x^2 + 25x + 24 )
2. ( x^2 + 11x + 24 )
3. ( x^2 -14x + 24 )
4. ( x^2 + 5x - 24 )
5. ( x^2 - 2x - 24 )
6. ( x^2 + 23x - 24 )

gcf review
factor out a gcf from each of the following expressions
r1) ( 20 + 2x )
r2) ( 6x - 4x^3 )
r3) ( 9x^2y + 12x^5y )

Explanation:

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Trinomial Factoring

1) $x^2 + 25x + 24$

Step1: Find pair summing to 25, product 24

Pairs: $1,24$ (1+24=25, 1×24=24)

Step2: Write factored form

$(x+1)(x+24)$

2) $x^2 + 11x + 24$

Step1: Find pair summing to 11, product 24

Pairs: $3,8$ (3+8=11, 3×8=24)

Step2: Write factored form

$(x+3)(x+8)$

3) $x^2 -14x + 24$

Step1: Find pair summing to -14, product 24

Pairs: $-2,-12$ (-2+(-12)=-14, (-2)×(-12)=24)

Step2: Write factored form

$(x-2)(x-12)$

4) $x^2 + 5x - 24$

Step1: Find pair summing to 5, product -24

Pairs: $8,-3$ (8+(-3)=5, 8×(-3)=-24)

Step2: Write factored form

$(x+8)(x-3)$

5) $x^2 - 2x - 24$

Step1: Find pair summing to -2, product -24

Pairs: $-6,4$ (-6+4=-2, (-6)×4=-24)

Step2: Write factored form

$(x-6)(x+4)$

6) $x^2 + 23x - 24$

Step1: Find pair summing to 23, product -24

Pairs: $24,-1$ (24+(-1)=23, 24×(-1)=-24)

Step2: Write factored form

$(x+24)(x-1)$
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GCF Review

R1) $20 + 2x$

Step1: Identify GCF of 20 and 2x

GCF = 2

Step2: Factor out GCF

$2(10 + x)$

R2) $6x - 4x^3$

Step1: Identify GCF of 6x and $4x^3$

GCF = $2x$

Step2: Factor out GCF

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

R3) $9x^2y + 12x^5y$

Step1: Identify GCF of terms

GCF = $3x^2y$

Step2: Factor out GCF

$3x^2y(3 + 4x^3)$

Answer:

Trinomial Factoring:

1. $(x+1)(x+24)$
2. $(x+3)(x+8)$
3. $(x-2)(x-12)$
4. $(x+8)(x-3)$
5. $(x-6)(x+4)$
6. $(x+24)(x-1)$

GCF Review:
R1. $2(10 + x)$
R2. $2x(3 - 2x^2)$
R3. $3x^2y(3 + 4x^3)$