Question

instructions: factor each polynomial.

1. $4x^3 + 6x^2 - 2x - 3$
2. $2x^3 + 2x^2 + 3x + 3$
3. $5x^3 + 25x^2 - x - 5$
4. $3x^3 - 4x^2 - 12x + 16$
5. $x^4 - 9x^2 + 18$
6. $x^4 - 11x^2 + 28$
7. $x^4 + 3x^2 - 18$
8. $7x^4 + 24x^2 + 20$

Explanation:

Step1: Factor by grouping

Group the first two terms and the last two terms: $(4x^{3}+6x^{2})+(-2x - 3)$
Factor out the GCF from each group: $2x^{2}(2x + 3)-1(2x + 3)$

Step2: Factor out the common binomial factor

Factor out $(2x + 3)$: $(2x^{2}-1)(2x + 3)$

Step1: Factor by grouping

Group the first two terms and the last two terms: $(2x^{3}+2x^{2})+(3x + 3)$
Factor out the GCF from each group: $2x^{2}(x + 1)+3(x + 1)$

Step2: Factor out the common binomial factor

Factor out $(x + 1)$: $(2x^{2}+3)(x + 1)$

Step1: Factor by grouping

Group the first two terms and the last two terms: $(5x^{3}+25x^{2})+(-x - 5)$
Factor out the GCF from each group: $5x^{2}(x + 5)-1(x + 5)$

Step2: Factor out the common binomial factor

Factor out $(x + 5)$: $(5x^{2}-1)(x + 5)$

Step1: Factor by grouping

Group the first two terms and the last two terms: $(3x^{3}-4x^{2})+(-12x + 16)$
Factor out the GCF from each group: $x^{2}(3x - 4)-4(3x - 4)$

Step2: Factor out the common binomial factor

Factor out $(3x - 4)$: $(x^{2}-4)(3x - 4)$

Step3: Factor the difference of squares

Factor $(x^{2}-4)$ as $(x - 2)(x + 2)$: $(x - 2)(x + 2)(3x - 4)$

Answer:

$(2x^{2}-1)(2x + 3)$

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