Question

1. $12g^2 - 37g + 28$ 8. $6k^2 - 11k + 4$ 9. $9w^2 + 9w + 2$ 10. $12a^2 + 5a - 2$ 11. $15b^2 + 14b - 8$ 12. $5t^2 + 12t - 9$

Explanation:

Step1: Split middle term (Q7)

$12g^2 - 16g - 21g + 28$

Step2: Factor by grouping (Q7)

$4g(3g - 4) - 7(3g - 4) = (3g - 4)(4g - 7)$

Step3: Split middle term (Q8)

$6k^2 - 8k - 3k + 4$

Step4: Factor by grouping (Q8)

$2k(3k - 4) - 1(3k - 4) = (3k - 4)(2k - 1)$

Step5: Split middle term (Q9)

$9w^2 + 6w + 3w + 2$

Step6: Factor by grouping (Q9)

$3w(3w + 2) + 1(3w + 2) = (3w + 2)(3w + 1)$

Step7: Split middle term (Q10)

$12a^2 + 8a - 3a - 2$

Step8: Factor by grouping (Q10)

$4a(3a + 2) - 1(3a + 2) = (3a + 2)(4a - 1)$

Step9: Split middle term (Q11)

$15b^2 + 20b - 6b - 8$

Step10: Factor by grouping (Q11)

$5b(3b + 4) - 2(3b + 4) = (3b + 4)(5b - 2)$

Step11: Split middle term (Q12)

$5t^2 + 15t - 3t - 9$

Step12: Factor by grouping (Q12)

$5t(t + 3) - 3(t + 3) = (t + 3)(5t - 3)$

Answer:

1. $\boldsymbol{(3g - 4)(4g - 7)}$
2. $\boldsymbol{(3k - 4)(2k - 1)}$
3. $\boldsymbol{(3w + 2)(3w + 1)}$
4. $\boldsymbol{(3a + 2)(4a - 1)}$
5. $\boldsymbol{(3b + 4)(5b - 2)}$
6. $\boldsymbol{(t + 3)(5t - 3)}$