Question

1. $12g^2 - 37g + 28$ 8. $6k^2 - 11k + 4$

Explanation:

Step1: Split middle term (Q7)

Find two terms that multiply to $12g^2 \times 28 = 336g^2$ and add to $-37g$: $-21g$ and $-16g$.
$12g^2 -21g -16g +28$

Step2: Factor by grouping (Q7)

Group terms and factor out GCFs:
$3g(4g -7) -4(4g -7)$
Factor out $(4g-7)$: $(3g-4)(4g-7)$

Step3: Split middle term (Q8)

Find two terms that multiply to $6k^2 \times 4 = 24k^2$ and add to $-11k$: $-8k$ and $-3k$.
$6k^2 -8k -3k +4$

Step4: Factor by grouping (Q8)

Group terms and factor out GCFs:
$2k(3k -4) -1(3k -4)$
Factor out $(3k-4)$: $(2k-1)(3k-4)$

Answer:

1. $(3g-4)(4g-7)$
2. $(2k-1)(3k-4)$