(B) \( t^{2}+4 t-21 \) (C) \( t^{2}+5 t-6 \) (D) \( t^{2}-2 t-8 \) (E) \( t^{2}-10 t-11 \) (F) \( t^{2}+4 t-12 \) (G) \( t^{2}-8 t-20 \) (H) \( t^{2}-t-72 \)

Below are the factorizations for each quadratic: (B) t² + 4t – 21   We need two numbers that multiply to –21 and add to 4. Since 7 × (–3) = –21 and 7 + (–3) = 4, we have:   t² + 4t – 21 = (t + 7)(t – 3). (C) t² + 5t – 6   Find factors of –6 that add to 5. Since 6 × (–1) = –6 and 6 + (–1) = 5, we get:   t² + 5t – 6 = (t + 6)(t – 1). (D) t² – 2t – 8   Look for two numbers multiplying to –8 and adding to –2. Since 2 × (–4) = –8 and 2 + (–4) = –2, the factorization is:   t² – 2t – 8 = (t + 2)(t – 4). (E) t² – 10t – 11   We need two numbers whose product is –11 and whose sum is –10. Since (–11) × 1 = –11 and (–11) + 1 = –10, we have:   t² – 10t – 11 = (t – 11)(t + 1). (F) t² + 4t – 12   Find two numbers multiplying to –12 and adding to 4. Since 6 × (–2) = –12 and 6 + (–2) = 4, the factorization is:   t² + 4t – 12 = (t + 6)(t – 2). (G) t² – 8t – 20   We seek two numbers whose product is –20 and whose sum is –8. Since (–10) × 2 = –20 and (–10) + 2 = –8, we get:   t² – 8t – 20 = (t – 10)(t + 2). (H) t² – t – 72   We need numbers that multiply to –72 and add to –1. Since 8 × (–9) = –72 and 8 + (–9) = –1, it factors as:   t² – t – 72 = (t + 8)(t – 9). Each quadratic factors into two binomials as shown above.