solved the math
Answers
Answer:
-1(t-4) (t+1)
Step-by-step explanation:
Rearrange terms
4
+
3
−
1
2
4+3t-1t^{2}
−
2
+
3
+
4
-t^{2}+3t+4
2
Common factor
4
+
3
−
1
2
4+3t-1t^{2}
−
1
(
2
−
3
−
4
)
-1(t^{2}-3t-4)
3
Use the sum-product pattern
−
1
(
2
−
3
−
4
)
-1(t^{2}{\color{#c92786}{-3t}}-4)
−
1
(
2
+
−
4
−
4
)
-1(t^{2}+{\color{#c92786}{t}}{\color{#c92786}{-4t}}-4)
4
Common factor from the two pairs
−
1
(
2
+
−
4
−
4
)
-1(t^{2}+t-4t-4)
−
1
(
(
+
1
)
−
4
(
+
1
)
)
-1(t(t+1)-4(t+1))
5
Rewrite in factored form
−
1
(
(
+
1
)
−
4
(
+
1
)
)
-1(t(t+1)-4(t+1))
−
1
(
−
4
)
(
+
1
)
Step-by-step explanation:
The first term is, -t2 its coefficient is -1 .
The middle term is, +3t its coefficient is 3 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant -1 • 4 = -4
Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is 3 .
-4 + 1 = -3
-2 + 2 = 0
-1 + 4 = 3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 4
-t2 - 1t + 4t + 4
Step-4 : Add up the first 2 terms, pulling out like factors :
-t • (t+1)
Add up the last 2 terms, pulling out common factors :
4 • (t+1)
Step-5 : Add up the four terms of step 4 :
(-t+4) • (t+1)
Which is the desired factorization
Final result :