4. Let g(m) be the first derivative of 0*m - 1 - 10/3*m**3 - s*m**4 + 1/3*m**6 - 2*m**2 + 2/5*m**5. Factor g(w).
2*w*(w - 2)*(w + 1)**3
Let c = 68/9 - 322/45. Factor -c*q**2 + 0 + 4/5*q.
-2*q*(q - 2)/5
Let f(d) be the first derivative of d**4/18 + d**3/6 + d**2/6 + 4*d - 4. Let r(t) be the first derivative of f(t). Let r(n) = 0. What is n?
-1, -1/2
Let f be ((-5)/(-20))/(1/1). Suppose 3*z + 5 = 14. Let f*x**z + 0*x + 0 + 0*x**2 = 0. What is x?
0
Let u(w) be the third derivative of -w**8/1512 + 2*w**7/945 + w**6/135 - w**5/135 - w**4/36 - 23*w**2. What is x in u(x) = 0?
-1, 0, 1, 3
Suppose -22*b = -21*b. Factor -8/3*j**4 + 14/3*j**3 + b + 4/3*j**2 + 0*j.
-2*j**2*(j - 2)*(4*j + 1)/3
Let n = -23/280 - 1/56. Let x = n - -3/5. Let 1/2*u**2 + 0*u + x*u**3 + 0 = 0. Calculate u.
-1, 0
Factor -2/5*m**2 - 2*m + 0.
-2*m*(m + 5)/5
Suppose 70 = 17*j + 2. Let 2/5*n**3 - 2/5*n + 3/5*n**j - 4/5*n**2 + 1/5 = 0. What is n?
-1, 1/3, 1
Suppose r + 5*i - 8 = i, -4*i + 8 = -5*r. Let n(j) = j**2 + 5*j - 6. Let y be n(-6). Determine u, given that 1/3*u + r*u**2 - 1/3*u**3 + y = 0.
-1, 0, 1
Suppose 0 = 5*y - 3 - 2. Let h be -1 + y + (-2 - -5). Factor 0*x**2 - x**h + 1/2 + x - 1/2*x**4.
-(x - 1)*(x + 1)**3/2
Let n(r) be the third derivative of r**5/210 + r**4/21 + r**3/7 + 2*r**2. Factor n(b).
2*(b + 1)*(b + 3)/7
Let q(y) be the first derivative of -y**3/5 - 2*y**2/5 - y/5 + 3. Factor q(h).
-(h + 1)*(3*h + 1)/5
Let z(m) be the first derivative of m**6/6 - m**5/5 - m**4/2 + 2*m**3/3 + m**2/2 - m + 6. Factor z(i).
(i - 1)**3*(i + 1)**2
Suppose b - 12 - 7 = -5*l, 13 = -l + 4*b. Suppose l*y = -0*s + 4*s + 27, -5*y = s - 22. Let 2*u - y*u**2 - 2 + 2 = 0. Calculate u.
0, 2/5
Suppose -3*u + 19 = 4. Suppose u*m = 2 + 8. Factor 0 + 0*n - 2/5*n**m.
-2*n**2/5
What is q in 28*q**2 - 2*q**3 - 2*q**3 - 60*q - 54 + 90 = 0?
1, 3
Let m be ((-10)/6)/((-7)/21). Let p(u) be the third derivative of 0*u + 2*u**2 + 0*u**4 + 0 - 1/150*u**m + 0*u**3. Factor p(d).
-2*d**2/5
Let 0 + 6*y + 3/2*y**3 - 6*y**2 = 0. What is y?
0, 2
Let v(j) = -5*j**3 + 7*j**2 + 6*j. Let l(b) = b**3 - 5*b**2 - 5*b. Let x be l(6). Let c(q) = 11*q**3 - 15*q**2 - 13*q. Let d(i) = x*c(i) + 13*v(i). Factor d(g).
g**2*(g + 1)
Let t(n) be the second derivative of n**8/4480 + 11*n**7/15120 + n**6/2160 - n**4/3 - 3*n. Let i(x) be the third derivative of t(x). Factor i(f).
f*(f + 1)*(9*f + 2)/6
Let i(y) be the second derivative of -y**6/75 + y**5/50 + y**4/10 - y**3/3 + 2*y**2/5 - 13*y. Solve i(n) = 0 for n.
-2, 1
Suppose -5*g + 4*m = -33, -3 = -5*g + 3*m + 28. Factor 16/3*u + 4/3 + 7/3*u**4 + 25/3*u**2 + 19/3*u**3 + 1/3*u**g.
(u + 1)**3*(u + 2)**2/3
Factor 0 + 3/5*u**3 + 1/5*u - 3/5*u**2 - 1/5*u**4.
-u*(u - 1)**3/5
Let y(x) be the third derivative of -x**4/12 - 5*x**3/3 - 12*x**2. Let j be y(-6). Factor 0 + 1/4*t**j - 1/2*t.
t*(t - 2)/4
Let d(r) = r**2 - 8*r - 9. Suppose -25 = -5*z - 2*n - 3*n, -4*z + n + 10 = 0. Let q(l) = l**2 - 4*l - 5. Let x(p) = z*d(p) - 5*q(p). Let x(y) = 0. What is y?
-1
Let y(q) be the first derivative of 3 + 0*q + 1/5*q**3 - 3/10*q**2 - 3/25*q**5 + 3/20*q**4. What is s in y(s) = 0?
-1, 0, 1
Factor 3*v**4 + 5*v - 12*v**3 + 4*v - 69*v**2 - 9 + 3*v + 75*v**2.
3*(v - 3)*(v - 1)**2*(v + 1)
Let z be 1 + -3 + 3 + 3. Let 2*h**3 + 21 - 19 + 0*h**z - 4*h**2 - h + 2*h**4 - h**5 = 0. What is h?
-1, 1, 2
Determine o, given that 18*o - 7*o**2 + 8*o**4 - o**2 - 4*o**5 - 14*o = 0.
-1, 0, 1
Let i(p) = -p - 8. Let a be i(0). Let f(d) = -d**3 - 8*d**2 - 3*d + 5. Let r be f(a). Find y such that 29*y**2 - r*y**2 - 6*y**4 - 3*y + 9*y**3 = 0.
-1/2, 0, 1
Let n(k) be the third derivative of 0*k + k**2 - 1/120*k**6 - 1/24*k**4 + 0 - 1/24*k**5 + 0*k**3. Factor n(z).
-z*(z + 2)*(2*z + 1)/2
Let r = 5 + 0. Let j(n) be the first derivative of 1/5*n + 2/5*n**2 + 3 + 2/5*n**3 + 1/25*n**r + 1/5*n**4. Factor j(o).
(o + 1)**4/5
Let z(m) = -m**2 + 8*m - 7. Let p be z(7). Determine u, given that -u + 0 - 8*u - 3*u**2 + p = 0.
-3, 0
Let q(k) be the second derivative of -1/15*k**6 + 2/3*k**3 + 0 + 7*k - 1/5*k**5 + 0*k**4 + k**2. Find a such that q(a) = 0.
-1, 1
Let z = -2/19 - -35/152. Let t(p) be the second derivative of 1/12*p**3 + 0 - z*p**2 + 2*p - 1/48*p**4. Factor t(j).
-(j - 1)**2/4
Suppose 4 = b + 2. Let x = -169 + 339/2. Factor -x*d + 0 + 1/2*d**b.
d*(d - 1)/2
Let h be (-6)/4*(-5 + 36/8). Factor -h*w + 0*w**2 + 1/4*w**3 - 1/2.
(w - 2)*(w + 1)**2/4
Let u(w) be the second derivative of w**6/600 + w**5/100 + w**4/40 + w**3/30 + w**2 + 2*w. Let h(d) be the first derivative of u(d). Solve h(n) = 0.
-1
Suppose 3*h - 3 = 2*j - 58, 5*h + 25 = 0. Let b be (j/(-25))/(6/(-5)). Find y such that b*y**2 + 2/3 + 4/3*y = 0.
-1
Suppose 4*j = -4*c - 8, 0 = 6*c - 2*c - 5*j - 28. Let f be (2/6)/((-2)/(-24)). Factor u**c + 0*u**2 + 6*u + u**2 + f.
2*(u + 1)*(u + 2)
Suppose 2*q**3 - 4 + 229*q - 119*q - 116*q = 0. What is q?
-1, 2
Let w(p) be the first derivative of -4/5*p - 3 + 1/5*p**2 + 2/15*p**3. Suppose w(h) = 0. Calculate h.
-2, 1
Let q(c) be the third derivative of -c**6/160 - c**5/80 + c**4/32 + c**3/8 + c**2. Factor q(u).
-3*(u - 1)*(u + 1)**2/4
Let k(b) = b**2 - 3*b + 6. Suppose 0 = -5*u + 5 + 5. Suppose -1 = -u*p + 7. Let n(y) = -9*y**2 + 24*y - 48. Let x(w) = p*n(w) + 33*k(w). Factor x(a).
-3*(a - 1)*(a + 2)
Suppose -2*j = -2*d - 7*j - 12, -3*d - j - 18 = 0. Let l be (-14)/(-7)*d/(-4). Factor 0 - 1/4*o**l - 1/4*o + 1/2*o**2.
-o*(o - 1)**2/4
Let l be -3 + 11 + (-5)/1. Find u such that 3*u - l*u**3 + 9/2*u**4 - 9/2*u**2 + 0 = 0.
-1, 0, 2/3, 1
Let h(u) be the second derivative of -u**7/357 - 8*u**6/255 - 3*u**5/34 + 4*u**4/51 + 16*u**3/51 + 23*u. Let h(s) = 0. What is s?
-4, -1, 0, 1
Let t be (6 + 0)/(12/6). Let k(v) be the second derivative of 2*v**4 + 2*v + 2*v**t + 0 + 9/20*v**5 + 0*v**2. Let k(s) = 0. What is s?
-2, -2/3, 0
Let p(m) = 4*m**3 - 10*m**2 - 16*m - 14. Suppose -13*k - 24 = -9*k. Let j(b) = -b**3 + 1. Let r(t) = k*j(t) - p(t). Let r(i) = 0. What is i?
-2, -1
Let s(y) be the second derivative of y**4/30 + 2*y**3/15 + y**2/5 - 22*y. Find z such that s(z) = 0.
-1
Suppose 0 = -2*n + 10 + 22. Let w be (-13 + n)*(0 + 1). Solve 8/3*l**5 + 0*l + 2/3*l**2 - 8/3*l**w - 2/3*l**4 + 0 = 0.
-1, 0, 1/4, 1
Let p(k) be the second derivative of 5/42*k**4 + 2*k + 0 + 2/7*k**3 + 1/7*k**2. Factor p(u).
2*(u + 1)*(5*u + 1)/7
Let z(r) = -r**3 + 3*r**2 + 2*r + 1. Let t be z(4). Let o = 22/3 + t. Find h, given that -o*h**4 - 1/3 + 4/3*h**3 + 4/3*h - 2*h**2 = 0.
1
Let z = 15 - 11. Let n be 0 + z/(8/3). Factor s**2 - n*s + 1/2.
(s - 1)*(2*s - 1)/2
Suppose 1 = 4*q - 3*q - j, -5*q = 3*j - 13. Let f be (-4)/(-6) + (-36)/(-27). Determine c so that -c + f*c**q - 5*c**2 + 4*c**2 = 0.
0, 1
Let r(q) be the second derivative of q**7/2940 - q**6/630 + q**3/2 + q. Let o(g) be the second derivative of r(g). Factor o(w).
2*w**2*(w - 2)/7
Factor -16/7 + 20/7*u**2 - 8/7*u + 2/7*u**5 + 2/7*u**3 - 8/7*u**4.
2*(u - 2)**3*(u + 1)**2/7
Let h = 89 - 242. Let s = h - -615/4. Find t, given that 1/4*t**2 + 1/2 - s*t = 0.
1, 2
Let x(g) = g**2 - 7. Let d be x(3). Find z, given that 1/3*z**d + 1/3*z**3 + 0 - 1/3*z - 1/3*z**4 = 0.
-1, 0, 1
Let g(n) be the third derivative of n**9/20160 - n**8/3360 + n**7/1680 + n**5/30 + 6*n**2. Let d(s) be the third derivative of g(s). Factor d(b).
3*b*(b - 1)**2
Suppose -3*t - o = o + 3, 2*t - o = 5. Let g = t - -3. Factor 0*c + 3*c**5 - 3*c**g + c + c**4 - 2*c**2 + 4*c**4 - 4*c**3.
c*(c - 1)*(c + 1)**2*(3*c - 1)
Let t be 15/45 - (-2)/(-6). Let g(z) be the second derivative of -1/6*z**3 + t - 5/36*z**4 + z + 1/3*z**2. Suppose g(y) = 0. Calculate y.
-1, 2/5
Let a be 54/36*(-16)/(-6). Determine o, given that -2/7*o**5 + 0 + 2/7*o**3 + 0*o - 2/7*o**a + 2/7*o**2 = 0.
-1, 0, 1
Let g(s) be the third derivative of -s**5/150 + 7*s**4/60 + 6*s**3/5 - 25*s**2 - s. Suppose g(b) = 0. What is b?
-2, 9
Let n(s) be the first derivative of -12/5*s**5 - 1 + 0*s - 4/3*s**3 + 2*s**2 - 5*s**4. Factor n(q).
-4*q*(q + 1)**2*(3*q - 1)
Let v(z) be the second derivative of 5*z**7/24 - 13*z**6/12 + 27*z**5/16 - 5*z**4/12 - 5*z**3/6 + 7*z. Let v(k) = 0. What is k?
-2/7, 0, 1, 2
Let v = -1249 + 3703/3. Let m = v - -15. Factor m*a**3 + a - a**2 - 1/3.
(a - 1)**3/3
Let p(d) be the second derivative of -d**4/12 + d**3/6 + 9*d. Suppose p(j) = 0. Calculate j.
0, 1
Let h(l) = -