culate f.
0
Let i(u) be the first derivative of -2*u**3 - 9*u**2/2 - 3*u - 6. Factor i(m).
-3*(m + 1)*(2*m + 1)
Let d(n) be the second derivative of n**4/24 + n**3/6 + n**2/4 - 2*n. Factor d(w).
(w + 1)**2/2
Let q be 2 + 12/20 + (-7)/(-5). Let v(r) be the second derivative of 3*r - 1/12*r**q + 0 + 0*r**2 + 0*r**3. What is g in v(g) = 0?
0
Let q be 609/126 + (-1)/(-6). Factor -1/2*k**q + 0*k**3 + 0 + k**4 - k**2 + 1/2*k.
-k*(k - 1)**3*(k + 1)/2
Let d(u) be the second derivative of u**5/20 + u**4/2 + 3*u**3/2 + 2*u**2 + 27*u. Factor d(i).
(i + 1)**2*(i + 4)
Let z = 21 + -18. Let n(l) be the first derivative of 3 + 1/6*l**4 + 1/6*l - 7/18*l**z + 1/6*l**2. Determine u, given that n(u) = 0.
-1/4, 1
Let u(j) be the first derivative of j**4/4 + j**3/3 - j**2/2 + 6. Let i(c) = -8*c**3 - 14*c**2 - 4*c - 3. Let a(w) = -i(w) - 5*u(w). Let a(l) = 0. Calculate l.
-1
Let s(h) be the second derivative of -h**4/12 - 5*h**3/3 - 25*h**2/2 + 2*h - 22. Factor s(n).
-(n + 5)**2
Find j such that 2/5*j**4 - 6/5*j**3 - 2/5*j + 6/5*j**2 + 0 = 0.
0, 1
Let f(d) be the first derivative of 3*d**4/4 + d**3 - 3*d**2/2 - 3*d - 17. Factor f(z).
3*(z - 1)*(z + 1)**2
Let k = -39/8 - -569/120. Let v = 8/15 - k. Factor 2/3*n**2 - v - 2/3*n + 2/3*n**3.
2*(n - 1)*(n + 1)**2/3
Let 0 + 3/5*w**3 + 0*w**2 + 3/5*w**4 + 0*w = 0. What is w?
-1, 0
Let t(w) = w**3 - 13*w**2 + 12*w + 5. Let a be t(12). Suppose 2*f - a*b = -f, -3*f - b = 0. Solve -2/7*c**3 + 0 + 0*c + f*c**2 = 0 for c.
0
Let l(i) = 24*i**4 + 54*i**3 + 45*i**2 - 3. Let f(h) = -47*h**4 - 109*h**3 - 90*h**2 - h + 7. Let b(q) = 3*f(q) + 5*l(q). Factor b(p).
-3*(p + 1)**3*(7*p - 2)
Let r(q) be the first derivative of -2*q**3/21 - q**2/7 + 12. Factor r(c).
-2*c*(c + 1)/7
Let u(p) = p**2 + 2*p. Let w be u(2). Let g = w + -8. Factor -2/5*b**3 - b**4 + g*b**2 + 0*b + 0.
-b**3*(5*b + 2)/5
Let h be (-50)/(-2)*(-5)/(-25). Let x(b) be the third derivative of -1/180*b**h + 0 + 1/36*b**4 + 0*b - b**2 + 0*b**3. Factor x(v).
-v*(v - 2)/3
Suppose 15*p**2 - 5*p - 15*p**3 + 5*p**4 + 3 + 1 - 4 = 0. What is p?
0, 1
Let -66 - 272 - 2397*s**3 - 52*s + 2449*s**3 + 2*s**4 + 336*s**2 = 0. Calculate s.
-13, -1, 1
Let w(m) = -4*m**4 - 2*m**3 + 3*m - 3. Let x(o) = 0 + 0*o - 4 - 3*o**3 - 5*o**4 + 4*o. Let u(q) = -4*w(q) + 3*x(q). Factor u(j).
j**3*(j - 1)
Suppose 3*h + 1 = 7. Suppose -3*a = h*o - o + 10, o = 5*a + 22. Factor -2*v + 3*v**3 + 4*v**o - 3*v**2 - 1 - v.
(v - 1)*(v + 1)*(3*v + 1)
Let o(z) be the first derivative of 0*z + 8/5*z**5 - 1/3*z**6 + 8/3*z**3 + 4 - 3*z**4 - z**2. Factor o(u).
-2*u*(u - 1)**4
Let q(g) be the third derivative of 3*g**6/55 + 2*g**5/55 + g**4/132 - 4*g**2 - 7. What is x in q(x) = 0?
-1/6, 0
Let p(k) be the first derivative of -k**3 - 27*k**2/2 - 24*k - 3. Let p(t) = 0. Calculate t.
-8, -1
Let o(m) = 17*m**2 + m. Let y be o(1). Suppose 0 = 5*p - y + 8. Factor -1/2*k**p + 1/2*k + 0.
-k*(k - 1)/2
Solve 1/2*t**5 - 3*t**2 + 0*t + 1/2*t**3 + 2*t**4 + 0 = 0.
-3, -2, 0, 1
Let j(s) be the second derivative of -7/10*s**6 + 0 + 3/14*s**7 + 1/3*s**3 + 1/20*s**5 + 3/4*s**4 + 0*s**2 - 4*s. Let j(f) = 0. Calculate f.
-1/3, 0, 1, 2
Let s(q) be the third derivative of 2*q**2 + 0 + 0*q**6 + 0*q + 0*q**4 + 1/80*q**5 + 0*q**3 - 1/280*q**7. Factor s(u).
-3*u**2*(u - 1)*(u + 1)/4
Let j(h) be the second derivative of 3*h**5/20 - h**4 + 5*h**3/2 - 3*h**2 + 17*h. Factor j(v).
3*(v - 2)*(v - 1)**2
Factor -2/7*z**3 + 4/7*z**2 - 4/7 + 2/7*z.
-2*(z - 2)*(z - 1)*(z + 1)/7
Let a(n) be the first derivative of 0*n + 2*n**2 + 49/6*n**6 + 2 + 126/5*n**5 + 109/4*n**4 + 12*n**3. Factor a(u).
u*(u + 1)**2*(7*u + 2)**2
Let g(f) be the third derivative of f**5/10 + f**4/4 + f**3/4 - 19*f**2. Factor g(n).
3*(2*n + 1)**2/2
Let l = -2/37 - -115/74. Let z(f) be the first derivative of -2 - 6*f + f**3 - l*f**2. Factor z(b).
3*(b - 2)*(b + 1)
Let w(r) = 142*r**3 + 30*r**2 - 128*r - 23. Let k(i) = -47*i**3 - 10*i**2 + 43*i + 8. Let a(u) = 7*k(u) + 2*w(u). Find o, given that a(o) = 0.
-1, -2/9, 1
Factor 4/7*f + 2/7*f**3 - 6/7*f**2 + 0.
2*f*(f - 2)*(f - 1)/7
Let w(p) = 5*p**2 - 2*p - 3. Let t(a) = -20*a**2 + 9*a + 11. Let h(u) = 2*t(u) + 9*w(u). Factor h(i).
5*(i - 1)*(i + 1)
Let j(p) be the first derivative of -4/5*p - 16/5*p**3 - 3 - 9/10*p**4 - 13/5*p**2. Suppose j(v) = 0. Calculate v.
-2, -1/3
Let v(w) = -w**5 + 2*w**2 + w**4 + w**2 - 4*w**2 - 1 + 3*w**3 - 2*w. Let s(x) = -1. Let n(a) = -s(a) + v(a). Factor n(d).
-d*(d - 2)*(d - 1)*(d + 1)**2
Let f(y) be the second derivative of -y**7/126 - y**6/15 - 13*y**5/60 - y**4/3 - 2*y**3/9 - 20*y. Factor f(d).
-d*(d + 1)**2*(d + 2)**2/3
Let x(n) be the second derivative of n**6/360 + n**5/20 + 3*n**4/8 - n**3/2 + n. Let a(p) be the second derivative of x(p). Suppose a(l) = 0. What is l?
-3
Let l(h) = 7*h**3 + 9*h**2 - 3*h - 11. Let a(c) = -8*c**3 - 10*c**2 + 2*c + 10. Let b(k) = 5*a(k) + 6*l(k). Suppose b(x) = 0. Calculate x.
-2, 2
Let m(q) be the second derivative of q**6/75 - q**5/75 - q**4/30 + 2*q**3/45 + q. Solve m(u) = 0.
-1, 0, 2/3, 1
Solve -8*p**2 + 48*p + p**2 + 5 + 139 + 11*p**2 = 0.
-6
Suppose -2*i + 8 + 4 = 0. Factor i*z + 9*z**2 + 2 - 4 - 1.
3*(z + 1)*(3*z - 1)
Factor -40*n + 43 + 5*n**2 - 7 - 2*n**2 + n**2.
4*(n - 9)*(n - 1)
Let v be -1*(-1 + -2)*1. Let d be 2 + 0 + 3 - v. Factor -d*h - 1/2*h**2 - 2.
-(h + 2)**2/2
Let j be (36/(-8) - -2)*(-1)/5. Let k = 8 - 13/2. Factor -3/2*t**3 - 5/2*t**2 + k*t + 2*t**4 + j.
(t - 1)**2*(t + 1)*(4*t + 1)/2
Let n(w) be the third derivative of 0*w + 0 - 1/21*w**5 - 1/140*w**6 + 5*w**2 - 2/21*w**3 - 3/28*w**4. Factor n(k).
-2*(k + 1)*(k + 2)*(3*k + 1)/7
Let z(c) be the third derivative of -c**6/200 - c**5/100 + 3*c**2. Solve z(r) = 0.
-1, 0
Let n be 32/20 - 2/(-5). Determine b so that -b**2 + 3*b**n - 2*b - 2*b = 0.
0, 2
Factor q**3 + 2 - 2*q**2 + 2*q - 2*q**3 - 3*q + 2*q.
-(q - 1)*(q + 1)*(q + 2)
Let s(n) be the second derivative of -n**7/21 - 2*n**6/45 + 2*n**5/15 + n**4/9 - n**3/9 + 34*n. Determine q so that s(q) = 0.
-1, 0, 1/3, 1
Let o = -72 + 76. Let a(g) be the second derivative of 0 - 1/3*g**3 - g**2 - 2*g + 1/3*g**o. Let a(u) = 0. What is u?
-1/2, 1
Let l be 6/(-24) + (-970)/(-8). Solve -5*y**4 + 6*y**3 + y**4 + 2*y**3 - l + 125 - 8*y = 0 for y.
-1, 1
Let q(g) = g**3 + 13*g**2 - 16*g - 19. Let k be q(-14). Factor j**2 + 5 + 2 - j - k.
(j - 2)*(j + 1)
Suppose -2*s - 4 = -2*o + 4*o, 3*s - 10 = o. Let k(r) be the first derivative of 5*r**2 + 4*r - s + 1/2*r**4 + 8/3*r**3. Find d, given that k(d) = 0.
-2, -1
Suppose 0 = 4*t - 4, -4*u - 10*t + 15 = -7*t. Solve -3*d**u + 3*d + 3/2*d**2 - 3/2 = 0.
-1, 1/2, 1
Let i(j) be the first derivative of -4/3*j**3 - 1/2*j**4 + 1 + 2/5*j**5 + 0*j**2 + 0*j. Factor i(x).
2*x**2*(x - 2)*(x + 1)
Let m = 100 - 298/3. Let q(d) be the first derivative of -2*d - 1/2*d**4 + d**2 - 3 + m*d**3. Factor q(h).
-2*(h - 1)**2*(h + 1)
Suppose -t - 6 = -4*t. Solve 0 - 1/2*d - 1/2*d**t = 0.
-1, 0
Let k(m) = -m**3 + 8*m**2 - 5*m - 4. Let x be k(7). Let o(s) = s**3 - 10*s**2 + s - 10. Let d be o(x). Determine u so that 4/3*u + d - 2*u**3 + 2/3*u**2 = 0.
-2/3, 0, 1
Let n(u) be the first derivative of u**4/4 + u**3/3 - 5*u**2/2 + 3*u + 5. Find b, given that n(b) = 0.
-3, 1
Suppose -10*g - 40*g + 200 = 0. Factor -g - 1/4*m**2 + 2*m.
-(m - 4)**2/4
Let y = 114/55 - 34/55. Factor 10/11*k**3 + 8/11*k + 2/11*k**4 + y*k**2 + 0.
2*k*(k + 1)*(k + 2)**2/11
Let f be (8 - 4)/(2/1). Let p be 42/15 - (-2)/(-1). Solve -2/5*n**f + 2/5*n + p = 0 for n.
-1, 2
Suppose 3*r + 4*i = 11, -4*r + 0*i + i = -40. Suppose 0 = -4*q + r + 3. Factor 4*c + 2*c**q - c**4 + 0*c + 2*c**2 - 1 - c**5 + 0*c - 5*c.
-(c - 1)**2*(c + 1)**3
Let m(r) = 45*r**2 - 35*r - 180. Let g(k) = -5*k**2 + 4*k + 20. Let p(d) = -35*g(d) - 4*m(d). Factor p(q).
-5*(q - 2)*(q + 2)
Suppose 8/9*b**3 - 4/9*b - 4/9*b**2 - 4/9*b**5 + 2/9 + 2/9*b**4 = 0. Calculate b.
-1, 1/2, 1
Let z(l) = 5*l**5 + 4*l**4 + 7*l**4 + l**2 + 13*l**3 - 5*l**3 + 2*l**3. Let c(f) = 4*f**5 + 10*f**4 + 10*f**3 + 2*f**2. Let d(y) = 3*c(y) - 2*z(y). Factor d(w).
2*w**2*(w + 1)**2*(w + 2)
Determine q so that -1 + 2 - 9*q + q**2 - 7 - 4*q**2 = 0.
-2, -1
Let b(n) = 4*n + 0*n**2 - 11 + 0*n**2 - 11*n**2. Let h(k) = 5*k**2 - 2*k + 5. Let c(p) = 6*b(p) + 13*h(p). Find m such that c(m) = 0.
-1
Let n(s) be the first derivative of -s**4/36 + s**3/18 + s**2/3 