second derivative of -1/189*f**7 - 1/15*f**5 - 1/27*f**3 + 0*f**2 + 0 - 4/135*f**6 - f - 2/27*f**4. Suppose x(p) = 0. What is p?
-1, 0
Let k(y) be the first derivative of y**5/15 + y**4/12 - y**3/3 - y**2/6 + 2*y/3 - 7. Determine h, given that k(h) = 0.
-2, -1, 1
Let r(j) be the first derivative of 3*j**5/5 - 3*j**4 + 9*j**3/2 - 3*j**2 + 4*j + 4. Let p(z) be the first derivative of r(z). Factor p(h).
3*(h - 2)*(2*h - 1)**2
Determine o so that -3*o**4 - o**4 + 3*o**5 + 0*o**4 + 7*o**4 = 0.
-1, 0
Let x(r) = r**2 + r - 1. Let q(i) = -4*i**3 - 20*i**2 - 4*i + 4. Let l(c) = -q(c) - 4*x(c). Find o, given that l(o) = 0.
-4, 0
Let b(g) = g**2 + 1. Let a(i) = -7*i**2 - 8. Let x be 19/(-6) + 2/12. Let s(j) = x*a(j) - 24*b(j). Let s(q) = 0. What is q?
0
Let u(g) be the first derivative of 2 + 5*g**2 + 2*g**3 + 13*g - 8*g - 9*g. Find o such that u(o) = 0.
-2, 1/3
Let l be 3/18 + (-7)/(-21). Factor -1/2*m - 1/2*m**5 + m**3 - m**2 + 1/2*m**4 + l.
-(m - 1)**3*(m + 1)**2/2
Suppose 0 = 3*k - 488 - 421. Let g be k/6 - 2/4. Solve 35*i - 8 - g*i**3 + i - 4*i - 10*i**2 = 0.
-1, 2/5
Let j be (-8)/12 - 240/(-198). Suppose j*i**4 + 0 - 2/11*i**5 + 4/11*i - 2/11*i**3 - 6/11*i**2 = 0. Calculate i.
-1, 0, 1, 2
Let w(b) be the first derivative of b**6/900 + b**5/300 + 2*b**3/3 + 2. Let v(m) be the third derivative of w(m). Factor v(k).
2*k*(k + 1)/5
Let g(b) be the third derivative of -b**8/30240 + b**7/2520 - b**6/540 + b**5/30 - 7*b**2. Let x(f) be the third derivative of g(f). What is p in x(p) = 0?
1, 2
Let k(a) be the third derivative of -7*a**5/180 + 17*a**4/24 - 7*a**3/9 + 26*a**2 + a. What is f in k(f) = 0?
2/7, 7
Let v(i) be the third derivative of -i**2 + 0*i**3 + 0*i - 1/60*i**4 + 1/150*i**5 + 0. Let v(q) = 0. Calculate q.
0, 1
Let c(m) be the third derivative of m**5/12 - 5*m**4/8 - 10*m**2. What is j in c(j) = 0?
0, 3
Let b(s) be the third derivative of -s**8/1680 - s**7/210 + 4*s**2 + 9*s. Let b(p) = 0. What is p?
-5, 0
Find i such that -16*i + 34*i - 12 - 21*i**2 + 25*i + 5*i = 0.
2/7, 2
Suppose -4*h + h = -u - 26, -2*h + u + 18 = 0. Factor -2*s**5 + s**2 + s**3 + 4*s**2 + 5*s**3 + 3*s**2 - 4*s**4 - h*s.
-2*s*(s - 1)**2*(s + 2)**2
Suppose 3*q - 4 - 2 = 0. Let x(m) be the first derivative of -4/3*m + 5/12*m**4 + 2/3*m**q + 2 + 13/9*m**3. Determine c, given that x(c) = 0.
-2, -1, 2/5
Let s be 0/(-5 + 1) + 1*2. Let 0*j**s + 2/3*j**3 - 2/3*j + 0 = 0. What is j?
-1, 0, 1
Factor 320 - 3517*d - 2395*d**2 + 397*d - 10985*d**3 + 12535*d**2.
-5*(13*d - 4)**3
Let a = 8 + -12. Let z(q) = -3*q**4 - 10*q**3 - 7*q**2 - 3*q. Let n(y) = -2*y**4 - 10*y**3 - 8*y**2 - 4*y. Let c(l) = a*z(l) + 3*n(l). Factor c(t).
2*t**2*(t + 1)*(3*t + 2)
Let k = -64 - -67. Let g(l) be the second derivative of 0 + 2/7*l**2 + k*l + 1/42*l**4 + 1/7*l**3. Factor g(p).
2*(p + 1)*(p + 2)/7
Let r(t) = 4*t**3 + 5*t**2 - 3*t + 32. Let b(q) = -2*q**3 - 2*q**2 + 2*q - 16. Let s(u) = -13*b(u) - 6*r(u). Find a such that s(a) = 0.
-2, 2
Suppose 0 = 16*h - 17*h. Let i = -40 + 121/3. Suppose -1/3*v**3 + 1/3*v**5 + 0 - i*v**4 + 1/3*v**2 + h*v = 0. What is v?
-1, 0, 1
Let l(y) = 2*y**5 - 3*y**4 - 6*y**3 - 5*y**2 - 4. Let m(n) = -n**4 - n**3 - n**2 - 1. Let s(z) = l(z) - 4*m(z). Factor s(a).
a**2*(a - 1)*(a + 1)*(2*a + 1)
Let -2/5*x - 2/5*x**3 - 4/5*x**2 + 0 = 0. Calculate x.
-1, 0
Let d(y) be the third derivative of -4*y**2 - 1/12*y**4 + 1/60*y**5 + 0 + 0*y + 0*y**3. Factor d(w).
w*(w - 2)
Solve 1 - 1/2*s**3 - 3/2*s**4 + 9/2*s + 9/2*s**2 = 0.
-1, -1/3, 2
Let j(c) = c**2 - 3*c - 11. Let a(m) = -m + 1. Let t(g) = 5*a(g) + j(g). Let p be t(9). Factor 4*i**5 + i + 0 + 33/4*i**p + 14*i**4 - 7*i**2.
i*(i + 2)**2*(4*i - 1)**2/4
Let g(h) be the second derivative of 1/12*h**3 - 1/12*h**4 + 0*h**2 + 0 + 4*h + 1/40*h**5. Factor g(q).
q*(q - 1)**2/2
Suppose 3*r - 8 = -5. Let z(c) = 5*c**2 - 8*c + 4. Let s(w) = -w**2. Let m(l) = r*s(l) + z(l). Find o such that m(o) = 0.
1
Factor 0*j**2 - 2/9*j**3 - 2/9*j**5 - 4/9*j**4 + 0 + 0*j.
-2*j**3*(j + 1)**2/9
Let a = 1 + 2. Let b = 5 - a. Suppose 8*x**5 - 4*x + 4*x**5 - 12*x**2 - 32*x**4 + 40*x**3 + b - 6*x**4 = 0. Calculate x.
-1/3, 1/2, 1
Let t(w) be the first derivative of -w**6/75 - w**5/50 - 2*w - 1. Let v(d) be the first derivative of t(d). Let v(s) = 0. What is s?
-1, 0
Let f(h) be the second derivative of 13*h**5/15 + 6*h**4 + 40*h**3/3 + 16*h**2/3 - 36*h. Let f(k) = 0. Calculate k.
-2, -2/13
Let s be -3 - (1/5 - (-52)/(-10)). Let -2/3*n - 1/3 - 1/3*n**s = 0. What is n?
-1
Let a(v) be the second derivative of v**8/6720 - v**7/1680 + v**6/1440 + v**3/6 - 5*v. Let n(f) be the second derivative of a(f). Suppose n(g) = 0. What is g?
0, 1
Suppose -g = -q - 2*g - 1, -5*q = 2*g - 10. Suppose 22 = q*r - 10. Factor 2 - r*c**3 + 2*c**4 + 2*c - 4*c**2 + 16*c**2 - 10*c.
2*(c - 1)**4
Let h(z) = 2*z**2 + 7*z - 26. Let q be h(-6). Factor -4/3*y**2 + 0 - 2/3*y + 0*y**3 + 4/3*y**q + 2/3*y**5.
2*y*(y - 1)*(y + 1)**3/3
Let s(l) be the first derivative of -1/20*l**5 - 2*l + 1 + 0*l**2 + 0*l**3 + 1/12*l**4. Let t(c) be the first derivative of s(c). Factor t(m).
-m**2*(m - 1)
Factor 2*t**2 + 1/6*t**3 + 32/3 + 8*t.
(t + 4)**3/6
Let p(c) = c**5 - c**3 + c**2 - c + 1. Let h(f) = 14*f**5 + 9*f**4 - 26*f**3 - 34*f**2 - 31*f + 3. Let s(i) = 5*h(i) - 35*p(i). Factor s(t).
5*(t - 2)*(t + 1)**3*(7*t + 2)
Let l(d) = 7*d - 84. Let y be l(12). Let -2/5*x**2 + 2/5*x + y = 0. What is x?
0, 1
Let u(h) be the first derivative of 2*h**5/85 - h**4/34 - 2*h**3/17 + h**2/17 + 4*h/17 - 7. Let u(b) = 0. Calculate b.
-1, 1, 2
Let n be 22/5 - 4/10. Suppose -2*k + n + 6 = 0. Factor 0*r + 2/3*r**2 + 1/3*r**k + 5/3*r**3 + 0 + 4/3*r**4.
r**2*(r + 1)**2*(r + 2)/3
Let z(m) be the third derivative of m**5/210 + 3*m**2. Determine c, given that z(c) = 0.
0
Let d be (0/(-1))/(-2 + 4). Let a = 4 + d. Find i such that 0 + 0*i**3 + 0*i**2 + 0*i - 2/5*i**a - i**5 = 0.
-2/5, 0
Factor 0 - 2/9*b**2 + 14/9*b.
-2*b*(b - 7)/9
Let t = 858/5 - 170. Solve -8/5 - 2/5*k**2 + t*k = 0.
2
Let w = -71/6 + 571/48. Let m(n) be the third derivative of w*n**4 + 1/240*n**6 - 2*n**2 - 1/40*n**5 + 0*n - 1/12*n**3 + 0. What is k in m(k) = 0?
1
Let p be 1*3*(-36)/(-27). Let f(x) be the first derivative of 0*x**3 - x + 1/5*x**5 + 2 + x**2 - 1/2*x**p. What is q in f(q) = 0?
-1, 1
Let a(g) be the first derivative of 3*g**5/5 - 2*g**4 + 7*g**3/3 - g**2 + 2. Let a(b) = 0. What is b?
0, 2/3, 1
Factor 19*o**2 + 36*o - 7*o**2 + 8 + 16*o**2.
4*(o + 1)*(7*o + 2)
Suppose -o - 2*x - 7 = 0, 0 = 5*o + 4*x - 0*x + 5. Solve 3/5*k**o + 0 + 1/5*k - 3/5*k**2 - 1/5*k**4 = 0 for k.
0, 1
Let k = -490 + 490. Suppose -2/3*c**2 - 4/3*c + k = 0. What is c?
-2, 0
Determine w, given that 0*w + w**2 - 2*w - 9*w**3 + 3*w - 9*w**4 = 0.
-1, -1/3, 0, 1/3
Find q such that -4/3*q**3 + 4/3*q - 5/2*q**2 + 8/3*q**4 - 1/6 = 0.
-1, 1/4, 1
Find x such that 0 - 12*x**5 + 4/5*x**2 - 38/5*x**3 + 0*x + 94/5*x**4 = 0.
0, 1/6, 2/5, 1
Let a = 105 + -105. Let w(t) be the second derivative of -1/30*t**6 - 1/12*t**4 + 1/8*t**5 + 0*t**3 + 0 + a*t**2 - t. Suppose w(v) = 0. What is v?
0, 1/2, 2
Let t = 89/404 + 3/101. Determine w so that -1/2*w + t + 1/4*w**2 = 0.
1
Factor -w**2 + 12*w + 4*w**2 - 6*w**2 + 0*w**2.
-3*w*(w - 4)
Let k(x) be the first derivative of -6*x**5/55 - x**4/22 - 2. Let k(v) = 0. Calculate v.
-1/3, 0
Solve 0*i + 3/2*i**2 - 1/2*i**3 + 0 = 0 for i.
0, 3
Suppose 0 = -l - a - 3, -4 = 2*l + 3*a + 7. Suppose 4*n + 54 = 2*c, -c - n = 4*c - 102. Find q such that -q**2 + c*q**4 + 0*q**l - 5*q**4 = 0.
-1/4, 0, 1/4
Suppose -5*j - 5*h + 10 = 0, -2*j - h = -1 - 3. Factor 5*r**4 - j*r + 4*r**2 - 5*r**4 + 2*r**3 - 5*r**4 + r**4.
-2*r*(r - 1)*(r + 1)*(2*r - 1)
Let n(o) = -o**2 - 11*o - 6. Let y(i) = 12*i + 6. Let u(b) = -3*n(b) - 2*y(b). Factor u(x).
3*(x + 1)*(x + 2)
Let g be 171/(-33) - (-6)/33. Let c(r) = 12*r**2 - 48*r + 27. Let b(j) = 3*j**2 - 12*j + 7. Let p(k) = g*c(k) + 21*b(k). Factor p(w).
3*(w - 2)**2
Let k(w) = 6*w**3 - 46*w**2 - 20*w. Let l(q) = -q**3 + 9*q**2 + 4*q. Let a(i) = 3*k(i) + 16*l(i). Factor a(u).
2*u*(u + 1)*(u + 2)
Factor 0 - 52/15*f**4 - 16/15*f**3 + 0*f**2 + 14/15*f**5 + 0*f.
2*f**3*(f - 4)*(7*f + 2)/15
Let y(z) = z**3 + z**2 - z - 1. Let w(h) = 7*h**3 + 7*h**2 - 6*h - 6. Suppose 8*b - 7*b = 6. Let q be (-4)/(-6)*9/(-6). Let o(l) = b*y(l) + q*w(l). Factor o(p).
-p**2*(p + 