Calculate t.
0
Suppose 8*w = 7*w + 5. Let i(u) be the third derivative of 1/90*u**w + 0*u**3 - 3*u**2 + 0 + 1/18*u**4 + 0*u - 1/180*u**6. What is o in i(o) = 0?
-1, 0, 2
Let m(y) be the third derivative of -1/16*y**4 + 0*y + 0 + 0*y**3 - 6*y**2 - 1/80*y**5. Let m(u) = 0. What is u?
-2, 0
Let z(f) be the second derivative of f**5/80 + 5*f**4/48 + f**3/8 - 9*f**2/8 + 24*f. Find h such that z(h) = 0.
-3, 1
Let l(b) = -b**3 - b**2 - 1. Suppose 2*o - 4*o = 2. Let n(f) = 49*f**4 - 71*f**3 + 38*f**2 - 4*f + 6. Let r(x) = o*n(x) - 6*l(x). Factor r(g).
-g*(g - 1)*(7*g - 2)**2
Let v(q) be the second derivative of q**6/180 - q**5/30 + q**4/12 - q**3/9 + q**2/2 - 3*q. Let b(d) be the first derivative of v(d). Factor b(g).
2*(g - 1)**3/3
Suppose -3*q = 3*s - 21, 0*q = q - 4. Determine t so that -2*t**2 + t**2 + 0*t**2 - t**2 - t**s = 0.
-2, 0
Let x(l) be the first derivative of -2*l**5/15 + 2*l**3/3 - 2*l**2/3 + 9. Determine f so that x(f) = 0.
-2, 0, 1
Let r = -57/16 - -4283/1200. Let i(y) be the second derivative of 0 - 3*y + 0*y**2 + r*y**6 - 1/60*y**4 - 1/100*y**5 + 0*y**3 + 1/210*y**7. Factor i(j).
j**2*(j - 1)*(j + 1)**2/5
Let k(n) be the third derivative of 0*n**4 + 0 + 0*n**5 + 0*n**3 - 1/525*n**7 + 1/300*n**6 + 0*n + 3*n**2. Solve k(v) = 0 for v.
0, 1
Let j(m) be the first derivative of -2*m**3/3 - 6*m**2 - 18*m - 6. Factor j(a).
-2*(a + 3)**2
Let h(n) be the first derivative of -n**4/20 - 2*n**3/5 - 9*n**2/10 - 3. Solve h(v) = 0 for v.
-3, 0
Let t(i) be the second derivative of 2*i**7/21 - 4*i**6/15 - i**5/5 + 2*i**4/3 - 28*i. Factor t(b).
4*b**2*(b - 2)*(b - 1)*(b + 1)
Factor -r + 2*r**2 + 1 + 13*r**2 - 4 - 2*r - 9*r**3.
-3*(r - 1)**2*(3*r + 1)
Let u(d) be the second derivative of -d**5/30 + 7*d**4/18 - 16*d**3/9 + 4*d**2 + 14*d. Factor u(r).
-2*(r - 3)*(r - 2)**2/3
Suppose 0 = -4*f + 2*u + 92, 6*u - 3*u = -3*f + 51. Let x be (-2)/7 - (-13)/f. Suppose 0 - x*j**2 - 1/3*j = 0. What is j?
-1, 0
Let v(f) = 18*f**2 - f + 2. Let b be v(1). Let n = 21 - b. Factor 0*h + 0*h**n + 0 + 2/9*h**4 - 2/9*h**3.
2*h**3*(h - 1)/9
Let a(t) = t**2 - 6*t + 5. Let f be a(5). Let b(d) be the first derivative of 2 + 0*d**2 - 2*d**4 + 6/5*d**5 + f*d + 2/3*d**3. Factor b(k).
2*k**2*(k - 1)*(3*k - 1)
Let c(j) = 3*j**2 + 9*j + 6. Let f(x) = -2*x**2 - 5*x - 3. Suppose 8 - 14 = -2*s. Let m(t) = s*c(t) + 5*f(t). Determine h so that m(h) = 0.
-1, 3
Let a(p) be the first derivative of -1/2*p**2 + 1/2*p**4 + 0*p - 1/6*p**6 + 0*p**3 + 0*p**5 + 2. Factor a(c).
-c*(c - 1)**2*(c + 1)**2
Let y(c) be the third derivative of 2*c**7/175 - 11*c**6/200 + c**5/20 + c**4/20 + 3*c**2. Find z, given that y(z) = 0.
-1/4, 0, 1, 2
Let o be (-2)/4 + (-18)/(-4). Let 10/7*a + 2*a**o - 4/7*a**3 - 12/7*a**2 - 6/7*a**5 - 2/7 = 0. Calculate a.
-1, 1/3, 1
Factor 118*f**4 - 24 + 15*f**2 - 6*f**3 + 16*f**3 - 123*f**4 - 20*f + 4.
-5*(f - 2)**2*(f + 1)**2
Factor 2/3 - 2/3*i**2 - 1/3*i**3 + 1/3*i.
-(i - 1)*(i + 1)*(i + 2)/3
Let v be 4/24*-17 - -3. Let q(y) be the second derivative of 2*y + 1/3*y**2 + 1/36*y**4 + v*y**3 + 0. What is h in q(h) = 0?
-2, -1
Let m(s) = -25*s**3 - 48*s**2 - 79*s - 47. Let n(h) = -3*h**3 - 6*h**2 - 10*h - 6. Let x(w) = 6*m(w) - 51*n(w). Suppose x(t) = 0. Calculate t.
-2
Let o(y) = -6*y**4 + 6*y**3 - 14*y**2. Let h(v) = -2*v**4 + 2*v**3 - 5*v**2. Let k(z) = -14*h(z) + 5*o(z). Let k(m) = 0. Calculate m.
0, 1
Let g(a) be the first derivative of 1/24*a**6 + 0*a**4 + 2 + 0*a - 1/8*a**2 - 1/10*a**5 + 1/6*a**3. Find x, given that g(x) = 0.
-1, 0, 1
Let q(h) be the second derivative of -h**7/126 + h**6/18 - 2*h**5/15 + h**4/9 + 2*h. Factor q(d).
-d**2*(d - 2)**2*(d - 1)/3
Let f(t) be the third derivative of t**9/45360 - t**7/7560 - t**4/12 - 2*t**2. Let u(m) be the second derivative of f(m). What is k in u(k) = 0?
-1, 0, 1
Let s(y) be the third derivative of -y**7/210 + y**6/60 + y**5/60 - y**4/12 + y**2. Factor s(b).
-b*(b - 2)*(b - 1)*(b + 1)
Let j be -3*2/3 + 4 + 0. What is x in 1 - 5/2*x**4 - 7/2*x**3 + 7/2*x + 3/2*x**j = 0?
-1, -2/5, 1
Let o(k) be the first derivative of 2*k**6/15 - 4*k**5/5 + k**4 - 5*k - 3. Let r(j) be the first derivative of o(j). Suppose r(f) = 0. Calculate f.
0, 1, 3
Let n = -7 + 11. Determine k so that -n*k + 5*k + k**2 + 4*k**2 - 18*k + 6 = 0.
2/5, 3
Let o = 71 - 68. Let i(j) be the third derivative of 0*j**o - 1/40*j**6 + 0 + 0*j**4 + 0*j - 1/60*j**5 - 1/336*j**8 + j**2 - 1/70*j**7. Factor i(m).
-m**2*(m + 1)**3
Let m(o) = -3*o**4 - o**3 + o**2 - o - 2. Let v(y) = -7*y**4 - 3*y**3 + 2*y**2 - 2*y - 5. Let q(c) = -5*m(c) + 2*v(c). Factor q(x).
x*(x - 1)**2*(x + 1)
Let f(c) = -117*c**3 - c**2. Let g be f(-1). Let y be g/33 + 2/(-11). Determine z, given that -8/3*z**5 + y*z**3 + 2*z**2 - 2/3*z + 0 - 2*z**4 = 0.
-1, 0, 1/4, 1
Let t(w) be the first derivative of -w**7/420 + w**6/36 - 2*w**5/15 + w**4/3 - w**3 - 3. Let b(s) be the third derivative of t(s). Factor b(a).
-2*(a - 2)**2*(a - 1)
Let p = -6443/36 + 179. Let r(n) be the second derivative of -1/6*n**2 - p*n**4 + 0 + n - 1/9*n**3. Factor r(b).
-(b + 1)**2/3
Factor -3*z**3 - 4*z - z**2 - 6*z**2 - z**3 - z**2.
-4*z*(z + 1)**2
Suppose 4*a - 12 = -0*a. Let h be a + ((-3)/3 - 0). Factor -f**4 - f - h*f**3 + f + 3*f**3.
-f**3*(f - 1)
Factor -14*i**2 + 9*i**2 - 48*i + 9*i**2.
4*i*(i - 12)
Let -7*j + 5*j**2 - 6*j + 11*j + 7*j**3 = 0. Calculate j.
-1, 0, 2/7
Let x(l) be the third derivative of 0*l + 5*l**2 + 0*l**4 - 1/90*l**5 + 0*l**3 + 0. Factor x(q).
-2*q**2/3
Factor 3/4*l**2 + 0 + 3/2*l.
3*l*(l + 2)/4
Let g = 9871/30 + -329. Let t(o) be the second derivative of o + 0 + 1/15*o**3 + 0*o**2 - g*o**4. Find s, given that t(s) = 0.
0, 1
Let b be ((-1)/3)/(28/264). Let r = b + 24/7. Factor -8/7*h**3 + 0*h - r*h**4 - 8/7*h**2 + 0.
-2*h**2*(h + 2)**2/7
Suppose d - 3*d = -6. Factor 11*n**2 + 3*n**3 + 0*n**d - 8*n**2.
3*n**2*(n + 1)
Let u(a) be the first derivative of -4 + 1/24*a**4 + 1/3*a + 0*a**3 - 1/4*a**2. Suppose u(y) = 0. What is y?
-2, 1
Factor -3219 + 3223 - 3*i**2 + i**2 - 2*i.
-2*(i - 1)*(i + 2)
Let y(x) = -x**3 - 7*x**2 - x - 7. Let z be y(-7). Factor -1 + 0 + 2*w**2 - 1 + z*w**2.
2*(w - 1)*(w + 1)
Let p(z) = z**4 + 12*z**3 + 16*z**2 + 10*z + 5. Let m(n) = 15*n**4 + 192*n**3 + 255*n**2 + 159*n + 81. Let l(b) = 2*m(b) - 33*p(b). Factor l(d).
-3*(d + 1)**4
Let g(i) be the third derivative of 0*i + 0 + 0*i**4 - i**2 + 1/135*i**5 + 0*i**6 - 1/945*i**7 - 1/27*i**3. Factor g(v).
-2*(v - 1)**2*(v + 1)**2/9
Suppose -2*y = -14 + 6. Let z = y - 2. Factor 1 + 6*k**z - 5*k + 2*k**3 - 7*k**4 - 3*k**5 + 6*k**5 + 0*k**3.
(k - 1)**3*(k + 1)*(3*k - 1)
Let y(x) be the third derivative of -x**5/12 - 5*x**4/24 + 5*x**3 - 25*x**2. Factor y(w).
-5*(w - 2)*(w + 3)
Let r(n) = -n**2 + 9*n. Let t be r(9). Factor 0*c + t + 2/9*c**2 - 2/9*c**3.
-2*c**2*(c - 1)/9
Let h(v) be the second derivative of v**6/45 - v**5/12 + v**4/36 + 5*v**3/18 - v**2/2 - 37*v. What is f in h(f) = 0?
-1, 1, 3/2
Suppose 0 = 3*a - z - 42 - 148, -2*a + 131 = -5*z. Let i = a - 185/3. Find v such that 4*v - 7/3*v**3 - 3*v**2 + i = 0.
-2, -2/7, 1
Solve 9 + 18*o - 1 - 4*o**3 - 6*o = 0 for o.
-1, 2
Let i(m) = 2*m**2 + 14*m + 4. Let z be i(-7). What is h in 0*h - h**2 + h**z + 5/2*h**5 - 5/2*h**3 + 0 = 0?
-1, -2/5, 0, 1
Let p(y) be the second derivative of -2*y**6/15 + y**5/5 + y**4 - 2*y**3/3 - 4*y**2 - 23*y. What is x in p(x) = 0?
-1, 1, 2
Let d be -9 - ((-488)/40 - -2). Factor 2/5*p + 6/5 - 2/5*p**3 - d*p**2.
-2*(p - 1)*(p + 1)*(p + 3)/5
Let i(v) = 15*v**3 + 9*v**2 + 18*v + 6. Let x(h) = -7*h**3 - 5*h**2 - 9*h - 3. Let p(c) = 4*i(c) + 9*x(c). Find q such that p(q) = 0.
-1
Let k(l) = 2*l - 7. Let o be k(5). Suppose 0*w**4 - w**2 - w - 4*w**3 + 5*w**o + w**4 = 0. What is w?
-1, 0, 1
Let x be (-3 - (-120)/(-35)) + 7. Factor 12/7*v**2 + 2/7*v - x.
2*(2*v - 1)*(3*v + 2)/7
Let m be ((6/5)/3)/(39/78). What is n in -2/5*n + 2/5*n**3 - m*n**2 + 4/5 = 0?
-1, 1, 2
Let i(x) be the first derivative of -x**6/195 - 3*x**5/65 - x**4/6 - 4*x**3/13 - 4*x**2/13 + 5*x - 2. Let n(c) be the first derivative of i(c). Factor n(j).
-2*(j + 1)**2*(j + 2)**2/13
Let r be (-3)/(2 - 11) - 15/(-9). Factor 0 + 2/7*m**r + 0*m.
2*m**2/7
Factor -2/11 - 6/11*l + 8/11*l**2.
2*(l - 1)*(4*l + 1)/11
Let l(z) be the first derivative of z**6/40 - z**5/10 - z**4/8 + z**3 + 5*z**2/2 + 7. Let k(d) be the seco