(a) be the first derivative of 0*a - 5 + 0*a**2 + 0*a**4 - 1/10*a**5 + z*a**3. Solve j(d) = 0.
-1, 0, 1
Let k(s) be the second derivative of 1/30*s**7 - 2/5*s**2 + 1/30*s**6 + 8/15*s**3 - 23/100*s**5 + 2 - 1/60*s**4 - 3*s. Find r, given that k(r) = 0.
-2, -1, 2/7, 1
Suppose -4*y = -16, -4*t + 3*t + 5*y + 17 = 0. Factor 37 + 2*d - d**3 - d**2 - t.
-d*(d - 1)*(d + 2)
Let m(v) = -v**2 + 2*v - 4. Let w(o) = -o**2 - 2. Let i(r) = m(r) - 2*w(r). Solve i(p) = 0 for p.
-2, 0
Let s be -14*6/15 + 22 + -14. Suppose 0 = -0*f - 3*f. Factor f + s*k + 12/5*k**2 + 3/5*k**3.
3*k*(k + 2)**2/5
Let z be ((-1)/(-4))/(6 - 3715/620). Let b(x) = -x**2 + 30*x + 35. Let p be b(z). Determine m so that 0 + 8/9*m - 4/9*m**p + 4/9*m**2 - 8/9*m**3 = 0.
-2, -1, 0, 1
Let y(v) = 8*v**5 - 5*v**4 + 7*v**3 + 5*v**2 - 5*v. Let p(q) = -13*q**5 + 7*q**4 - 10*q**3 - 8*q**2 + 8*q. Let k(u) = 5*p(u) + 8*y(u). Factor k(r).
-r**3*(r - 1)*(r + 6)
Let k be 14/(-6 + 4 - -4). Let r be (-8)/(-84)*3*k. Factor -1/5*l - 1/5*l**3 + 0 + 2/5*l**r.
-l*(l - 1)**2/5
Suppose 2*i - 14 = -k, -401 = -5*i - 371. Factor 0*j + 0 + 5/2*j**k.
5*j**2/2
Let w(o) be the second derivative of 5*o**4/14 + 76*o**3/21 + 5*o**2/7 - 75*o + 2. Factor w(q).
2*(q + 5)*(15*q + 1)/7
Let m(g) = -g + 3. Let p be m(-13). Factor 0 + 25*s**3 - 29*s**3 - 12*s + 0 - p*s**2.
-4*s*(s + 1)*(s + 3)
Suppose -25 = -2*l + 5. Let d be 2/(-2)*(-6)/2. Let -22 + 22 - 21*a**d + 6*a**2 + l*a**4 = 0. What is a?
0, 2/5, 1
Suppose 2*m = -4*a - 8, -2*a + 5*m + 0 = 4. Let n be (-9)/(-6)*(0 - a). Let 6*u - 2*u**3 + 10*u**2 - n*u**5 - u**2 - u**4 - u**3 - 8*u**4 = 0. Calculate u.
-2, -1, 0, 1
Let f(d) = -d**3 + 5*d**2. Let w(s) = s**3 - 12*s**2 + 7*s - 4. Let z(c) = -4*f(c) - 2*w(c). Solve z(b) = 0 for b.
-4, 1
Let f(q) be the third derivative of -q**6/540 - 23*q**5/270 + 2*q**4/9 + 146*q**2. Factor f(k).
-2*k*(k - 1)*(k + 24)/9
Suppose 40 = 27*w - 17*w. Let t(q) be the first derivative of -1/4*q**w + 9 - 1/3*q**2 + 0*q + 4/15*q**5 - q**3. Factor t(y).
y*(y - 2)*(y + 1)*(4*y + 1)/3
Let c(i) = -i**3 + 2*i**2 + 3*i. Let m be c(-2). Let a(d) = d**2 - 11*d + 12. Let o be a(m). Factor -o*p + 11*p - 8*p + p**2.
p*(p + 1)
Let m(g) = g**3 - 7*g**2 + 10*g + 2. Let z be m(5). Solve -980 - 14*t - 5*t**4 + 63*t**3 + 15*t**z - 13*t**3 - 686*t = 0.
-2, 7
Let k be 12/(-30) - 77/(-5). Suppose -3*r + 4 = -r. Factor -8*b**3 - 1 + 10*b**2 + 1 + 11*b + r*b**4 - k*b.
2*b*(b - 2)*(b - 1)**2
Suppose 235*t + 2*t**3 - 47*t**2 + 3*t**3 - 70*t + 0*t**3 - 123*t**2 = 0. Calculate t.
0, 1, 33
Let i = -34 - -34. Let p(l) be the third derivative of i*l**3 + 0*l**5 + 0 + 1/180*l**6 + 0*l + 5*l**2 - 1/315*l**7 + 0*l**4. Determine g so that p(g) = 0.
0, 1
Suppose 4856*y + 32 + 2*y**3 - 2418*y - 2422*y - 14*y**2 = 0. Calculate y.
-1, 4
Let b = 12413 - 12411. Suppose -8 - 2/5*c**5 - 86/5*c**3 - 154/5*c**b - 22/5*c**4 - 128/5*c = 0. What is c?
-5, -2, -1
Let h(l) be the third derivative of l**7/24 + 11*l**6/80 - l**5/20 - l**4/12 + 40*l**2 - 2. Suppose h(c) = 0. Calculate c.
-2, -2/7, 0, 2/5
Let u be ((-8)/(17 - -7))/((8/36)/(-2)). Factor 2/17*x**5 + 0 + 2/17*x**4 - 2/17*x**2 - 2/17*x**u + 0*x.
2*x**2*(x - 1)*(x + 1)**2/17
Let i(n) = -20*n**5 - 56*n**4 - 64*n**3 - 8*n**2 - 12*n + 16. Let y(s) = -s**3 - s + 1. Let r(l) = -i(l) + 16*y(l). Solve r(p) = 0.
-1, 0, 1/5
Let k = 1153/76 - 274/19. Solve 1/4*h**4 + k*h**3 - h + 0*h**2 + 0 = 0.
-2, 0, 1
Let b(x) = -4*x**4 + x**4 - 2 + 11*x**3 - 3 - 3*x**2. Let v(d) = -4*d**4 + 16*d**3 - 4*d**2 - 8. Suppose k + 129 = 121. Let w(h) = k*b(h) + 5*v(h). Factor w(f).
4*f**2*(f - 1)**2
Let o be 20/3 + -1*(-1)/3. Let v = -3 + 8. Factor 1 - 10*n + o*n + v*n + n**2.
(n + 1)**2
Let a = -9 - -10. Let s be 1 - (0/(-1) - a). Factor 4*v**s + 0*v**3 + 2 + v**3 + 3*v + 2*v.
(v + 1)**2*(v + 2)
Let w = 2751 - 2749. Let s(b) be the third derivative of 0*b + 0*b**3 + 0 + w*b**2 + 1/6*b**4 - 1/30*b**5. Factor s(z).
-2*z*(z - 2)
Let m(p) be the second derivative of p**6/30 - p**5/10 - p**4/4 + 4*p**3/3 - 2*p**2 - 23*p. Suppose m(i) = 0. Calculate i.
-2, 1, 2
Let t(k) be the third derivative of -k**5/30 + 5*k**4/6 - 3*k**3 + 64*k**2. Solve t(l) = 0 for l.
1, 9
Find x, given that x + 1/8*x**5 + 9/4*x**3 + 0 + 5/2*x**2 + 7/8*x**4 = 0.
-2, -1, 0
Let m(x) be the first derivative of -5*x**3/12 - 7*x**2/4 + 3*x/4 - 434. Factor m(q).
-(q + 3)*(5*q - 1)/4
Let 42*w**4 + 6*w - 18*w**3 + 121*w**2 - 68*w**3 - 79*w**2 - 4 = 0. What is w?
-2/7, 1/3, 1
Let f = 33 + -27. Let x be (0 - 9/(-39))/(f/8). Factor 6/13*q + x - 2/13*q**3 + 0*q**2.
-2*(q - 2)*(q + 1)**2/13
Let o = -725/13 - -56. Let r = o - -33/26. Factor r*j**2 + 0 + 3*j.
3*j*(j + 2)/2
Let l = 230 + -230. Let y(u) be the first derivative of l*u + 5 - 1/4*u**4 + 0*u**3 + 1/2*u**2. Solve y(x) = 0 for x.
-1, 0, 1
Let n(f) be the first derivative of -1/4*f**6 - 3/10*f**5 + 1/2*f**3 + 0*f**2 + 3/8*f**4 + 0*f + 4. Factor n(b).
-3*b**2*(b - 1)*(b + 1)**2/2
Suppose 9 = 3*q + 3. Let i be q*(-2 + 21/6). Let k(c) = -8*c**2 + 11*c - 3. Let t(p) = 4*p**2 - 5*p + 1. Let z(b) = i*k(b) + 5*t(b). Factor z(o).
-4*(o - 1)**2
Let i(c) be the second derivative of 8/7*c**7 + 0*c**3 + 1/4*c**4 + 0*c**2 + 0 + 27/20*c**5 + 12/5*c**6 + 12*c. Determine k so that i(k) = 0.
-1, -1/4, 0
Let q(j) be the third derivative of -1/390*j**5 - 1/13*j**3 + 0*j + 0 - 16*j**2 + 1/39*j**4. Factor q(g).
-2*(g - 3)*(g - 1)/13
Let g be -29 + 22 + (5 - (0 - 4)). Suppose -1/2*u**3 - g*u**2 - 1 - 5/2*u = 0. What is u?
-2, -1
Let c = 68932/5 - 13785. Factor c*p**2 + 2/5 - 9/5*p.
(p - 1)*(7*p - 2)/5
What is m in 4/11 + 10/11*m**2 - 14/11*m = 0?
2/5, 1
Let q = 2993 + -5965/2. Determine h, given that q*h**2 - 39*h - 12 = 0.
-2/7, 4
Let s(m) be the second derivative of m**9/15120 - m**7/4200 + 7*m**3/3 - 6*m. Let q(x) be the second derivative of s(x). Factor q(w).
w**3*(w - 1)*(w + 1)/5
Solve 3*s**3 - 59*s + 101 + 12*s**2 - 5 - 25*s = 0 for s.
-8, 2
Let x(q) be the first derivative of -3*q**4/4 + 22*q**3/3 - 16*q**2 - 32*q + 4. Suppose x(h) = 0. Calculate h.
-2/3, 4
Factor -160*t**2 - 1585 + 397 + 3630*t - 5055*t - 1062 - 5*t**3.
-5*(t + 2)*(t + 15)**2
Let a = -27197/5 - -5443. Factor 3 + 33/5*r + a*r**2.
3*(r + 1)*(6*r + 5)/5
Let x(o) be the second derivative of o**5/20 + 7*o**4/6 - 34*o**3/3 + 36*o**2 + 7*o - 4. What is b in x(b) = 0?
-18, 2
Suppose 3*u - 24 - 6 = 0. Find v such that -8*v**5 + 6*v**2 + 5 - u*v**3 + 15*v - 15*v**4 + 4*v**2 + 3*v**5 = 0.
-1, 1
Let p(w) be the second derivative of -8*w**2 + 0 - 1/3*w**4 + 10/3*w**3 - 27*w. Factor p(i).
-4*(i - 4)*(i - 1)
Factor -1/8*l**3 + 0*l + 0 - 3/4*l**2.
-l**2*(l + 6)/8
Let x be 36/(-24) - (-31)/12*3. Determine l so that 5/2 + 105/4*l**2 + x*l**4 - 85/4*l**3 - 55/4*l = 0.
2/5, 1
Let t(d) be the second derivative of 9409*d**6/70 - 5529*d**5/14 + 8637*d**4/28 + 190*d**3/7 + 6*d**2/7 - 150*d. Factor t(z).
3*(z - 1)**2*(97*z + 2)**2/7
Let o be 27/(-6)*6/(-9). Suppose -3*t + 2*c = -0*c, -2*t - o*c + 13 = 0. Factor 3*x**2 + x**t - x**2.
3*x**2
Let a(h) be the third derivative of h**8/84 + 2*h**7/15 + 3*h**6/10 - 9*h**5/5 - 9*h**4 - 6*h**2 - 47. Solve a(n) = 0.
-3, 0, 2
Solve -7*t + 9 + 5*t + 5 - 8 - 8*t**2 = 0 for t.
-1, 3/4
Let y(a) be the second derivative of -5*a**7/252 + 5*a**6/36 - 25*a**4/9 + 100*a**3/9 - 20*a**2 + 87*a. Factor y(i).
-5*(i - 2)**4*(i + 3)/6
Let y(m) be the second derivative of -m**8/9240 + m**6/1980 + 11*m**3/6 + 2*m. Let q(w) be the second derivative of y(w). Factor q(f).
-2*f**2*(f - 1)*(f + 1)/11
Factor 2/5*y**2 + 23328/5 + 432/5*y.
2*(y + 108)**2/5
Factor 2/3*u**2 + 0 - 20*u.
2*u*(u - 30)/3
Let l(i) be the third derivative of i**6/420 - 2*i**5/15 + 221*i**4/84 - 338*i**3/21 - 42*i**2 + 3. Find n, given that l(n) = 0.
2, 13
Let n = -419 - -1259/3. Let o(g) be the second derivative of -2/3*g**4 + 0 + 1/5*g**5 - 4*g + g**2 - n*g**3 + 1/5*g**6. Factor o(m).
2*(m - 1)*(m + 1)**2*(3*m - 1)
Let l(j) be the second derivative of -6/5*j**6 + 0 + 36*j + 14/5*j**5 - 3*j**4 + 4/3*j**3 + 4/21*j**7 + 0*j**2. Find s such that l(s) = 0.
0, 1/2, 1, 2
Let g(x) be the first derivative of -4*x**3/3 + 114*x**2 - 440*x - 206. Let g(b) = 0. What is b?
2, 55
Let u(k) be the second derivative of 1/140*k**5 - 3/7*k**2 - 1/42*k**3 + 1/14*k**4 + 19*k + 0. Solve u(l) = 0 for l.
-6, -1, 1
Let q be (-10 + 15 + (-30)/8)*(-4)/(-6). Fin