r d(j).
-j**2*(j + 4)/6
Let w(q) be the second derivative of -q**4/6 + 2*q**3 - 5*q**2 + 2*q - 15. Suppose w(k) = 0. What is k?
1, 5
Let z be -1 - ((-8)/3 - -1). Let j be (-2014)/8056 + -2*2/(-16). Factor -z*m**3 + 0*m**2 + 0 + j*m + 4/3*m**4 - 2/3*m**5.
-2*m**3*(m - 1)**2/3
Let z be 1 - ((-95)/15 - -7). Let o(m) be the second derivative of 0*m**2 - 1/12*m**4 + 0 + 6*m - z*m**3. Let o(n) = 0. Calculate n.
-2, 0
Let x(i) = -i - 1. Let q be x(3). Let k be (-10)/q - 1/(-2). Find c such that 8 - 3 + 3*c**3 + k*c**2 - 5 = 0.
-1, 0
Suppose -26 + 8 = -6*b. Factor 8*g**2 + 16*g + 15*g + 85*g**b - 89*g**3 + g.
-4*g*(g - 4)*(g + 2)
Let u(h) be the first derivative of -1/18*h**3 - 11 + 7/6*h - 1/2*h**2. Factor u(n).
-(n - 1)*(n + 7)/6
Let g(a) be the third derivative of a**8/80640 - a**6/720 + a**5/20 - 15*a**2. Let o(z) be the third derivative of g(z). Factor o(x).
(x - 2)*(x + 2)/4
Let s(v) = 19*v**2 - 3 + 6*v - 16*v**2 - v**3 - 3. Let h be s(4). Factor 1/2*c**3 - 3/2*c**h + 3/2*c - 1/2.
(c - 1)**3/2
Suppose 8/3*u - 2/3*u**3 + 0*u**2 + 0 = 0. What is u?
-2, 0, 2
Let y(h) be the first derivative of -5*h**3/3 - 130*h**2 - 255*h - 127. Factor y(v).
-5*(v + 1)*(v + 51)
Let r(n) be the second derivative of 26*n - 1/6*n**3 + 0 - 3/5*n**2 - 1/60*n**4. Factor r(l).
-(l + 2)*(l + 3)/5
Let h be 4/14 + (26961/(-5040))/19. Let l(n) be the third derivative of -1/48*n**4 + 0*n + 5*n**2 + 0*n**3 + 0 + 1/480*n**6 + h*n**5. Factor l(a).
a*(a - 1)*(a + 2)/4
Let g(k) = -3*k**2 + 107*k + 124. Let m(p) = p**2 - 54*p - 63. Let n(o) = 4*g(o) + 7*m(o). What is a in n(a) = 0?
-1, 11
Let u(y) = y**3 + 9*y**2 + 2. Let g be u(-9). What is h in -29*h**5 + 3*h**4 - 4*h**g + h**4 - 4*h**3 + 33*h**5 = 0?
-1, 0, 1
Let g(k) = -7*k**4 - 2*k**3 + 57*k**2 - 121*k + 88. Let r(m) = 40*m**4 + 13*m**3 - 341*m**2 + 727*m - 528. Let w(u) = -34*g(u) - 6*r(u). What is o in w(o) = 0?
-11, 2
Let m(i) = -7*i**3 - i**2 + i + 1. Let h be m(-1). Suppose 0 = j - h*j + 10. Factor -2*x**5 + 4*x**4 - 2*x**2 - j*x**2 + 0*x + 2*x.
-2*x*(x - 1)**3*(x + 1)
Factor 4/9*o + 0 + 10/9*o**2 - 2/9*o**4 - 2/9*o**5 + 2/3*o**3.
-2*o*(o - 2)*(o + 1)**3/9
Let t(z) be the second derivative of z**4/4 - 15*z**3 + 84*z**2 - 270*z. Find n such that t(n) = 0.
2, 28
Suppose 22 = 4*l - 2. Suppose l*r - r - 3*q = -12, 0 = -5*r + 4*q - 16. Let r + 4 - 4 - n**3 - n**2 = 0. What is n?
-1, 0
Let a(t) be the third derivative of t**6/240 - t**4/16 - t**3/6 + 5*t**2 - 16. Factor a(n).
(n - 2)*(n + 1)**2/2
Let n = 4 - 2. Let y be ((6*-2)/n)/(-2). Factor 0*i**4 + i**4 + y*i**4 - 5*i**2 + i**2.
4*i**2*(i - 1)*(i + 1)
Let v(r) be the second derivative of 1/54*r**4 - 16*r - 1/180*r**5 + 0*r**2 + 0 - 1/54*r**3. Factor v(b).
-b*(b - 1)**2/9
Factor 0*a**5 + 237*a**3 - 3*a**5 - 183*a**3 - 12*a**4 + 3*a**4.
-3*a**3*(a - 3)*(a + 6)
Suppose -3*r = 2*n - 18, -n + 5*r - 2 = r. Let z be 21/9 - 2/n. Factor -3*m**2 + 7*m + 2*m - 13*m + 4*m**z + 4.
(m - 2)**2
Let n(j) = -j**2 + 5*j + 1. Let t be n(4). Suppose -q - 4*x - x + 22 = 0, -t*q + 4*x - 6 = 0. Factor u**2 + 10*u**3 + 6*u**2 + 1 + 0*u**q + 5*u - 7*u**3.
(u + 1)**2*(3*u + 1)
Let j(c) = 5*c**2 - 11*c + 6. Let v be j(2). Let p = 26/15 + -7/5. Suppose 0*r + 1/3*r**v - p*r**5 + 0 + 0*r**2 + 2/3*r**3 = 0. Calculate r.
-1, 0, 2
Let f = 509/2020 - 1/505. Let b(h) be the third derivative of -f*h**4 - 1/240*h**6 + 0*h + 1/20*h**5 + 2/3*h**3 - 9*h**2 + 0. Suppose b(l) = 0. Calculate l.
2
Let f(q) be the first derivative of -2*q**7/945 + q**6/90 - 2*q**4/27 - 2*q**2 - 13. Let y(n) be the second derivative of f(n). Factor y(m).
-4*m*(m - 2)**2*(m + 1)/9
Let q(v) = 30*v**4 + 50*v**3 + 20*v**2 - 10*v - 15. Let x(r) = -32*r**4 - 49*r**3 - 19*r**2 + 10*r + 18. Let k(p) = 6*q(p) + 5*x(p). Factor k(w).
5*w*(w + 1)*(w + 2)*(4*w - 1)
Factor 0*q + 0 + 4*q**3 - 2/5*q**4 - 10*q**2.
-2*q**2*(q - 5)**2/5
Let r(m) = m**2 + 5*m + 8. Let c be r(-4). Factor -4*z**2 + 5*z + c*z**2 + 2*z**2 + z.
2*z*(z + 3)
Let r = -27664/5 + 5533. Determine h so that 2/5*h**2 + 1/5*h**3 + r*h + 0 = 0.
-1, 0
Let a(i) be the second derivative of i**7/63 - 8*i**6/45 + 7*i**5/10 - 7*i**4/9 - 20*i**3/9 + 8*i**2 + 138*i. Solve a(l) = 0.
-1, 2, 3
Let f(v) be the third derivative of v**7/1890 + 7*v**6/540 + v**5/15 - 11*v**4/24 - 35*v**2. Let c(u) be the second derivative of f(u). Solve c(x) = 0.
-6, -1
Solve 4*c**2 + 45*c + 16*c + 59*c + 342 + 558 = 0 for c.
-15
Let c(d) be the first derivative of -2 + 1/20*d**5 - 2/3*d**3 + 1/12*d**4 + d - 2*d**2. Let f(g) be the first derivative of c(g). Factor f(j).
(j - 2)*(j + 1)*(j + 2)
Let a be ((-30)/50)/((-1)/10). Let v(j) = 3*j**2 - 6*j + 3. Let k(s) = 4*s**2 - 7*s + 3. Let c(z) = a*v(z) - 4*k(z). Let c(g) = 0. Calculate g.
1, 3
Let z = 11674 + -35006/3. Suppose 12*x**2 + 40/3*x + z + 14/3*x**3 + 2/3*x**4 = 0. What is x?
-2, -1
Let g = -684 - -688. Factor 0 + 0*o + 2/5*o**g + 4/5*o**2 - 6/5*o**3.
2*o**2*(o - 2)*(o - 1)/5
Let u(z) be the first derivative of -8*z - 6 + 7/6*z**3 - 1/4*z**4 + 3*z**2. Let l(q) be the first derivative of u(q). Suppose l(x) = 0. What is x?
-2/3, 3
Factor 11 + 17 + 32*f**2 - 4 - 32*f - 20*f**3 + 74*f + 34*f.
-4*(f - 3)*(f + 1)*(5*f + 2)
Let z(i) = -i + 8. Let r be z(4). Factor -36*t**3 + 137*t - 4*t**5 + 28*t**2 - 145*t + 0*t**5 + 20*t**r.
-4*t*(t - 2)*(t - 1)**3
Solve -36 - 44 - 143*i - 47*i**2 - 6*i**3 - 23*i**2 + 7*i**3 + 8 = 0 for i.
-1, 72
Let i(w) be the first derivative of w**6/540 - w**4/36 - 5*w**3/3 - 18. Let f(m) be the third derivative of i(m). Factor f(k).
2*(k - 1)*(k + 1)/3
Factor -152 - 84*z + z**2 + 3*z**2 + 152*z.
4*(z - 2)*(z + 19)
Let w(y) be the third derivative of -y**6/280 - 5*y**5/28 - 187*y**4/56 - 363*y**3/14 - 90*y**2 - 1. Suppose w(t) = 0. What is t?
-11, -3
Let s(g) be the second derivative of g**5/50 + 28*g**4/15 - 649*g. Let s(i) = 0. Calculate i.
-56, 0
Let z(f) be the second derivative of -f**5/130 + f**4/13 + 21*f**3/13 - 392*f**2/13 + 20*f - 6. Factor z(d).
-2*(d - 7)**2*(d + 8)/13
Determine h, given that -60 - h**4 + 13 + 23*h + 23 - 15*h**2 + 14 + 2*h**4 + h**3 = 0.
-5, 1, 2
Factor 5*t**2 + 69*t**3 + 20*t**2 + t**2 + 33*t**4 + 13*t**2 - 9*t**4 - 6*t.
3*t*(t + 1)*(t + 2)*(8*t - 1)
Let s(k) be the first derivative of -k**3/21 - 20*k**2/7 + 140. Factor s(r).
-r*(r + 40)/7
Let r(y) = -y**3 - 2*y**2 + 4*y + 2. Let c be r(-3). Let l be -3 - c/1 - -5. Factor -6*j**4 + 4*j**2 - 6*j + 3 + 0*j**5 + l*j**5 - j**5 - 1 + 4*j**3.
2*(j - 1)**4*(j + 1)
Suppose 11 = r + 3*f, 2*r = -0*r + 2*f - 2. Factor -2*h + 5 - 3 + 3 + h**r - 4.
(h - 1)**2
Let g(b) be the third derivative of 1/105*b**5 + 0 + 2/21*b**3 + 24*b**2 + 0*b - 1/21*b**4. Let g(s) = 0. What is s?
1
Let a(m) = -5*m**5 - 18*m**4 - 42*m**3 - 29*m**2 - 14. Let t(i) = -3*i**5 - 9*i**4 - 21*i**3 - 15*i**2 - 8. Let r(n) = -4*a(n) + 7*t(n). What is v in r(v) = 0?
-1, 0, 11
Let j = 88 + -82. Factor -24*k**2 + 36*k**2 + j*k - 4*k**4 - 3*k + 5*k.
-4*k*(k - 2)*(k + 1)**2
Factor 29*d + 7*d - 2*d**2 - 72 - 12*d.
-2*(d - 6)**2
Let n(t) be the third derivative of -13/42*t**7 - 5/12*t**4 + 0 + 0*t**3 - 5/112*t**8 - 11/12*t**5 + 0*t - 19/24*t**6 + 15*t**2. Solve n(w) = 0 for w.
-2, -1, -1/3, 0
Let y(n) be the first derivative of 0*n**2 + 1/42*n**6 + 0*n**3 + 0*n - 4 + 1/28*n**4 - 2/35*n**5. Find b such that y(b) = 0.
0, 1
Let i be -3 - (9 + 252/(-27))*198/14. Suppose -2*h - 2*h + 12 = 0. Solve -i*z - 96/7*z**4 + 16*z**h - 6/7*z**2 + 2/7 = 0 for z.
-1/3, 1/4, 1
Suppose 0*w - 2*w + 12 = 0. Suppose 74 = 4*k - w. Factor k*t**2 - 6 - 10 + 8*t - 2*t**5 - 2*t**3 + 0 - 8*t**4 + 0*t**3.
-2*(t - 1)**2*(t + 2)**3
Let x = 4639 + -13915/3. Suppose -x*j**2 - 2/9*j + 4/9 = 0. Calculate j.
-1, 2/3
Let d = 2948 + -14739/5. Factor 3/5*k + d*k**2 + 2/5.
(k + 1)*(k + 2)/5
Let s(a) = a**4 + a**3 - a**2 - 1. Let z = -50 - -49. Let d(q) = -7*q**4 + 38*q**3 - 118*q**2 + 160*q - 78. Let j(c) = z*d(c) - 2*s(c). Solve j(i) = 0.
2
Let j = 719/459 - 26/17. Let a(h) be the first derivative of -j*h**6 - 1/9*h**2 + 8/45*h**5 + 0*h - 1/3*h**4 + 8/27*h**3 - 1. Factor a(n).
-2*n*(n - 1)**4/9
Let n(j) be the second derivative of 1/8*j**3 + 0 + 11*j - 1/48*j**4 + 1/2*j**2. Factor n(t).
-(t - 4)*(t + 1)/4
Let g(x) be the third derivative of -6/35*x**7 - x**3 + 16*x**2 + 7/10*x**5 + 0 - 1/10*x**6 + 1/16*x**8 + 0*x - 3/8*x**4. Suppose g(c) = 0. Calculate 