= 0.
-2/5, 2
Let c(m) be the first derivative of 1/18*m**6 - 4/15*m**5 + 1/3*m**4 + 0*m + 0*m**3 + 0*m**2 + 7. Factor c(v).
v**3*(v - 2)**2/3
Suppose 6 = -k + 3, 0 = 5*y + k - 12. Let t(o) be the first derivative of 12*o - 3/2*o**4 - 7 + 3/5*o**5 - y*o**3 + 6*o**2. Solve t(v) = 0 for v.
-1, 2
Let u(f) be the first derivative of 27 - 5/3*f**3 - 4*f + 4*f**2 + 1/4*f**4. Find a, given that u(a) = 0.
1, 2
Let h(y) be the first derivative of y**4/12 + 10*y**3/9 - 4*y**2 + 125. What is r in h(r) = 0?
-12, 0, 2
Let c(s) be the first derivative of 5 + 1/42*s**4 - s**2 + 0*s - 1/7*s**3 + 1/210*s**5. Let p(g) be the second derivative of c(g). Factor p(w).
2*(w - 1)*(w + 3)/7
Let d(w) be the second derivative of 0*w**3 + 2/5*w**6 + 0*w**4 - 5*w + 0*w**2 + 2/21*w**7 + 2/5*w**5 + 0. Suppose d(p) = 0. Calculate p.
-2, -1, 0
Let m(x) = x**2 - 12*x + 11*x - x**3 + 0*x**3. Let q(g) = -4*g**5 - 28*g**4 - 70*g**3 - 82*g**2 - 30*g. Let o(w) = -2*m(w) - q(w). Factor o(a).
4*a*(a + 1)*(a + 2)**3
Suppose -22*i - 5 = -23*i + x, 5*x = 0. Let b(a) be the third derivative of a**2 + 1/72*a**4 + 0*a**3 - 1/180*a**i + 0 + 0*a. Factor b(g).
-g*(g - 1)/3
Let u(r) be the first derivative of -3/80*r**5 + 1/8*r**3 + 0*r + 1/16*r**4 + 1/2*r**2 + 3. Let t(n) be the second derivative of u(n). Factor t(f).
-3*(f - 1)*(3*f + 1)/4
Solve w**3 - 4*w**2 - w**5 + 2*w**5 - 5*w**3 + 0*w**3 + w**4 = 0.
-2, -1, 0, 2
Suppose 0 = 5*l - 44*f + 43*f - 7, 0 = f - 3. Let z(r) be the third derivative of -1/300*r**5 + 0*r**3 - 1/60*r**4 + 8*r**l + 0 + 0*r. Factor z(d).
-d*(d + 2)/5
Let j(z) be the first derivative of -z**4/26 + 112*z**3/39 - 784*z**2/13 + 351. Solve j(h) = 0.
0, 28
Let u(y) be the third derivative of y**6/360 + 11*y**5/60 + 121*y**4/24 + 1331*y**3/18 + 2*y**2 - 28. Determine i, given that u(i) = 0.
-11
Let r(m) be the first derivative of m**6/12 + 41*m**5/10 + 399*m**4/8 - 147*m**3/2 + 51. Factor r(x).
x**2*(x - 1)*(x + 21)**2/2
Factor 142*r**3 + 5*r**4 - 63*r + 7198*r + 2865*r**2 - 635*r - 392*r**3 + 3380.
5*(r - 26)**2*(r + 1)**2
Let s(u) be the second derivative of u**4/30 - 2*u**3/15 - 3*u**2/5 - 8*u. Suppose s(l) = 0. What is l?
-1, 3
Let x(f) = -13*f**3 + 19*f**2 - 16*f. Let i be (-1)/(-5) - 549/45. Let o(y) = 32*y**3 - 48*y**2 + 40*y. Let k(a) = i*x(a) - 5*o(a). Let k(j) = 0. Calculate j.
0, 1, 2
Let n(x) = x**2 - 11*x - 10. Let o be n(12). Suppose 3*a - 7 = o. Factor 4/7*d**2 - 4/7*d**4 + 4/7*d**a - 4/7*d + 0.
-4*d*(d - 1)**2*(d + 1)/7
Let x(i) be the second derivative of -7*i**6/60 - i**5/6 + i**4/6 - 6*i**2 - 9*i. Let p(y) be the first derivative of x(y). Factor p(n).
-2*n*(n + 1)*(7*n - 2)
Let g be 11/(-3)*268/(-1474). Determine k so that 2/9 + 8/9*k**4 + g*k**3 - 10/9*k**2 - 2/3*k = 0.
-1, 1/4, 1
Suppose 4*a - 75 = 3*k, 3*a = 4*a + 3*k - 30. Determine r so that 43*r**2 - 9*r**5 - 10*r**2 + 3*r**2 - 24*r - a*r**4 + 18*r**3 = 0.
-2, 0, 2/3, 1
Let m(j) be the first derivative of -j**5/10 + 11*j**4/4 - 16*j**3 - 72*j**2 - 288. Find x such that m(x) = 0.
-2, 0, 12
Find b, given that -22*b**3 + 2*b**4 + 70*b**2 - 76*b**2 + 44*b**2 - 5*b - 13*b = 0.
0, 1, 9
Let j(a) = -2*a**2 - a + 1. Let i(d) = 117*d**2 + 123*d + 6. Let g(r) = -i(r) + 3*j(r). Factor g(z).
-3*(z + 1)*(41*z + 1)
Let l(h) be the second derivative of h**8/840 - h**7/300 + h**6/450 + h**3/2 + 22*h. Let r(o) be the second derivative of l(o). Solve r(b) = 0 for b.
0, 2/5, 1
Let a = -45 - -49. Factor -4*r**2 + r**3 - r + a*r - r + r**3.
2*r*(r - 1)**2
Let f(h) = 4*h**3 - 14*h**2. Let u(v) = -v**3. Let q(i) = -f(i) - 3*u(i). Find a such that q(a) = 0.
0, 14
Let x be ((-6 + 3)/12)/(5/(-40)). Let q(k) be the first derivative of -4/15*k**3 + 1/5*k**x + 1/10*k**4 - 9 + 0*k. Let q(n) = 0. Calculate n.
0, 1
Factor -2*g**3 + 0 - 16*g + 76/3*g**2.
-2*g*(g - 12)*(3*g - 2)/3
Factor -195/2*m - 175/2*m**3 + 5 + 180*m**2.
-5*(m - 1)**2*(35*m - 2)/2
Let y be (-14)/(-4) + (-3)/6. Let i be 1*13 + (1 - y). Factor 11*v - 14*v**2 - 4 + v + i*v - 5*v.
-2*(v - 1)*(7*v - 2)
Let g be (7 - (-20)/(-5)) + 0. Factor 6*a**2 - 5*a**4 + 2*a**g - 2*a**3 + 5*a**3 - a**2 - 5*a**5.
-5*a**2*(a - 1)*(a + 1)**2
Let d(f) = -f**2 - 8*f + 4. Let j be d(-8). Let g(o) be the third derivative of 0 + 1/90*o**5 + 1/9*o**3 + 3*o**2 + 0*o - 1/18*o**j. Find h such that g(h) = 0.
1
Let x(k) be the third derivative of -2*k**7/21 - 7*k**6/24 + 43*k**5/6 - 155*k**4/8 + 15*k**3 + 66*k**2. What is w in x(w) = 0?
-6, 1/4, 1, 3
Let j be 2 - ((3 - 8) + 4). Suppose -37 = -4*k + j. Determine w, given that -34*w**4 - 59*w**4 - 71*w**2 - k*w**4 - 153*w**3 - 20*w**5 + 5*w + 6 = 0.
-3, -1, -2/5, 1/4
Let p(f) = -f**2 - 466*f + 939. Let r be p(2). Find y, given that 21/2*y**2 + 9/2*y**r - 3/2*y**4 - 27 - 45/2*y = 0.
-2, -1, 3
Let r(h) be the third derivative of h**8/1680 + h**7/630 - h**6/180 - h**5/30 + 5*h**4/6 + 13*h**2. Let a(u) be the second derivative of r(u). Factor a(x).
4*(x - 1)*(x + 1)**2
Let d(u) be the third derivative of u**5/120 + 7*u**4/48 + 5*u**3/6 - 30*u**2 + 3*u. Factor d(f).
(f + 2)*(f + 5)/2
Let a(w) = w**3 + 3*w**2 - 5*w. Let p be a(-4). Suppose 2*z + p*v - 16 = -0*v, v = z + 1. Factor -3/2*o**3 - 3/2*o + 0 + 3*o**z.
-3*o*(o - 1)**2/2
Solve -23*a**3 + 24*a - 12*a + 19*a**3 - 8 = 0.
-2, 1
Let s(h) be the first derivative of -3/4*h**2 + 1/4*h**4 - 15 + 1/12*h**6 + 7/3*h**3 - 1/2*h**5 - 9/2*h. What is f in s(f) = 0?
-1, 1, 3
Let w(f) = -f**2 - 8*f - 4. Let t be w(-8). Let r(g) = -g**3 - 2*g**2 - 6*g - 6. Let m be r(t). Solve -2*s**3 - m*s + 50*s + 2*s**2 = 0 for s.
0, 1
Let p(r) = -r**4 + r**3 - r**2 + 1. Let w(g) = -18*g**2 + 3*g**4 - 1 + 25*g**3 + 128*g + 26*g**2 - 2*g**3 + 89*g**2. Let z(y) = -p(y) - w(y). Factor z(k).
-2*k*(k + 4)**3
Let m(k) = -k**3 - 3*k**2 + 2*k + 4. Let a(c) = 2*c**3 + 7*c**2 - 4*c - 10. Let z(s) = 2*a(s) + 5*m(s). Solve z(p) = 0.
-2, 0, 1
Let o(v) = v**2 + 10*v - 24. Let p be o(-13). Suppose -2*g**2 + p*g + 0*g**2 - 15*g = 0. What is g?
0
Let n = 34547 + -34543. Factor -24/5*k - 3/5*k**5 - 3/5*k**2 + 3/5*k**n + 3*k**3 - 12/5.
-3*(k - 2)**2*(k + 1)**3/5
Let w(y) be the third derivative of 47/525*y**7 + 29/200*y**6 + 1/30*y**4 + 24*y**2 + 0 + 1/48*y**8 + 0*y**3 + 8/75*y**5 + 0*y. Determine a so that w(a) = 0.
-1, -2/5, -2/7, 0
Let l = -125 + 143. Let m be ((-8)/66)/(2 - 40/l). Factor 4/11*g**2 + 0 + 2/11*g - m*g**3.
-2*g*(g - 1)*(3*g + 1)/11
Suppose 0 = 9*x - 8*x - 3. Factor 12*p**x - 5*p - 12*p - 16*p**2 + 21*p.
4*p*(p - 1)*(3*p - 1)
Let a(w) = w**2 + 7*w + 9. Let m be a(-6). What is n in 2/13*n**m + 0 - 2/13*n - 2/13*n**4 + 2/13*n**2 = 0?
-1, 0, 1
Let o = 816/77 + -115/11. Factor -1/7*i**2 + 0 + o*i**4 + 1/7*i - 1/7*i**3.
i*(i - 1)**2*(i + 1)/7
Let k = 11 - 5. Suppose -5*a = -k*a. Find m, given that a*m - 3*m**4 - 5*m**2 - 2*m**3 - m**3 + 8*m**2 + 3*m = 0.
-1, 0, 1
Let k(s) be the second derivative of 2 + 3/5*s**6 + 24*s**3 - 29*s**4 + 864*s**2 - 4*s + 1/14*s**7 - 9/4*s**5. Factor k(f).
3*(f - 3)**2*(f + 4)**3
Let a(i) = i**2 - 5*i - 6. Suppose g = 2*n - 3*g - 6, 0 = -3*n + g - 6. Let r be a(n). Factor 2*z + 4*z + r + 6*z + 2*z**2.
2*(z + 3)**2
Let y(n) = n**2 + 72*n + 335. Let g be y(-67). Find a, given that 0 + 0*a**2 + 2/7*a**4 + g*a + 0*a**3 = 0.
0
Let t(b) be the second derivative of -b**4/54 + 38*b**3/27 - 361*b**2/9 + 94*b + 4. Find d, given that t(d) = 0.
19
Suppose -5*y + 6*y = -2, -4*z - 4 = 2*y. Suppose t**4 + 0*t + 1/2*t**5 + z + 0*t**3 + 0*t**2 = 0. Calculate t.
-2, 0
Let g(i) = i**2 + i - 9. Let l be g(-4). Factor l*o**2 + 3*o - 5*o**2 - o.
-2*o*(o - 1)
Let l(r) be the third derivative of -22*r**2 + 1/70*r**7 + 1/10*r**6 + 1/2*r**3 + 0 + 1/2*r**4 + 3/10*r**5 + 0*r. Determine b, given that l(b) = 0.
-1
Let l(v) = -3*v**3 + 185*v**2 - 684*v + 658. Let u(a) = -35*a**3 + 2220*a**2 - 8210*a + 7895. Let s(q) = 25*l(q) - 2*u(q). Suppose s(x) = 0. Calculate x.
2, 33
Suppose -7*q = -8 - 6. Solve 1 + 3*r**2 + 3 + q + 9*r + 0 = 0 for r.
-2, -1
Let h be 4 - (-2)/(-4) - (-1)/(-1). Let j = -11/6 + h. Factor 2/3*p - 2/3*p**3 - j*p**2 + 2/3.
-2*(p - 1)*(p + 1)**2/3
Let v = 53 + -33. Let a = v - 2. Solve -2*j**3 + 3*j - a*j**2 - 54 - 19*j - 38*j = 0.
-3
Let r(a) be the first derivative of -a**4/12 + a**3/3 + 3*a**2/2 - 19*a - 21. Let l(u) be the first derivative of r(u). Let l(b) = 0. Calculate b.
-1, 3
Let y = -9 - -7. Let v = 5 + y. 