 0.
0, 1
Let f(n) be the second derivative of -n**5/4 - 25*n**4/12 - 35*n**3/6 - 15*n**2/2 - n + 4. Let f(q) = 0. Calculate q.
-3, -1
Let t(c) be the second derivative of 25*c - 1/5*c**5 + 6*c**2 + 5/3*c**4 + 0 - 14/3*c**3. Suppose t(k) = 0. Calculate k.
1, 3
Let b(q) = -q**3 - 5*q**2 - 8*q + 23. Let i(r) = -4*r**3 - 21*r**2 - 33*r + 91. Let l(h) = 22*b(h) - 6*i(h). Factor l(n).
2*(n - 1)*(n + 4)*(n + 5)
Let w(q) be the first derivative of -4/15*q**5 + 0*q + 2/3*q**2 + 4/9*q**3 - 1/3*q**4 + 22. Factor w(z).
-4*z*(z - 1)*(z + 1)**2/3
Solve -6/5*r**5 + 16/5*r**2 + 12/5*r**3 - 16/5*r**4 - 6/5*r + 0 = 0.
-3, -1, 0, 1/3, 1
Let h(g) be the third derivative of -g**5/30 + g**4/2 + 7*g**3/3 + 4*g**2 + 2*g. Let p be h(7). Factor -2/7 + p*f**2 + 4/7*f**3 + 2/7*f**4 - 4/7*f.
2*(f - 1)*(f + 1)**3/7
Let w be 1 + -4 - (-40)/10. Let t be (-65)/(-20) + (w - (5 + -1)). Factor t*k - 1/4*k**3 + 1/4*k**2 - 1/4.
-(k - 1)**2*(k + 1)/4
Let o = -3800 + 3802. Let -2*c**3 + 14/9*c**o - 4/9*c + 10/9*c**4 - 2/9*c**5 + 0 = 0. What is c?
0, 1, 2
Let d(z) be the first derivative of -z**3/4 + 3*z**2/8 + 2. Suppose d(a) = 0. Calculate a.
0, 1
Factor 8*n**3 + 2*n**4 + 361 - 12*n**2 - 56*n - 229 - 2*n**3 - 180.
2*(n - 3)*(n + 2)**3
Let p = -4579/4 - -1147. Let -1/4*m**3 - p*m**2 - 27/4 - 27/4*m = 0. What is m?
-3
Suppose -z = 4*r - 5*r, -2*r - 2*z = 0. Let f(k) be the third derivative of -2*k**2 + r*k + 0*k**3 + 1/100*k**5 + 0 + 1/20*k**4. Factor f(y).
3*y*(y + 2)/5
Let h(x) = -x**2 - x + 1. Let c be ((-5)/3)/((-24)/432). Let z(p) = -75*p**2 - 65*p + 40. Let y(l) = c*h(l) - z(l). Suppose y(u) = 0. Calculate u.
-1, 2/9
Suppose 2*a = 2*f - 2, 3*f - 26 = -2*a - 2*f. Solve 6*m - 59*m**3 + 35*m**2 + 14*m**a - 28*m**2 + 14*m**4 = 0 for m.
-2/7, 0, 1/2, 3
Let i(y) be the second derivative of 9/16*y**3 + 1/32*y**4 + 0 + 3/2*y**2 + 12*y. Factor i(g).
3*(g + 1)*(g + 8)/8
Let b(x) be the first derivative of 12 + 28/3*x**2 + 16/15*x**5 + 16/3*x + 25/6*x**4 + 76/9*x**3 + 1/9*x**6. Solve b(v) = 0 for v.
-2, -1
Let o(a) be the second derivative of 8/21*a**3 - 4*a + a**2 + 0 + 1/42*a**4. Factor o(n).
2*(n + 1)*(n + 7)/7
Let y(z) be the first derivative of -6 - 1/12*z**3 + 1/40*z**5 + 6*z + 0*z**4 + 1/120*z**6 - 1/8*z**2. Let d(k) be the first derivative of y(k). Factor d(t).
(t - 1)*(t + 1)**3/4
Let w(p) = -p**3 - 4*p**2 - 2*p - 3. Let n be w(-5). Suppose -u - 3*u + n = 0. Find k, given that u*k + 16/3 - 12*k**2 + 10/3*k**3 = 0.
-2/5, 2
Factor -96 + 208*s - 2/3*s**4 + 52/3*s**3 - 386/3*s**2.
-2*(s - 12)**2*(s - 1)**2/3
Let i(z) be the third derivative of -z**6/780 - z**5/30 + 29*z**4/156 - 5*z**3/13 + 68*z**2. Factor i(g).
-2*(g - 1)**2*(g + 15)/13
Let u(o) be the third derivative of -o**8/80640 + o**7/5040 - o**5/5 + o**2. Let k(r) be the third derivative of u(r). Factor k(m).
-m*(m - 4)/4
Let u(q) = -2*q**3 - 7*q**2 - 4*q. Let o be u(-3). Factor -3*f**5 - f**5 + 5*f**3 + o*f**4 + 3*f**3 + f**4.
-4*f**3*(f - 2)*(f + 1)
Let c = -8212 + 41144/5. Let 24/5*b**4 + c*b**3 + 39/5*b + 18*b**2 + 6/5 = 0. What is b?
-2, -1/2
Let k(w) be the first derivative of -4*w**3 - 45*w**2/2 + 12*w - 24. Factor k(i).
-3*(i + 4)*(4*i - 1)
Let a = -3486300 + 2356739311/676. Let z = a + -1/169. Factor 3/4*v**4 + z*v**3 - 3/4*v + 0 - 3/4*v**2.
3*v*(v - 1)*(v + 1)**2/4
Let i(r) be the first derivative of 11/6*r**3 + 43 + r**2 + 0*r + 3/4*r**4 - 9/40*r**5. Factor i(x).
-x*(x - 4)*(3*x + 2)**2/8
Suppose 141*y - 146*y + 4*v + 12 = 0, 2*v = 3*y - 6. Determine s, given that 0*s + y + 2/9*s**2 = 0.
0
Let t(n) be the first derivative of -n**5/5 - 45*n**4/2 - 1933*n**3/3 + 2070*n**2 - 2116*n - 905. Factor t(v).
-(v - 1)**2*(v + 46)**2
Let y(p) be the second derivative of 0*p**3 + 4*p + 0 + 1/18*p**4 + 0*p**2 + 1/15*p**5 + 1/45*p**6. Factor y(w).
2*w**2*(w + 1)**2/3
Suppose 13 + 13 = 2*l - 5*a, 19 = l - 4*a. Let k(w) = 13*w**3 + w**2 + w - 1. Let n be k(1). Factor 8*g + 4*g**2 - 2*g**4 + n*g**3 - 20*g**2 - 4*g**l.
-2*g*(g - 2)**2*(g - 1)
Let i be -1 + 1/((-3)/(-9)). Factor 2 + 9*b**2 - 18*b**2 + 10*b**i + 3*b.
(b + 1)*(b + 2)
Let a(b) be the third derivative of -b**8/3360 - b**7/336 - 7*b**6/720 - b**5/80 + 4*b**3/3 - 12*b**2. Let g(d) be the first derivative of a(d). Factor g(s).
-s*(s + 1)**2*(s + 3)/2
Suppose c - 1 = 2*s, 3*s = c - 3*c + 16. Factor 15 - 4 + s*o**2 - 8*o - 3.
2*(o - 2)**2
Let j(k) be the third derivative of k**7/105 - 47*k**6/30 + 496*k**5/5 - 16337*k**4/6 + 29791*k**3/3 - 668*k**2. Let j(a) = 0. What is a?
1, 31
Factor -2/15*k**2 + 0 + 136/15*k.
-2*k*(k - 68)/15
Let m(u) be the second derivative of -u**5/5 - 5*u**4/3 + 29*u**3/2 - 36*u**2 - 65*u. Factor m(a).
-(a + 8)*(2*a - 3)**2
Let o be 1 + 0 - 12/(-20). Suppose -196*d = 3*t - 195*d - 2, 2*t = 5*d + 24. Factor -2/5*q**t + o*q - 6/5.
-2*(q - 3)*(q - 1)/5
Let w(r) be the second derivative of -r**5/60 + r**4/6 + r**3/2 - 9*r**2 + 77*r. Factor w(j).
-(j - 6)*(j - 3)*(j + 3)/3
Suppose -4*t**2 + 167*t - 17*t - 26*t = 0. Calculate t.
0, 31
Let y(r) be the second derivative of 1372*r**2 + 1001/15*r**6 + 9016/3*r**3 - 3*r - 6619/10*r**5 + 12775/6*r**4 + 0 - 7/3*r**7. Factor y(t).
-2*(t - 7)**3*(7*t + 2)**2
Let p(y) = 2*y. Let x be (2 - -2) + 3/(-1). Let v be p(x). Factor -5*a**3 + v*a**3 + 2*a**2 + a + 2*a**3 + 2*a**3.
a*(a + 1)**2
Let u(i) be the third derivative of 1/504*i**8 + 0 - 1/45*i**7 + 1/30*i**6 + 0*i + 0*i**4 + 0*i**3 + 0*i**5 + 32*i**2. Factor u(d).
2*d**3*(d - 6)*(d - 1)/3
Let i be 154/30 + ((3040/(-15))/(-19))/4. Solve 3/5*w**4 + i*w**2 + 6/5 - 19/5*w**3 - 29/5*w = 0.
1/3, 1, 2, 3
Let o be (4/16)/(3/(-32))*(-63)/210. Let 4/5*v**4 + 0*v + 0 - 1/5*v**5 - o*v**3 + 0*v**2 = 0. Calculate v.
0, 2
Suppose -2*t - 3 = 4*z + 35, -3*t + 4*z - 67 = 0. Let r = t - -21. Suppose 0*f**4 + 0*f**2 + r*f - 1/2*f**5 + 0 + 0*f**3 = 0. Calculate f.
0
Let k be (-204)/(-819) - (-8)/(-52). Factor k*i**3 + 0*i**2 + 0 - 2/21*i.
2*i*(i - 1)*(i + 1)/21
Let u = 2317/180 - 449/36. Solve -26/5*l**2 + 2/5*l**3 - u*l + 26/5 = 0 for l.
-1, 1, 13
Let f(g) be the second derivative of g**7/70 - g**6/25 - 9*g**5/100 + 65*g. Factor f(j).
3*j**3*(j - 3)*(j + 1)/5
Let t = -13639/4 - -3411. Determine d, given that 1/2 + t*d - 7/4*d**2 = 0.
-2/7, 1
Let n = -12220/3 - -4081. Factor 4/3*l - 8/3 + n*l**3 + 5/3*l**4 + 10*l**2.
(l + 1)*(l + 2)**2*(5*l - 2)/3
Let a be (-1349)/8 - (-69)/(-184). Let j = a + 347/2. Determine q so that 3/2*q**2 - j*q + 0 = 0.
0, 3
Suppose 0 = 5*d - 3*b - 3, 3*b = -d + 21 - 6. Suppose -m = -2*o + 6, -5*o = -6*o + m + d. Determine s so that 4/9*s + 1/9*s**o + 0 + 4/9*s**2 = 0.
-2, 0
Let n(j) = j**3 - 40*j**2 - 43*j + 86. Let w be n(41). Let s(h) be the first derivative of 4*h**3 - 6 + 24*h**2 + 64*h + 1/4*h**w. Let s(k) = 0. What is k?
-4
Let d(b) = -3*b**5 - b**4 - b - 1. Let f(z) = 116*z**5 - 478*z**4 + 195*z**3 + 415*z**2 - 323*z + 57. Let w(h) = 3*d(h) - f(h). Find m such that w(m) = 0.
-1, 2/5, 1, 3
Let h be (1 + -2)/((-101)/303). Let n(a) be the first derivative of 0*a + 7 + 2/3*a**h + 1/4*a**4 + 1/2*a**2. Find j, given that n(j) = 0.
-1, 0
Let d(s) be the first derivative of s**6/1020 + s**5/255 - s**4/51 - 8*s**3/51 - s**2/2 - 4. Let t(n) be the second derivative of d(n). What is o in t(o) = 0?
-2, 2
Factor -66*a + 68 + 66 - 207 + 69 - 62*a**2.
-2*(a + 1)*(31*a + 2)
Let t(c) be the second derivative of c**4/42 + 3*c**3/7 + 2*c**2 - 255*c. Factor t(u).
2*(u + 2)*(u + 7)/7
Find m such that 19*m - 6 - 10/3*m**4 + 1/3*m**5 + 38/3*m**3 - 68/3*m**2 = 0.
1, 2, 3
Let s(o) be the first derivative of -4 - 2 + 0*o + 0*o + o**3. Let s(f) = 0. What is f?
0
Let z = 1/6911 + -4568175/27644. Let y = z + 166. What is l in y*l**2 + 3/4*l**3 - 3/4*l**4 + 0 - 3/4*l**5 + 0*l = 0?
-1, 0, 1
Let g be 54/(-21) - (-10 + -3 + 7). Factor g*a**2 - 3*a - 3/7.
3*(a - 1)*(8*a + 1)/7
Let b(r) be the second derivative of 6*r**7/7 - 58*r**6/15 + 24*r**5/5 - 4*r**4/3 - 21*r + 1. Let b(q) = 0. Calculate q.
0, 2/9, 1, 2
Let o(q) be the first derivative of 1/2*q**3 - 3/10*q**5 + 0*q + 0*q**4 + 18 + 0*q**2. Factor o(t).
-3*t**2*(t - 1)*(t + 1)/2
Let o(a) be the first derivative of -a**7/168 + a**6/30 - a**5/16 + a**4/24 + 13*a + 21. Let m(n) be the first derivative of o(n). Factor m(k).
-k**2*(k - 2)*(k - 1)**2/4
Let z(y) be the first derivative of y**4/18 + 64*y**3/27 - 304*y**2/9 + 1280*y/9 - 739.