i(r) be the first derivative of 6 + 3/8*r**2 + 9/8*r**g + 3/8*r**5 + 0*r + 9/8*r**4. What is x in i(x) = 0?
-1, -2/5, 0
Let m(i) be the first derivative of -i**5/14 + i**4/6 - 2*i**3/21 + 15*i - 2. Let f(u) be the first derivative of m(u). Suppose f(w) = 0. What is w?
0, 2/5, 1
Let d(t) be the second derivative of t**7/27 + 16*t**6/135 + 11*t**5/90 + t**4/27 - 114*t. Factor d(o).
2*o**2*(o + 1)**2*(7*o + 2)/9
Find h, given that -2/11*h**5 + 0*h - 12/11*h**4 - 8/11*h**2 - 18/11*h**3 + 0 = 0.
-4, -1, 0
Let l(u) be the first derivative of -2*u**5/45 - 19*u**4/18 + 14*u**3/3 - 65*u**2/9 + 44*u/9 + 193. Suppose l(i) = 0. Calculate i.
-22, 1
Let i(k) be the second derivative of -k**4/84 - k**3/42 + 3*k**2/7 - 61*k. Find v such that i(v) = 0.
-3, 2
Let o(l) = 5*l**2 + 10*l + 6. Let v(u) = 6*u**2 + 11*u + 6. Let s(f) = -5*o(f) + 4*v(f). Let r be s(-4). Factor -4*n**2 + n + n + 0*n**r + 2*n**3.
2*n*(n - 1)**2
Let h(v) be the first derivative of v**6/1440 - v**5/60 + 7*v**4/96 + 11*v**3 + 3. Let x(b) be the third derivative of h(b). Factor x(f).
(f - 7)*(f - 1)/4
Let b(g) be the third derivative of g**6/60 + 7*g**5/30 - g**4/12 - 7*g**3/3 + 3*g**2 + 13. Suppose b(c) = 0. What is c?
-7, -1, 1
Solve -136/9*f - 2/9*f**5 + 26/9*f**4 + 34/9*f**3 - 56/9 - 74/9*f**2 = 0 for f.
-1, 2, 14
Let w(d) = 17*d**4 - 31*d**3 - 52*d**2 - 4*d + 8. Let l(m) = -5*m**4 + 10*m**3 + 17*m**2 + 2*m - 3. Let b(x) = -8*l(x) - 3*w(x). Find q, given that b(q) = 0.
-1, 0, 2/11, 2
Let w(n) = -8*n**2 + 8. Let q(j) = -33*j**2 + 33. Suppose 0 = -p - 4*i - 11 - 0, -5*i = p + 15. Let a(z) = p*q(z) - 21*w(z). Suppose a(t) = 0. Calculate t.
-1, 1
Suppose -26*d + 96 - 118 + 100 = 0. Solve -r**d + 0 + 0*r**2 + 4/3*r - 1/3*r**4 = 0.
-2, 0, 1
Let h(l) be the second derivative of -l**5/20 - l**4/8 + 5*l**2 - 22*l. Let y(c) be the first derivative of h(c). Find n, given that y(n) = 0.
-1, 0
Let v(m) be the first derivative of 4*m**3/45 - m**2/3 - 14*m/15 + 27. Solve v(c) = 0 for c.
-1, 7/2
Let r(w) be the second derivative of -7/405*w**6 + 0*w**2 - 7/6*w**3 - 1/36*w**5 - 1/54*w**4 + 0 - w. Let f(y) be the second derivative of r(y). Factor f(d).
-2*(4*d + 1)*(7*d + 2)/9
Let i be 93 + 0 + -1 + 0. Factor i + 3*l**3 - 3*l - 92.
3*l*(l - 1)*(l + 1)
Determine x so that 3 + 4 + 15*x + 17*x + 2 + 3*x**3 + 15*x**2 - 11*x = 0.
-3, -1
Let m(k) be the first derivative of -k**4/4 - 145*k**3/3 - 2664*k**2 - 5184*k - 909. Suppose m(i) = 0. Calculate i.
-72, -1
Let j(k) be the third derivative of k**8/168 + 4*k**7/105 - 19*k**6/60 + 7*k**5/15 - 152*k**2. Factor j(f).
2*f**2*(f - 2)*(f - 1)*(f + 7)
Let y be (-43)/10*(3 + (-117)/(-126)). Let b = 120/7 + y. Solve -3*a**2 + 3/2*a**3 + 5/2*a - 3/4 - b*a**4 = 0.
1, 3
Let k = 28 + -24. Find l, given that -134*l**2 + 68*l + 60*l**2 - k - 215*l**2 = 0.
2/17
Let j be (-4)/144*(-1 - -3 - 4). Let o(i) be the third derivative of j*i**4 + 0*i + 1/9*i**3 - 4*i**2 + 1/90*i**5 + 0. Solve o(a) = 0 for a.
-1
Let l(d) be the first derivative of -d**4/5 - 8*d**3/5 + 72*d**2/5 + 864*d/5 - 72. Factor l(p).
-4*(p - 6)*(p + 6)**2/5
Let v(a) = -2*a - 9. Let f be v(-5). Let i be ((-3)/9)/(f/(-12)). Suppose -3 + i*k**4 + 6*k**3 - 2*k - 4*k - k**4 = 0. Calculate k.
-1, 1
Let f be ((-5)/(-2))/(95/190). Let n(u) be the third derivative of 1/160*u**6 + 0*u + 0*u**3 + 3/40*u**f + 0 - 7*u**2 + 9/32*u**4. Factor n(b).
3*b*(b + 3)**2/4
Let s(z) be the third derivative of 0*z - 17*z**2 + 0 + 5/6*z**3 - 1/12*z**5 + 0*z**4. Find x, given that s(x) = 0.
-1, 1
Let t(k) be the third derivative of k**8/336 + 2*k**7/105 - k**6/40 - 11*k**5/30 - k**4/6 + 4*k**3 + k**2 + 43*k. Find z, given that t(z) = 0.
-3, -2, 1, 2
Let k = -13405/6 - -2235. Let j(u) be the first derivative of 9 + 1/2*u**2 + 0*u + k*u**3. Factor j(m).
m*(5*m + 2)/2
Let u(p) be the second derivative of -3*p**5/40 - 93*p**4/8 - 23*p**3 + 65*p. Factor u(k).
-3*k*(k + 1)*(k + 92)/2
Let v(x) be the first derivative of -x**4/16 + 55*x**3/12 + x**2/8 - 55*x/4 - 312. Suppose v(u) = 0. Calculate u.
-1, 1, 55
Suppose 0 = p + 34 - 32. Let d be -6*(-5)/(-10)*p + -3. Determine z so that 0*z**2 + 0 + 0*z + 3/7*z**4 + 3/7*z**d = 0.
-1, 0
Suppose 0 = -3*c, -28*c = -5*z - 26*c + 20. Let b(w) be the first derivative of -2*w**2 - 5 + 1/3*w**3 + z*w. Find m, given that b(m) = 0.
2
Let h(i) be the first derivative of -i**7/3780 + i**6/540 - i**4/27 + 10*i**3 + 2. Let a(q) be the third derivative of h(q). Factor a(l).
-2*(l - 2)**2*(l + 1)/9
Let l(h) be the third derivative of -h**5/105 - 8*h**4/21 - 40*h**3/7 - 324*h**2. Factor l(b).
-4*(b + 6)*(b + 10)/7
Let w be (-6)/54 + -6*4/(-108). Factor w*x**2 + 2/9 - 1/3*x.
(x - 2)*(x - 1)/9
Let k(q) be the second derivative of q**4/4 - 5*q**3/6 + 2*q**2 - q. Let f(l) = 54 + 61 - 116 - l. Let b(x) = 4*f(x) + k(x). Determine v, given that b(v) = 0.
0, 3
Let w(k) be the third derivative of k**7/42 + 23*k**6/6 + 191*k**5 + 5060*k**4/3 + 19360*k**3/3 - 47*k**2 - 5*k. Factor w(y).
5*(y + 2)**2*(y + 44)**2
Let k(i) = 9*i**2 + 34*i - 36. Let s(j) = 19*j**2 + 74*j - 71. Let a(y) = -9*k(y) + 4*s(y). Factor a(b).
-5*(b - 2)*(b + 4)
Let a(b) be the second derivative of -b**4/18 + 4*b**3 - 108*b**2 - 119*b. Factor a(q).
-2*(q - 18)**2/3
Let u(j) be the third derivative of -j**6/24 + j**5/4 + 5*j**4/6 - 12*j**2 - 3. Factor u(a).
-5*a*(a - 4)*(a + 1)
Let n be 1*5/(-15)*-6. Suppose 3*d - n*a - 2 = 0, -5 + 4 = a. Factor 3/4*z**2 + d - 1/4*z.
z*(3*z - 1)/4
Factor 3*x**2 - 18*x + 9*x - 8*x**2 + 2*x**3 + 11*x.
x*(x - 2)*(2*x - 1)
Let p(o) be the second derivative of o**5/2 + 37*o**4/6 + 77*o**3/5 - 441*o**2/5 + 75*o. Factor p(z).
2*(z - 1)*(5*z + 21)**2/5
Let z(f) be the first derivative of 20*f**4 + 40*f**3/3 - 35*f**2/2 + 5*f + 20. Suppose z(o) = 0. What is o?
-1, 1/4
Solve 6*w**3 - 11*w**5 - 4224*w**4 - 9*w + 4233*w**4 - 3 - 6*w**2 + 14*w**5 = 0.
-1, 1
Let h(a) be the first derivative of -a**6/30 + 2*a**5/15 + 9*a**2 - 16. Let n(b) be the second derivative of h(b). Let n(p) = 0. What is p?
0, 2
Suppose k = 4*d + 12, 2*d = -4*k + 3*d + 123. Suppose -k = -0*f - 4*f. Find b such that -56*b**2 - 2*b + f*b + 98*b**3 - b + 3*b = 0.
0, 2/7
Determine c so that 1/3*c**5 - 14/3*c + 13/3*c**3 + 1/3*c**2 - 8/3 + 7/3*c**4 = 0.
-4, -2, -1, 1
Solve 7 - 5*q + 17*q**2 + 18*q**2 - 37 = 0 for q.
-6/7, 1
Suppose -3*r - 2*w = -696 + 695, 2*r + w = 2. Suppose 3/2*m**3 + 0 + 3/2*m + r*m**2 = 0. What is m?
-1, 0
Let z = -59/57 - -26/19. Let a(t) be the first derivative of z*t + 7/12*t**2 + 9 + 1/12*t**4 + 7/18*t**3. Solve a(b) = 0.
-2, -1, -1/2
Let m(t) = 3*t**2 - 3*t + 2. Suppose x = -3*n - 0*x, x = -n - 2. Let z be m(n). Factor 12*u + 9*u**3 - 3/2*u**4 - 18*u**z + 0.
-3*u*(u - 2)**3/2
Let u(g) be the third derivative of 16/5*g**3 + 0*g + 4/5*g**4 + 1/200*g**6 + 1/10*g**5 + 23*g**2 + 0. Let u(r) = 0. Calculate r.
-4, -2
Find w such that -12/11*w**4 + 0 - 16/11*w**3 + 14/11*w + 12/11*w**2 + 2/11*w**5 = 0.
-1, 0, 1, 7
Let j = 25 - 25. Let m = -21 - -23. Suppose 1/3*c**m + j + 1/3*c = 0. Calculate c.
-1, 0
Let i(d) be the first derivative of -d**3/6 + 41*d**2/4 - 783. Factor i(c).
-c*(c - 41)/2
Let v be 0 - ((-3 - -1) + -1). Suppose -2 = 2*g, -4 = 5*c - 0*g + 4*g. Factor 2 - v*s**2 + c + s**2.
-2*(s - 1)*(s + 1)
Let p(r) be the first derivative of 1/18*r**3 - 2*r - 1/120*r**5 + 0*r**2 + 1/72*r**4 + 4. Let c(x) be the first derivative of p(x). Factor c(h).
-h*(h - 2)*(h + 1)/6
Factor 8/3 - 16/9*i**2 + 2/3*i**3 - 14/9*i.
2*(i - 3)*(i - 1)*(3*i + 4)/9
Let g(v) be the second derivative of 0*v**4 + 0 + 0*v**2 - 1/33*v**3 + 1/55*v**5 - 1/231*v**7 - v + 0*v**6. Solve g(l) = 0 for l.
-1, 0, 1
Let 0 + 2*f**4 - 128/3*f**2 + 40*f - 82/3*f**3 = 0. Calculate f.
-2, 0, 2/3, 15
Let a(s) be the first derivative of -s**4/8 - 7*s**3/6 - 7*s**2/4 + 15*s/2 + 70. Factor a(h).
-(h - 1)*(h + 3)*(h + 5)/2
Solve -73*p**2 - 25*p**4 - 90*p + 35*p**2 + 112*p**2 + 91*p**2 - 10*p**3 = 0.
-3, 0, 3/5, 2
Let x be 2*(-3 + 2)*15/(-6). Suppose -20*a**3 + 22*a**4 - 14*a**3 - 3*a**5 - 2*a**x + a**3 - 4*a + 20*a**2 = 0. Calculate a.
0, 2/5, 1, 2
Suppose 0 - 2/3*t**3 + 56/3*t**2 - 392/3*t = 0. What is t?
0, 14
Let g = 70 - 126. Let n be g/12*12/(-14). Suppose -11/8*q**3 - 7/8*q**2 - 1/4 + 11/8*q + 9/8*q**n = 0. Calculate q.
-1, 2/9, 1
Let i(r) be the first derivative of -3*r**4 - 6*r + 11*r**3 