. Find d, given that n(d) = 0.
-1, 0, 133
Let y(a) be the second derivative of 0*a**2 - 2/15*a**3 + 2 + 13*a - 1/30*a**4. Find i such that y(i) = 0.
-2, 0
Let r(k) be the second derivative of -4*k**6/195 + 41*k**5/130 - 37*k**4/39 + 16*k**3/39 + 1597*k. What is s in r(s) = 0?
0, 1/4, 2, 8
Let f = 2/1183 - -18910/10647. Let d = 195526 + -195522. What is l in -2/9*l**d + 4/3*l**3 + 2 - f*l**2 - 4/3*l = 0?
-1, 1, 3
Let j = -2/983 + 1007/11796. Let l(w) be the first derivative of -j*w**6 + 3/5*w**5 + 4/3*w**3 + 0*w**2 - 3/2*w**4 + 3 + 0*w. Suppose l(m) = 0. Calculate m.
0, 2
Let f(p) be the first derivative of p**4/6 - 13*p**3/3 + 12*p**2 - 131*p + 77. Let k(r) be the first derivative of f(r). What is v in k(v) = 0?
1, 12
Suppose 3*q - 2*p - 14 = 2*q, -p + 125 = 5*q. Let n be 1 - (4 + (-80)/q). Solve 5/3*g**4 + 7/3*g**2 + 0 - 3*g**3 - n*g**5 - 2/3*g = 0.
0, 1, 2
Let v = -340 + 345. Suppose 2*x = -v*l + 4, 4*l + 3*x - 6 + 7 = 0. Factor 2/9*f**4 + 2/9*f**3 - 2/9*f**l - 2/9*f + 0.
2*f*(f - 1)*(f + 1)**2/9
Factor 11/4*z**2 - 4*z - 28.
(z - 4)*(11*z + 28)/4
Let h(n) = -30*n**5 - 134*n**4 + 54*n**3 + 42*n**2 + 6*n - 8. Let k(s) = s**5 - 9*s**4 + s**3 - s**2 + s. Let p(w) = h(w) - 10*k(w). Let p(c) = 0. Calculate c.
-1, -1/2, 2/5, 1
Let s(n) be the first derivative of -1/18*n**4 + 26/27*n**3 + 0*n + 0*n**2 - 40. Find c such that s(c) = 0.
0, 13
Let y be ((-69)/(-9) - 392/(-294)) + -7. Determine u so that -21/4*u**3 - 9/4*u**4 - 3/2*u - 1/4*u**5 - 19/4*u**y + 0 = 0.
-6, -1, 0
Let m(g) = g**3 - 36*g**2 + 313*g + 35. Let j be m(15). Let q(c) be the first derivative of 2/3*c**3 - 6*c**2 + c**4 - 1/5*c**j - 9*c + 20. Factor q(x).
-(x - 3)**2*(x + 1)**2
Let t = 233156 + -233153. Factor 36*a - 3/2*a**t - 33/2*a**2 + 216 + 3/8*a**4.
3*(a - 6)**2*(a + 4)**2/8
Let s be 3028/9 + (-24)/54. Factor 614 - 200 + 2*w**3 - 22 - 54*w**2 + s*w.
2*(w - 14)**2*(w + 1)
Suppose -31 = -4*r - 2*i + 7*i, 3*r = i + 15. Suppose -4*q + 49 = 2*f - 19, -3*q + 2*f + 37 = 0. Factor 17*z**4 - 5*z + r + q*z**2 - 12*z**4 - 15*z**3 - 4.
5*z*(z - 1)**3
Let z = -10812169/17 - -636011. Find w, given that -6/17*w**5 + z*w**3 - 4/17*w - 2/17*w**4 + 0 - 6/17*w**2 = 0.
-2, -1/3, 0, 1
Let -656/9*h**3 + 25696/9*h - 82/9*h**4 + 27104/9 + 5072/9*h**2 - 2/9*h**5 = 0. Calculate h.
-22, -2, 7
Suppose 2*t - 2 = t. Suppose h + 80 = 2*x + t*h, 4*x - 164 = -3*h. Factor 9*z**3 + z**5 + x*z + z**2 + 6*z**2 + 5*z**4 - 36*z.
z*(z + 1)**3*(z + 2)
What is h in 69/2 + 1/6*h**2 + 12*h = 0?
-69, -3
Let d be (118/(-10) - -11)*6/((-252)/5). Let u(g) be the first derivative of 19 - d*g**3 + 2/7*g**2 + 0*g. Determine s so that u(s) = 0.
0, 2
Let m(y) = -y**3 - 27*y**2 + 31*y + 86. Let n be m(-28). Factor -1848*s**n + 924*s**2 + 921*s**2.
-3*s**2
Let o(z) be the first derivative of -3*z**4/4 + 176*z**3 - 1047*z**2/2 + 522*z - 196. Factor o(s).
-3*(s - 174)*(s - 1)**2
Suppose -35 = -5*c - 10*l, 4*c - 300*l - 6 = -297*l. Factor -2/7*g**c - 1/7*g**4 - 1/7 + 2/7*g**2 + 1/7*g**5 + 1/7*g.
(g - 1)**3*(g + 1)**2/7
Solve -1161/8*d + 1/8*d**2 + 0 = 0.
0, 1161
Factor 9*r**2 + 0*r**2 + 10 - 11*r**2 + 0*r**2 - 12*r + 4*r**2.
2*(r - 5)*(r - 1)
Let v(k) be the first derivative of k**3/9 - 77*k**2/6 + 76*k/3 - 3329. Determine q, given that v(q) = 0.
1, 76
Let o(t) be the second derivative of -t**5/25 + 11*t**4/30 - 13*t**3/15 + 4*t**2/5 - 3356*t. Factor o(c).
-2*(c - 4)*(c - 1)*(2*c - 1)/5
Let r(u) be the second derivative of -3*u - 2/9*u**2 + 16 - 1/135*u**6 - 1/18*u**5 - 1/6*u**4 - 7/27*u**3. Suppose r(x) = 0. Calculate x.
-2, -1
Factor 4*r**3 + 15*r**4 + 3*r**5 + 14*r**3 - 979*r**2 + 979*r**2.
3*r**3*(r + 2)*(r + 3)
Let i(p) = 13*p**2 + 250*p + 232. Let t be (2/12)/(12/504). Let d(q) = -19*q**2 - 374*q - 348. Let n(k) = t*i(k) + 5*d(k). Let n(b) = 0. What is b?
-29, -1
Let s(x) = -x**3 + x**2 + x + 1. Let o be s(-1). Let f be o/(7/5 - 1). Solve -14*p**3 + 15*p**3 + 3*p**5 + 3*p**2 - 2*p + 7*p**f - 9*p**5 - 3*p**4 = 0 for p.
-1, 0, 1, 2
Let c(t) be the first derivative of 2*t**5/35 + 5*t**4/7 + 22*t**3/7 + 44*t**2/7 + 40*t/7 + 2044. Factor c(o).
2*(o + 1)*(o + 2)**2*(o + 5)/7
Suppose -266 = -4*o + 3*u, -4*o - 2*u = o - 321. Let s be 2/(-13) - (-270)/o. Let -6*p**2 + 0*p**4 + 17*p + p - 10*p**3 - 2*p**s = 0. What is p?
-3, 0, 1
Let d(n) be the second derivative of n**6/40 - 159*n**5/40 + 209*n**4/16 - 13*n**3 - 27*n + 71. Factor d(o).
3*o*(o - 104)*(o - 1)**2/4
Find s such that -9*s**4 - 1/3*s**5 - 825 - 90*s**3 - 955*s - 1274/3*s**2 = 0.
-11, -5, -3
Solve 120*w**4 + 1095/2*w**2 - 10*w**5 - 575/2*w - 845/2*w**3 + 105/2 = 0 for w.
1/2, 1, 3, 7
Suppose -4/7*j**2 - 64/7 - 32/7*j = 0. Calculate j.
-4
Determine x so that -2/3*x**4 - 500/3 - 2*x**3 + 50*x + 70/3*x**2 = 0.
-5, 2, 5
Suppose 6*c = 13 + 119. Suppose -5*j = 7 - c. Factor 6*p**3 - 107*p**2 - 3*p**4 - p**4 - 46*p**j + 7*p**2.
-4*p**2*(p + 5)**2
Let z(c) be the second derivative of -c**6/30 + c**5/3 - c**4/3 - 16*c**3/3 + 40*c**2 - c + 33. Let b(j) be the first derivative of z(j). Factor b(p).
-4*(p - 4)*(p - 2)*(p + 1)
Let v(h) = -h**3 + h**2 + 11*h - 11. Let i be v(3). What is r in 4*r**5 - 15*r**2 + 692*r**i - 4*r + r**5 - 6*r + 5*r**3 - 677*r**4 = 0?
-2, -1, 0, 1
Let y be (-1 + 1 - 389)/(18 - 19). Suppose 9*j + y = 416. Find f such that -18/5*f - 2/5*f**j + 12/5*f**2 + 8/5 = 0.
1, 4
Let m(a) be the first derivative of 2*a**3/9 - 37*a**2 + 216*a + 1916. Find n, given that m(n) = 0.
3, 108
Let w = 6791217/1086596 - -2/271649. Solve -1/2*r**3 + 9/2 - 21/4*r**2 - w*r = 0.
-9, -2, 1/2
Let w(s) be the first derivative of 15/2*s**2 + 12 - 1/48*s**5 + 0*s - 5/6*s**3 + 25/96*s**4. Let k(a) be the second derivative of w(a). Factor k(z).
-5*(z - 4)*(z - 1)/4
Let 457*w - 48*w**2 - 20*w**4 - 997*w + 540*w - 56*w**3 - 2*w**5 = 0. Calculate w.
-6, -2, 0
Suppose -6*m - 4*m + 35 = -3*m. Let i(w) be the third derivative of 1/21*w**3 + 1/420*w**6 - 1/210*w**m - 10*w**2 + 0*w + 0 - 1/84*w**4. Factor i(b).
2*(b - 1)**2*(b + 1)/7
Let w(l) be the first derivative of l**5/180 - 2*l**4/9 + 32*l**3/9 - 67*l**2/2 + 66. Let a(t) be the second derivative of w(t). Let a(z) = 0. What is z?
8
Suppose 36 = 3*h + 42. Let g be -1*4/(-4)*(h + 29). Factor 4*l**3 - 4*l**3 + 9*l**3 - g*l**2 - 21*l**2 + 54 + 45*l.
3*(l - 3)**2*(3*l + 2)
Factor 484*o + 15876 - 65*o**2 + 90*o**2 + 101*o + 675*o.
(5*o + 126)**2
Let y(g) be the second derivative of -g**5/30 + 10*g**4/9 - 59*g**3/9 - 80*g**2/3 - 67*g + 4. Find f, given that y(f) = 0.
-1, 5, 16
Suppose r - 22 = 12*r. Let d be (1/r - 3/(-3))*0. Suppose -25 + 2*p**2 - 11 - 3*p**2 + 12*p + d*p**2 = 0. What is p?
6
Let v(a) = a**2 + a + 1. Suppose -5*b = -16 + 6. Suppose -263 + 259 = -b*m. Let w(g) = -2*g**2 + 2*g - 9. Let p(h) = m*w(h) + 6*v(h). Factor p(t).
2*(t - 1)*(t + 6)
Let y(w) = 2*w**2 + 97*w - 145. Let c be y(-50). Suppose 0 = 2*z - 2*r - 10, c*z - 3*r + r - 22 = 0. Factor 1/9*i**5 + 1/9*i**2 + 0*i + 0 - 1/9*i**z - 1/9*i**3.
i**2*(i - 1)**2*(i + 1)/9
Suppose 6032*p = 6089*p - 114. Suppose -1/3*r + 4/9*r**p + 0 - 1/9*r**3 = 0. What is r?
0, 1, 3
Let v(a) be the third derivative of 2*a**7/945 - 67*a**6/540 + 31*a**5/90 + 49*a**4/54 - 64*a**3/27 + a**2 + 2040*a + 2. Suppose v(c) = 0. What is c?
-1, 1/2, 2, 32
Factor 632*a - 3481*a**2 - 98*a**4 + 18472*a**3 + 768*a - 1266*a**3 - 6327*a**2.
-2*a*(a - 175)*(7*a - 2)**2
Let p(v) be the third derivative of 1/840*v**8 + 0 - 1/150*v**6 + 0*v + 4/75*v**5 - 4/525*v**7 + 61*v**2 - 4/15*v**3 + 1/60*v**4. Let p(s) = 0. Calculate s.
-1, 1, 4
Let j be (-11 - (-2)/(-2))/(-10 + 9). Let k be 3/(-4) + 33/j. Factor 4*s**3 - 16*s**2 - 4 + 4*s + 10*s + 4*s**4 - 5 + 5 - k*s**5.
-2*(s - 1)**4*(s + 2)
Let n(y) = 36*y - 16. Let a be n(1). Suppose -5*d + 29 = 4*c, 3*c - 3 - 10 = -2*d. Factor 16 + 60*q**3 + a*q**d - 68*q**2 + 80*q**3 - 57*q**4 - 16*q - 35*q**4.
4*(q - 2)*(q - 1)**3*(5*q + 2)
Let u = 2398/9 - 2390/9. Let w(x) be the first derivative of 4/3*x**2 + u*x**3 + 0*x + 1/6*x**4 - 16. Solve w(m) = 0.
-2, 0
Factor 7992/7 - 396*g - 3/7*g**3 + 258/7*g**2.
-3*(g - 74)*(g - 6)**2/7
Let i be 61475/100 - 2/(-8). Let m = i + -4293/7. Solve -9/7*n + 9/7*n**3 + m - 15/7*n**2 + 3/7*n**4 = 0.
-4, -1, 1
Let c(y) be the third derivative of -y**6/600 - 2*y**5/15 - 56*y**4/15 - 256*y**3/5 - 8051*y**2. Factor c(p).
-(p + 8)**2*(p + 24)/5
Let z = 177 + -1