 3
Let r(m) be the first derivative of -m**5/5 + 9*m**4/2 + 36*m**3 + 79*m**2 + 69*m - 464. What is c in r(c) = 0?
-3, -1, 23
Let a(k) be the second derivative of 0 - 8/3*k**4 - 3*k**3 - 2/5*k**6 - 7/5*k**5 - 2*k**2 - 1/21*k**7 + 51*k. Factor a(i).
-2*(i + 1)**4*(i + 2)
Let m(l) be the second derivative of -7*l**6/15 - 3*l**5/10 + 7*l**4/6 + l**3 + l + 118. Factor m(i).
-2*i*(i - 1)*(i + 1)*(7*i + 3)
Suppose 6*x = 53*x - 42958. Let f = -914 + x. Factor f*w + 5/6*w**4 - 25/6*w**3 + 0 + 10/3*w**2.
5*w**2*(w - 4)*(w - 1)/6
Let s(p) be the third derivative of -1 - 190/9*p**4 + 400/9*p**3 + 19/90*p**6 + 9*p**2 + 0*p + 1/315*p**7 + 107/30*p**5. Suppose s(f) = 0. What is f?
-20, 1
Let l = 27422 - 219363/8. Factor -37/8*c + 3/4 - l*c**2.
-(c + 3)*(13*c - 2)/8
Let y(c) be the first derivative of -c**5/5 - 89*c**4/2 - 7741*c**3/3 + 8010*c**2 - 8100*c - 1757. Find n such that y(n) = 0.
-90, 1
Let k(m) be the second derivative of -3*m**6/70 + 3*m**5/70 + 39*m**4/28 + 5*m**3/7 - 36*m**2/7 - 1854*m. Let k(v) = 0. Calculate v.
-3, -1, 2/3, 4
Let a(i) = 3*i**2 - 24*i - 21. Let k(w) = -w**2 + w + 1. Let m = 75 + -76. Let b(o) = m*a(o) - 6*k(o). Find x such that b(x) = 0.
-5, -1
Factor 2/11*x**3 + 0 + 38/11*x - 40/11*x**2.
2*x*(x - 19)*(x - 1)/11
Suppose -q - 3*f + 24 = 0, -2*q = f - 4*f - 3. Let r be (-120)/(-90)*2*q/6. Factor -8/3 + 20/3*c - r*c**2.
-4*(c - 1)*(3*c - 2)/3
Let q(g) be the second derivative of -g**4/6 - 6044*g**3/3 - 9132484*g**2 + 10*g - 256. What is x in q(x) = 0?
-3022
Let i(w) be the second derivative of 0*w**4 - 47 + 2*w + 0*w**2 - 10/3*w**3 + 1/4*w**5. Factor i(l).
5*l*(l - 2)*(l + 2)
Let 19*f**2 + 13 + 6 + 21*f**2 + 31 - 85*f - 5*f**3 = 0. What is f?
1, 2, 5
Let g(j) be the second derivative of 81*j - 12*j**3 + 3/20*j**5 + 120*j**2 + 0 - 3/4*j**4. Determine w so that g(w) = 0.
-5, 4
Find x such that 288/5*x**2 - 4*x**3 - 372/5*x + 104/5 = 0.
2/5, 1, 13
Let i(b) be the first derivative of -2*b**3 - b**2 + 2*b - 22. Let p(j) = 31*j**2 + 9*j - 11. Let l(s) = -11*i(s) - 2*p(s). Solve l(y) = 0.
-1, 0
Let l = 135295/4 + -33821. Let s = -79 + 319/4. Solve -13/4*q + s + 5/4*q**3 - l*q**2 = 0.
-1, 1/5, 3
Find i, given that -5800*i + 340*i**2 - 16862 - 88*i**2 - 127*i**2 + 84142 = 0.
116/5
Let n(f) be the second derivative of f**5/8 - 65*f**4/12 + 355*f**3/12 - 115*f**2/2 - 732*f. Factor n(d).
5*(d - 23)*(d - 2)*(d - 1)/2
Let g(y) be the first derivative of -147*y**4/22 + 1162*y**3/33 - 465*y**2/11 - 450*y/11 - 2841. Factor g(x).
-2*(3*x + 1)*(7*x - 15)**2/11
Factor 17/4*r + 1/4*r**2 + 15.
(r + 5)*(r + 12)/4
Let l be ((-14)/(-7) - 88008)/(-8). Let f = l + -10922. Factor -7/4*z**3 + 49/2 - f*z - 24*z**2.
-(z + 7)**2*(7*z - 2)/4
Factor 5/4*z**2 - 1 - 1/4*z.
(z - 1)*(5*z + 4)/4
Let a(w) be the first derivative of w**6/60 + w**5/30 - w**4/18 - 114*w + 169. Let n(x) be the first derivative of a(x). What is o in n(o) = 0?
-2, 0, 2/3
Suppose 3*m - 5*b - 6 = -0*m, -4*b = -m + 2. Let j = -49/12 + 53/12. Determine g so that 8/3 - 2*g**m - 4/3*g + 1/3*g**4 + j*g**3 = 0.
-2, 1, 2
Let f(o) be the second derivative of 2*o**7/21 - 4*o**6/15 - 26*o**5/5 + 52*o**4/3 + 50*o**3/3 - 100*o**2 + 4664*o. Solve f(y) = 0 for y.
-5, -1, 1, 2, 5
What is z in 5/4*z**5 + 0 - 345/4*z**3 + 0*z - 15*z**4 + 100*z**2 = 0?
-5, 0, 1, 16
Let l = 75 + 28. Factor l*k - 4165 + 206*k - 2*k**2 - 85*k - 838 - 1269.
-2*(k - 56)**2
Let a(c) be the first derivative of 130 + 32/17*c - c**2 + 2/51*c**3. Factor a(l).
2*(l - 16)*(l - 1)/17
Let y(l) be the third derivative of 1/1785*l**7 - 34*l**2 + 1/102*l**4 + 0*l + 0 + 0*l**3 - 1/170*l**5 + 0*l**6. Let y(c) = 0. Calculate c.
-2, 0, 1
Suppose 0 = 297*n - 254*n + 32 - 204. Let g(q) be the second derivative of -1/84*q**n + 0 - 7*q + 1/21*q**3 + 3/14*q**2. Factor g(k).
-(k - 3)*(k + 1)/7
Let p(r) = -r. Let f be p(-5). Let -20*v**5 - f*v**3 + 18494*v - 18494*v - 25*v**4 = 0. Calculate v.
-1, -1/4, 0
Factor 30*n**4 + 275*n**3 + 614*n + 116*n**2 - 1375*n - 371*n**2 + 711*n.
5*n*(n - 1)*(n + 10)*(6*n + 1)
Suppose -2*o - 103 = -5*v, 3*o + 13 - 1 = 0. Suppose -k - v = -6*k - x, 3*x = -4*k + 13. Solve -757*f**2 + k*f**3 + 0*f**3 + 753*f**2 = 0.
0, 1
Let u(j) be the first derivative of -j**5/45 - 11*j**4/9 - 67*j**2 - 98. Let t(f) be the second derivative of u(f). Factor t(g).
-4*g*(g + 22)/3
Solve 49/4*u**3 + 7/4*u**5 - 68*u - 207/4*u**2 - 15 + 51/4*u**4 = 0.
-5, -3, -1, -2/7, 2
Let j be 1*8*-1 + -6*(-352)/192. Suppose 0*p + 0 + 1/6*p**2 - 1/3*p**j + 1/6*p**4 = 0. What is p?
0, 1
Let -1/6*d**4 - 37/2*d**2 - 21*d - 13/3*d**3 + 0 = 0. What is d?
-21, -3, -2, 0
Let h(n) = 4*n**3 + 17*n**2 - 13*n + 14. Let j be h(-5). Let c(o) be the second derivative of -18*o + 0 - 1/36*o**j + 1/3*o**2 - 1/18*o**3. Factor c(q).
-(q - 1)*(q + 2)/3
Factor -104/7*b + 4/7*b**2 + 76.
4*(b - 19)*(b - 7)/7
Let q(m) be the third derivative of 6/85*m**5 - 1/6*m**4 + 1/1785*m**7 + 11/51*m**3 + 0 + 4*m - 7/510*m**6 - 9*m**2. Factor q(n).
2*(n - 11)*(n - 1)**3/17
Let c = -212529/2 + 106266. Factor 1/4*n**2 + c - 5/4*n.
(n - 3)*(n - 2)/4
Let y(o) be the third derivative of 0*o + 0*o**3 + 0*o**4 + 7*o**2 - 1/100*o**5 + 1/300*o**6 + 1/1050*o**7 + 0. Find i such that y(i) = 0.
-3, 0, 1
Let d = 1191/959 + 6/137. Let c be 16 - (53 + -65 - (-760)/28). Find s, given that -3/7*s**2 - c + d*s = 0.
1, 2
Let i(b) be the third derivative of 0*b - 1/28*b**4 - 4*b**2 - 1/140*b**5 + 0 - 1/14*b**3. Factor i(t).
-3*(t + 1)**2/7
Let a be 0 + (578/17 - 12). Let k(y) be the second derivative of 1/9*y**4 - 1/30*y**5 + 0*y**2 + 0 + 0*y**3 - 1/45*y**6 + a*y. Determine m so that k(m) = 0.
-2, 0, 1
Let c(p) = -p + 7. Let a be c(5). Let j be 4/26 + ((-1116)/156 - -9). Find m such that m**3 - m**4 + 2*m**3 - 68*m**a + 64*m**j + m**3 = 0.
0, 2
Let a(w) = -30*w**3 - 146*w**2 - 150*w - 56. Let d(r) = -2*r**3 + 2*r - 2. Let l(t) = -2*a(t) + 22*d(t). Factor l(f).
4*(f + 1)*(f + 17)*(4*f + 1)
Let w(p) be the first derivative of -2*p**5/5 + 13*p**4 + 18*p**3 + 10. Factor w(f).
-2*f**2*(f - 27)*(f + 1)
Determine f so that 41/4*f + 45 - 1/4*f**2 = 0.
-4, 45
Let n(d) be the first derivative of 3*d**5/5 - 111*d**4/4 + 220*d**3 - 450*d**2 - 1846. Let n(k) = 0. What is k?
0, 2, 5, 30
Let v(b) be the first derivative of 0*b + 125 + 23/25*b**5 + 1/6*b**6 + 3/2*b**4 - 4/5*b**2 + 4/15*b**3. Solve v(s) = 0.
-2, -1, 0, 2/5
Let k = 226 + -211. Let i(b) = -b**5 - 5*b**4 + 8*b**3 + 19*b**2 - 19*b - 35. Let r(a) = a**4 - a**2 + a + 1. Let h(d) = k*r(d) + 5*i(d). Solve h(s) = 0.
-2, 2
Let l be (0 + 1 - 11)*(-6582)/43880. Factor -l*q**3 - 3969/2*q - 189/2*q**2 - 27783/2.
-3*(q + 21)**3/2
Let x(h) be the first derivative of h**3/5 + 10971*h**2/10 - 10974*h/5 + 5396. Factor x(s).
3*(s - 1)*(s + 3658)/5
Let -4/5*f**2 + 548/5*f + 552/5 = 0. Calculate f.
-1, 138
Let y(f) be the third derivative of -1/70*f**7 + 2/5*f**3 + 34*f**2 + 0 + 1/80*f**8 - 23/200*f**6 + 2/5*f**4 + 1/100*f**5 + 0*f. Let y(u) = 0. Calculate u.
-1, -2/7, 1, 2
Suppose 35*g + 76*g + 8570*g**2 - 8567*g**2 + 558 = 0. What is g?
-31, -6
Let b(l) be the second derivative of l**5/170 + 26*l**4/51 + l**3 + 2802*l. Factor b(m).
2*m*(m + 1)*(m + 51)/17
What is g in 12*g**2 - 8*g**2 - 1979*g - 21*g**2 + g**5 - 3*g**4 + 1973*g - 15*g**3 = 0?
-1, 0, 6
Suppose -44*q - 3 = 50*q - 191. Factor 0 + 3/4*z**q + 0*z.
3*z**2/4
Let j(y) = 3*y**3 - 163*y**2 + 814*y - 528. Let z(k) = -2*k**3 + 82*k**2 - 406*k + 272. Let r(p) = -3*j(p) - 7*z(p). Find s such that r(s) = 0.
1, 8
Let t(u) be the second derivative of u**5/4 + 5*u**4/4 - 545*u**3/6 + 1365*u**2/2 + u - 13. Find y such that t(y) = 0.
-13, 3, 7
Let u = 32 + -29. Factor 13*c**5 + 65*c**3 - 110*c**2 - 8 - 28*c - 57*c + c + 76*c**2 - u*c**5 + 51*c**4.
(c - 1)*(c + 2)**3*(10*c + 1)
Let u(b) be the first derivative of 4*b**5/5 + 55*b**4 + 428*b**3/3 + 106*b**2 - 424. Let u(t) = 0. What is t?
-53, -1, 0
Let c(j) = -4*j**2 + 18*j - 32. Let u(y) be the first derivative of -7*y**3/3 + 35*y**2/2 - 61*y - 102. Let m(h) = -11*c(h) + 6*u(h). Factor m(b).
2*(b - 1)*(b + 7)
Let h(b) = b**3 - 5*b**2 - 13*b + 76. Let a be h(4). Factor a*j**3 - 3*j**4 + 2*j**2 - 9*j**3 + 2*j**4 + 44*j + 3*j**2 - 47*j.
-j*(j - 1)**2*(j + 3)
Suppose 0 + 12*v + 4*v**4 + 24*v**2 + 1/3*v**5 + 47/3*v**3 = 0. What is v?
-6, -3, -2, -1, 0
Let g = -726944/11 + 66086. Factor -2*