Let f(s) be the second derivative of -1/720*s**6 + 0*s**4 + s**2 - 1/240*s**5 - 44*s + 0 + 1/3*s**3. Let n(q) be the second derivative of f(q). Factor n(h).
-h*(h + 1)/2
Let p(g) = -7*g**2 - 8*g + 3. Let r be p(3). Let q = r + 86. Solve 4*v**3 - v**3 + 24 - 4*v**q + 22*v**2 + 36*v = 0.
-2
What is t in 904/3*t**2 + 88/3*t**3 + 2/3*t**4 + 1664/3*t - 2560 = 0?
-30, -8, 2
Let i(f) be the second derivative of -5*f**4/36 - 40*f**3/9 - 65*f**2/2 - 1175*f. Factor i(u).
-5*(u + 3)*(u + 13)/3
Let d be 1/(((-21)/(-91))/3). Let b(m) = 15*m**2 - 16*m + 45. Let z(y) = -7*y**2 + 8*y - 22. Let i(r) = d*z(r) + 6*b(r). Factor i(p).
-(p - 4)**2
Let g(w) be the second derivative of w**6/150 + 37*w**5/100 + 7*w**4/6 + 599*w. Factor g(m).
m**2*(m + 2)*(m + 35)/5
Let a(y) be the third derivative of 2*y**2 + 0*y - 13 + 0*y**3 - 1/21*y**7 + 0*y**4 + 3/10*y**5 + 1/20*y**6 + 1/168*y**8. Solve a(z) = 0.
-1, 0, 3
Let u(a) be the second derivative of 1/20*a**5 - 4*a**2 - 2 - 2/3*a**3 + 1/2*a**4 - 1/30*a**6 - 50*a. Factor u(c).
-(c - 2)**2*(c + 1)*(c + 2)
Let k(w) be the first derivative of -w**8/336 - 2*w**7/21 - 8*w**6/9 + 5*w**3/3 + 5*w**2 - 176. Let b(z) be the third derivative of k(z). What is q in b(q) = 0?
-8, 0
Let w be (-584)/(-40) + -10 - 3/5. Let t(q) be the first derivative of -1/2*q**w + 2*q**3 + 5*q**2 + 4*q - 2/5*q**5 + 19. Solve t(o) = 0.
-1, 2
Factor 572907/4*t + 1/4*t**3 + 1311/4*t**2 + 83453453/4.
(t + 437)**3/4
Let v(j) be the first derivative of 2*j**5/45 + 7*j**4/18 - 20*j**3/9 + 1329. Solve v(x) = 0.
-10, 0, 3
Let m(h) be the third derivative of h**6/180 - 7*h**5/5 + 41*h**4/4 + h**2. Factor m(z).
2*z*(z - 123)*(z - 3)/3
Let c(d) be the third derivative of -1/6*d**3 - 1/18*d**4 - 1 - d**2 - 1/180*d**5 + 0*d. Factor c(g).
-(g + 1)*(g + 3)/3
Let k(z) be the second derivative of z**6/6 - 8*z**5 + 265*z**4/2 - 960*z**3 + 6885*z**2/2 + 4*z + 350. Let k(w) = 0. What is w?
3, 9, 17
Determine q so that -1/7*q**5 - 361 + 2558/7*q**2 - 31/7*q**4 - 94/7*q**3 + 95/7*q = 0.
-19, -1, 1, 7
Let c(n) be the first derivative of -7*n**2 + 112*n - 364. Let l be c(8). Let -1/4*r**2 + 1/12*r**4 + 0 + l*r + 1/6*r**3 = 0. What is r?
-3, 0, 1
Let p(q) = -36*q - 30. Let d be p(-1). Suppose d*j + 20*j - 52 = 0. What is n in 20/7*n**j - 16/7*n + 0 = 0?
0, 4/5
Let o(m) be the first derivative of 160*m**2 + 67 + 16/3*m**3 + 768*m - m**4. Factor o(p).
-4*(p - 12)*(p + 4)**2
Let i(k) be the second derivative of k**5/90 + 8*k**4/9 + 256*k**3/9 - 65*k**2/2 + 32*k - 3. Let m(u) be the first derivative of i(u). Factor m(l).
2*(l + 16)**2/3
Factor -23/4*j**2 - 1/4*j**3 + 0 + 25/2*j.
-j*(j - 2)*(j + 25)/4
Let m = -97589 - -97591. Factor -2/9*b**m + 16/9 + 14/9*b.
-2*(b - 8)*(b + 1)/9
Let n(k) = -34*k - 293. Let a be n(-9). Factor -a*t**3 + 91*t**2 + 48 + 164*t + 81*t**3 + 93*t**2.
4*(t + 1)**2*(17*t + 12)
Suppose 0 = -2*s - 92 + 98. Let g = 1768 - 22970/13. Solve -4/13*j**4 + 0*j + 4/13*j**2 - g*j**s + 0 + 14/13*j**5 = 0.
-1, 0, 2/7, 1
Find u, given that -1 + 2200*u**3 + 848 + 284*u - 2484*u - 2210*u**2 + 547 + 5*u**4 + 811 = 0.
-441, -1, 1
Let c(d) be the second derivative of -20 + 288/5*d**2 - 13/20*d**4 - 8/5*d**3 - 2*d - 3/100*d**5. Factor c(r).
-3*(r - 3)*(r + 8)**2/5
Let i(g) be the first derivative of -g**7/2100 + g**5/100 + g**4/30 - g**3/3 - 7*g**2 + 27. Let p(s) be the third derivative of i(s). Factor p(h).
-2*(h - 2)*(h + 1)**2/5
Let p(a) be the third derivative of 11/15*a**5 + 7 + 7/4*a**4 + 0*a + 1/60*a**6 - a**2 + 0*a**3. Suppose p(u) = 0. Calculate u.
-21, -1, 0
Let n be 4 + 10 + 70/((-63)/9). Let b(d) be the first derivative of 16/7*d - n - 4/21*d**3 + 0*d**2. Factor b(i).
-4*(i - 2)*(i + 2)/7
Solve 2*v**5 + 263538 + 726*v**4 + 131766*v**3 - 393855*v - 2826*v**2 + 650*v**2 - v**5 = 0.
-363, -2, 1
Factor -x**3 - 2/3*x**2 - 2/3*x**4 - 1/6*x - 1/6*x**5 + 0.
-x*(x + 1)**4/6
What is z in 196*z - 3489941 + z**2 + 3489941 = 0?
-196, 0
Let o = 5834/65 + 812/5. Let s = o - 252. Determine p, given that 0 - 4/13*p + s*p**3 + 2/13*p**2 = 0.
-2, 0, 1
Find o, given that -594*o**3 - 590*o**3 + 1779*o**3 + 2*o**2 + 15*o - 596*o**3 = 0.
-3, 0, 5
Let f(p) be the second derivative of -p**5/60 - 215*p**4/18 - 23744*p**3/9 - 44944*p**2 - 6847*p. Determine g so that f(g) = 0.
-212, -6
Let o(p) be the second derivative of p**4/6 + 226*p**3/3 + 225*p**2 - 20*p + 29. Factor o(g).
2*(g + 1)*(g + 225)
Suppose -17 = -k - 14. What is a in 22*a**k + a**4 + 32*a + 3*a**4 + 187*a**2 - 145*a**2 + 8 = 0?
-2, -1, -1/2
Let g be 10/(22*(-85)/(-2244)). Suppose 3/5*i**3 + 24/5*i + g - 33/5*i**2 = 0. What is i?
-1, 2, 10
Let z(o) = o + 9. Let u be z(-6). Suppose 2*x - u*g = -0*x + 16, 2 = -5*x - 3*g. Suppose 6*k - 6*k**3 + 2*k**2 - 8 + 8 + x*k**4 - 4 = 0. What is k?
-1, 1, 2
Let i be 2*(-4 + 35/10). Let x = 10 - i. Let -74*n**5 + 4*n + 5*n**4 - x*n**2 + 4 + 152*n**5 - 76*n**5 - 4*n**3 = 0. Calculate n.
-2, -1/2, 1
Let y = 761765 - 3047053/4. Solve -1/4*s**2 + y*s + 9/2 = 0 for s.
-2, 9
Let u be (-8)/12*(8 + (-13 + -3 - -2)). Let g(y) be the third derivative of -10*y**2 + 8*y**3 + 0*y - 2 - y**u + 1/20*y**5. Factor g(m).
3*(m - 4)**2
Let g = 351384 - 2445910/7. Find a, given that g*a**2 + 8/7 - 664/7*a = 0.
2/83
Let c(m) be the second derivative of m**7/63 - m**6/5 + 4*m**5/15 + 54*m. Factor c(f).
2*f**3*(f - 8)*(f - 1)/3
Let g(d) be the first derivative of -2*d**6/3 - 3588*d**5/5 - 201600*d**4 - 802816*d**3/3 - 10534. Factor g(q).
-4*q**2*(q + 1)*(q + 448)**2
Solve 2497/2*n**2 - 51*n**3 + 1/2*n**4 + 2652*n + 1352 = 0 for n.
-1, 52
Let i(t) be the first derivative of t**3/3 + 19*t**2/2 - 42*t + 975. Factor i(k).
(k - 2)*(k + 21)
Let 2*r**3 + 226/3*r - 28 - 40*r**2 + 4/3*r**4 = 0. What is r?
-7, 1/2, 2, 3
Let l(b) be the first derivative of b**3/5 - 57*b**2/5 - 504*b/5 - 957. Solve l(g) = 0.
-4, 42
Let q = -2/911 - -4561/2733. Let r(c) be the third derivative of 0*c + 16*c**2 - 11/24*c**4 + q*c**3 + 1/60*c**5 + 0. Suppose r(z) = 0. Calculate z.
1, 10
Let n = 8/547 - -27214/9299. Let m(y) be the first derivative of -2 - 10/17*y**2 - 2/51*y**3 - n*y. Factor m(t).
-2*(t + 5)**2/17
Let j(c) = 0*c - c - 2 + 1. Let w = 52 + -53. Let k(r) = -16*r**2 + 16*r - 8. Let o(n) = w*k(n) + 4*j(n). Find m, given that o(m) = 0.
1/4, 1
Let 304/7*l + 2/7*l**3 + 0 + 12*l**2 = 0. What is l?
-38, -4, 0
Let v(m) be the second derivative of -17*m**4/24 - 167*m**3/24 + 15*m**2/8 - 9950*m. Factor v(n).
-(n + 5)*(34*n - 3)/4
Suppose -8 = 4*r + 4*l, 10*l - 7*l + 2 = -5*r. Find o, given that -2/13*o**4 - 4/13*o**r + 0*o + 6/13*o**3 + 0 = 0.
0, 1, 2
Suppose -200/9*j**2 + 2200/9*j + 0 - 2/9*j**3 = 0. Calculate j.
-110, 0, 10
Let m(f) be the second derivative of 2/15*f**3 - 2 - 1/60*f**4 + 1/2*f**2 + 48*f. Solve m(y) = 0 for y.
-1, 5
Let f be ((-10 + 37)/(-9))/3 + 7/3. Find i, given that f*i - 2*i**2 + 2/3*i**3 + 0 = 0.
0, 1, 2
Let z(a) be the second derivative of -a**6/720 + 3*a**5/80 + 31*a**3/6 + a - 16. Let o(j) be the second derivative of z(j). Factor o(f).
-f*(f - 9)/2
Let l be ((-5566)/(-253))/(((-4)/3)/(-2)). Let b(u) = -u**3 + 31*u**2 + 67*u - 29. Let v be b(l). Factor 0 + 4/3*j**2 - 6*j**3 + 0*j + 14/3*j**v.
2*j**2*(j - 1)*(7*j - 2)/3
Let n(o) be the first derivative of 25*o**4 + 2/15*o**6 - 3*o**5 - 250/3*o**3 - 5 + 0*o**2 - 11*o. Let a(i) be the first derivative of n(i). Factor a(y).
4*y*(y - 5)**3
Let n(g) be the third derivative of 2*g - 23/240*g**5 - 1/2*g**3 + 0 - 1/160*g**6 - 1/3*g**4 + 18*g**2. Solve n(u) = 0.
-6, -1, -2/3
Let h(a) be the first derivative of a**3/6 + 53*a**2/2 - 336*a - 1304. Factor h(p).
(p - 6)*(p + 112)/2
Factor 44*x**2 + 1488*x - 208 + 53 + 20 - 137.
4*(x + 34)*(11*x - 2)
Let o(k) be the first derivative of -k**6/30 - k**5/10 + k**4/4 + 2*k**3/3 - 2*k**2 + 83*k + 1. Let p(s) be the first derivative of o(s). What is q in p(q) = 0?
-2, 1
Let f be 348/(-145)*180/(-16). Let k be (0 + 3)/f + (-155)/(-279). Factor -1/3*n**2 - k*n + 0.
-n*(n + 2)/3
Let j be (-2)/(-28)*(-26271)/(-5004). Factor -15/4*o**2 + 33/8*o + 0 - j*o**3.
-3*o*(o - 1)*(o + 11)/8
Let b(r) be the third derivative of -1/210*r**7 - 4*r**3 + 0 + 1/6*r**5 + 1/120*r**6 - 4*r**2 - 1/6*r**4 - 14*r. Suppose b(v) = 0. What is v?
-2, 2, 3
Find l, given that 467/2*l + 209 + 25*l**2 + 1/2*l**3 = 0.
-38, -11, -1
Let l(v) be the second derivative of 0 + 0