3*(j - 1)**2*(4*j + 63)
Let w(g) be the first derivative of -11*g**4 + 28*g**3 - 23*g**2 + 11*g - 20. Let y(a) = a**3 - a - 1. Let n(j) = -w(j) - 5*y(j). Factor n(x).
3*(x - 1)**2*(13*x - 2)
Let k(l) be the second derivative of -14*l**6/15 - 24*l**5/5 + 44*l**4/3 + 64*l**3 - 128*l**2 - 24*l - 19. Determine v, given that k(v) = 0.
-4, -2, 4/7, 2
Suppose -15*k = 31*k + 7912. Let o be (-215)/k - (-17)/4. Factor 1/2*c**4 - 3*c**3 + 0 - 3*c + o*c**2.
c*(c - 3)*(c - 2)*(c - 1)/2
Let o be (-6)/(-14) - 24/(-3808)*-68. Let -2/9*t**3 + 10/9*t**4 + 4*t - 2/9*t**5 + o - 14/3*t**2 = 0. Calculate t.
-2, 0, 1, 3
Let n(i) be the third derivative of i**5/60 + 7*i**4/6 + 115*i**3/6 - 275*i**2. Solve n(u) = 0.
-23, -5
Suppose 3*l - 14*p = -16*p + 2, 2*l + 3*p + 2 = 0. Suppose l*y - 26 = -11*y. Factor -1/4*o - 1/8*o**y - 1/8.
-(o + 1)**2/8
Let 8/3*x**3 + 20 - 298/3*x + 230/3*x**2 = 0. Calculate x.
-30, 1/4, 1
Let z be (0*6/30)/(3 - 1). Suppose z + 9/2*m**2 + 3/4*m**3 - 21/4*m = 0. What is m?
-7, 0, 1
Let u be 20/(-5)*(313/(-12) + 23). Solve 14/3*s - 2/3*s**4 + 19/3*s**3 - u*s**2 + 0 = 0 for s.
0, 1/2, 2, 7
Determine i, given that 45 - 1/4*i**2 - 6*i = 0.
-30, 6
Let g(y) be the first derivative of -3*y**5/10 + 15*y**4/4 + 6*y**3 - 15*y**2/2 - 33*y/2 - 705. Suppose g(h) = 0. What is h?
-1, 1, 11
Solve -2744/3 - 2746*a**2 - 2/3*a**4 + 2750/3*a**3 + 8234/3*a = 0.
1, 1372
Suppose -9*v = -62 + 26. Factor 59*r + 21*r + v*r**2 - 2*r**2.
2*r*(r + 40)
Let f(i) = -15*i**3. Let y(n) = 21*n**3 + 16*n - 8. Let d(t) = -14*t**3 - 10*t + 5. Let u(s) = 8*d(s) + 5*y(s). Let c(a) = -3*f(a) + 7*u(a). Factor c(g).
-4*g**3
Let u(h) be the third derivative of -h**6/30 + 2*h**5/3 + 9*h**4/2 - 24*h**3 + 3*h**2 - 158. Factor u(p).
-4*(p - 12)*(p - 1)*(p + 3)
Let y(a) = a**5 - a**4 - a**3 - 5*a. Let u(f) = f**5 - f**4 + 24*f**3 + 10*f**2 - 55*f - 15. Let v(g) = u(g) - 6*y(g). Factor v(c).
-5*(c - 3)*(c - 1)*(c + 1)**3
Factor 16*b + 1/2*b**2 + 56.
(b + 4)*(b + 28)/2
Let i(o) be the first derivative of -27/13*o**2 - 40/39*o**3 - 20/13*o + 54 - 3/26*o**4. Let i(u) = 0. Calculate u.
-5, -1, -2/3
Let d(v) be the second derivative of 3*v**5/20 + 113*v**4/4 + 3135*v**3/2 - 9747*v**2/2 - 2353*v. Find c such that d(c) = 0.
-57, 1
Suppose 2*c + 4*k = 1906, -3*c - c + 5*k + 3747 = 0. Factor c*o + o**3 - 4*o**2 + 4 - 3*o**3 - 941*o.
-2*(o - 1)*(o + 1)*(o + 2)
Let u(j) be the second derivative of 0*j**3 + 2*j - 1/6*j**4 + 45 + 0*j**2 + 1/10*j**5. Factor u(x).
2*x**2*(x - 1)
Suppose g + 15 = 4*g. Suppose g*v = -3*y - y + 118, -4*y + 30 = v. Factor -i**5 + 5*i + 24*i**3 - v*i**3 - 12*i**3 + 6*i**5.
5*i*(i - 1)**2*(i + 1)**2
Let s = 10 - 14. Let h(l) = -l**2 + 1. Let c(o) = -9*o**3 + o**2 - 19. Let m(b) = s*h(b) - c(b). Let q(j) be the first derivative of m(j). Factor q(t).
3*t*(9*t + 2)
Let a(m) be the third derivative of 8*m**7/315 - 11*m**6/45 - 77*m**5/60 + 343*m**4/72 + 343*m**3/9 - 1066*m**2. Suppose a(t) = 0. What is t?
-7/4, 2, 7
Let a(z) = 17*z**4 - 274*z**3 + 2048*z**2 - 18*z. Let j(k) = -4*k**4 + 68*k**3 - 512*k**2 + 4*k. Let l(v) = 4*a(v) + 18*j(v). Factor l(c).
-4*c**2*(c - 16)**2
Suppose 0 = -31*s + 82 + 476. Let c(o) = -6*o + 38. Let u be c(6). What is g in -8*g - 2*g**u - 18*g - 6*g - s + 12*g = 0?
-9, -1
Let y(b) = 7*b**3 + 7*b**2 - 6*b + 4. Let n(i) = -6*i**3 - 6*i**2 + 6*i - 3. Suppose -7*c - 14 = -35. Let o(q) = c*y(q) + 4*n(q). Suppose o(j) = 0. What is j?
-2, 0, 1
Suppose -9107 + 18211 - 9104 - 588*i - 3*i**2 = 0. Calculate i.
-196, 0
Suppose 0 = -3*y + 5*w - 63 - 7, -7*w = -2*y - 109. Find v such that 14/5*v**2 - 1/5*v**3 + 12/5 - y*v = 0.
1, 12
Let w(z) be the first derivative of z**3/3 + 56*z**2 - 585*z - 4765. What is q in w(q) = 0?
-117, 5
Let b(p) be the third derivative of -p**5/300 + 19*p**4/15 - 149*p**3/10 + 1751*p**2. Factor b(i).
-(i - 149)*(i - 3)/5
Suppose 323*y - 369 + 2*y**2 + 1029 - 185*y - 52*y = 0. Calculate y.
-33, -10
Let t(j) be the third derivative of -j**9/7560 - j**8/6300 + j**7/6300 - 25*j**3/6 + 110*j**2. Let o(v) be the first derivative of t(v). Factor o(h).
-2*h**3*(h + 1)*(3*h - 1)/15
Suppose -4*i + n = 2, -46 = -3*i - 21*n + 17*n. Suppose 0 + 9/4*t + 3/4*t**i = 0. Calculate t.
-3, 0
Let p(s) = 22*s**2 + 59*s - 5. Suppose 4*g + 3*n = -n + 24, -4*g = -2*n. Let j(z) = 10*z**2 + 29*z - 2. Let o(a) = g*p(a) - 5*j(a). Let o(c) = 0. Calculate c.
-9/2, 0
Suppose -4*q = -3*f - 2, 1 = -5*f + 11. Factor h**q - 3*h + 1290 - 1290.
h*(h - 3)
Suppose 75*t - 2 = -76*t + 150*t. Let a(i) be the first derivative of 3/4*i**4 + 0*i + t*i**3 + 3/2*i**2 - 6. Let a(o) = 0. What is o?
-1, 0
Let s(b) be the first derivative of -b**6/15 - 36*b**5/5 + 371*b**4/10 - 312*b**3/5 + 188*b**2/5 - 4678. Suppose s(c) = 0. Calculate c.
-94, 0, 1, 2
Factor 445/4 - 47/2*a + 1/4*a**2.
(a - 89)*(a - 5)/4
Let q(a) = 2*a - 15. Let c be q(9). Suppose -c*f = 4*w - 11, w - 4*f - 6 + 8 = 0. Factor 0 + 0*p**w - 2/3*p + 2/3*p**3.
2*p*(p - 1)*(p + 1)/3
Let g = -2215 - -1295. Let h = g - -19322/21. Factor -8/21 + 0*k - h*k**3 + 2/7*k**2.
-2*(k - 2)**2*(k + 1)/21
Let z(a) be the first derivative of -2*a**5/5 + 21*a**4/2 - 106*a**3/3 - 21*a**2 + 108*a + 473. Let z(p) = 0. Calculate p.
-1, 1, 3, 18
Solve -16*v**2 + 148/5*v**3 + 256 - 1344/5*v - 4/5*v**5 + 0*v**4 = 0.
-5, -4, 1, 4
Factor 5987*m**2 - 5*m**5 - 11935*m**2 - 5 - 45*m**4 + 5 - 150*m**3 + 5728*m**2 - 120*m.
-5*m*(m + 2)**3*(m + 3)
Let t(c) be the second derivative of c**7/147 + 2*c**6/7 - 9*c**5/10 + 16*c**4/21 - 238*c. Factor t(r).
2*r**2*(r - 1)**2*(r + 32)/7
Let o = -200 + 202. Let b(s) = 2*s**2 + 17*s + 21. Let y(j) = 2*j**2 + 16*j + 22. Let a(t) = o*b(t) - 3*y(t). Factor a(v).
-2*(v + 3)*(v + 4)
Let j(i) = -8*i**3 - 7*i**2 - 13 + 5*i**3 - 16*i**2 + 6*i**3 + 4*i**3. Let l(a) = -a**3 + 4*a**2 + 2. Let v(b) = -6*j(b) - 39*l(b). What is d in v(d) = 0?
-6, 0
Let i(p) = p**3 + 49*p**2 - 153*p + 154. Let v be i(-52). Let m be (-2)/12 + (20/(-15))/v. Factor 0 - 1/2*z**2 - m*z.
-z*(z + 1)/2
Solve -16*p**5 - 270*p**2 - 28*p**3 - 72*p**4 + 166*p**3 + 201*p**3 + 19*p**5 = 0 for p.
0, 1, 5, 18
Let v(r) be the first derivative of 2/15*r**5 + 11/6*r**4 - 1/9*r**6 + 14/9*r**3 + 241 - 16/3*r - 10/3*r**2. Suppose v(d) = 0. Calculate d.
-2, -1, 1, 4
Let d = 81 + -403/5. Let n be 1*2*21/(2310/44). Factor -n*v + 0 + d*v**2.
2*v*(v - 2)/5
Suppose -112/9 - 106/9*m - 17/9*m**2 + 4/9*m**3 = 0. What is m?
-2, -7/4, 8
Let h(g) be the second derivative of -g**5/16 + 29*g**4/24 + g**3 - 7*g - 85. Let h(z) = 0. Calculate z.
-2/5, 0, 12
Let p(x) be the third derivative of -x**5/120 - 251*x**4/12 - 63001*x**3/3 + 11*x**2 - 80*x. Factor p(w).
-(w + 502)**2/2
Suppose -4*g + 2 + 17 = l, 2*l + 7 = g. Suppose -4*t = g*x - 23, 0 = 3*t - 8*x + 5*x + 3. Factor -1/7*m - 3/7 + 2/7*m**t.
(m + 1)*(2*m - 3)/7
Let k(i) = -13*i**3 - 17*i**2 - 10*i - 4. Let j(d) = -1 - 37*d + 2 - 8 - 33*d**2 - 2 + 16*d - 27*d**3. Let o(y) = 4*j(y) - 9*k(y). Suppose o(f) = 0. What is f?
-2, -1/3, 0
Let k be ((-80)/(-144)*(-3)/2)/(5/(-15)). Let p(y) be the first derivative of 0*y**3 + 5 + 0*y**2 + 0*y - k*y**4 - 5/6*y**6 - 3*y**5. Factor p(b).
-5*b**3*(b + 1)*(b + 2)
Let o(w) = -19*w**4 - 3066*w**3 - 2*w**2 + 4*w. Let x(r) = 102*r**4 + 15328*r**3 + 11*r**2 - 22*r. Let y(g) = 11*o(g) + 2*x(g). Factor y(i).
-5*i**3*(i + 614)
Let n(b) be the third derivative of -1/120*b**6 - 21*b**3 + 43/8*b**4 - 7/12*b**5 + 1/210*b**7 + 0 + 0*b + 96*b**2. Let n(r) = 0. Calculate r.
-7, 2, 3
Let b(h) be the third derivative of h**7/70 - 3*h**6/10 - 1099*h**5/10 - 8349*h**4/2 - 31211*h**3/2 - 14717*h**2. Factor b(t).
3*(t - 59)*(t + 1)*(t + 23)**2
Let x = 49 + -37. Suppose 0 = -3*f + x*f - 27. What is d in 4*d**f + 5*d**4 - 5*d**5 - 20*d**4 - 5*d**2 - 17*d**3 - 2*d**3 = 0?
-1, 0
Let r(d) be the first derivative of -1125*d**6 - 1890*d**5 + 2610*d**4 + 5024*d**3/3 + 352*d**2 + 32*d + 1986. Suppose r(m) = 0. Calculate m.
-2, -2/15, 1
Let o(n) be the first derivative of -n**6/10 + 51*n**5/25 - 84*n**4/5 + 352*n**3/5 - 768*n**2/5 + 768*n/5 - 2712. Suppose o(u) = 0. Calculate u.
1, 4
Factor -168*s**2 + 117*s**2 + 261*s**2 - 58209 + 36432*s + 162753 + 324*s**2 + 2*s**3.
2*(s + 3)*(s + 132)**2
Let v(j) be the second derivative of 3*j**4/20 + 49*j**3/5 - 99*j**2/10 - 263*j + 3. Factor v(s).
3*(s + 33)*(3*s - 1)/5
Suppose -2*h + 6*c 