 g = 90 - 30. Suppose -o + g = 3*o. Factor -3 + 3 - 9*u**2 - 6*u**2 - o*u - 5*u**3 - 5.
-5*(u + 1)**3
Let m be (8/(-10))/(24/(-1140)). Factor -14*f**4 + 32*f - 10*f**2 + m*f**3 + 0*f**4 + 2*f**5 - 40*f**2 - 8.
2*(f - 2)**2*(f - 1)**3
Suppose -3*m = -14*l + 11*l + 15, 0 = -m - 3*l + 27. Let a be (-3)/(-2)*(-6)/(-4). Determine t so that -9/4*t**4 - 3/4*t**2 + a*t**m + 0*t + 0 + 3/4*t**5 = 0.
0, 1
Let z(s) = -16*s**3 + 12*s - 12. Let j(a) be the third derivative of -a**6/120 + a**4/24 - a**3/6 - 19*a**2. Let d(l) = 12*j(l) - z(l). Factor d(u).
4*u**3
Suppose 0 - 18/23*r**2 + 0*r + 2/23*r**3 = 0. Calculate r.
0, 9
Suppose 3*b - 4*s - 32 = 0, 4*b - 26 = 3*s - s. Let k = b - 10/3. Solve -8/3 + 2*j**2 + k*j**3 + 0*j = 0.
-2, 1
Let y(v) be the first derivative of v**4/3 - 40*v**3/3 + 38*v**2 - 112*v/3 + 153. Factor y(k).
4*(k - 28)*(k - 1)**2/3
Let o(s) be the third derivative of -s**7/5880 - s**6/1680 + s**5/140 - 19*s**4/24 + 21*s**2. Let l(q) be the second derivative of o(q). Factor l(m).
-3*(m - 1)*(m + 2)/7
Let d = -24686/5 - -4938. What is o in -d*o**2 - 80 + 16*o = 0?
10
Let k(c) be the third derivative of 0 - 1/100*c**5 + 0*c**3 + 3*c**2 + 0*c**4 + 0*c. Factor k(f).
-3*f**2/5
Let p be (-2 - (-21)/12)*-4. Let h = p - -1. Factor -3*k - 7*k**2 + 3*k**h + 2*k**5 + 2*k**4 + k + 2*k**4.
2*k*(k - 1)*(k + 1)**3
Suppose -3*c - 4 = -7*c + 2*k, 0 = -3*c + 2*k + 1. Let t(a) be the third derivative of 0 + 0*a**5 + 0*a - a**2 - 1/84*a**4 + 1/420*a**6 + 0*a**c. Factor t(f).
2*f*(f - 1)*(f + 1)/7
Let p(s) be the third derivative of -s**6/3960 + s**5/440 - s**4/132 - s**3/2 + 9*s**2. Let q(h) be the first derivative of p(h). Factor q(k).
-(k - 2)*(k - 1)/11
Let g(s) be the second derivative of s**6 + 11*s**5/10 - 28*s**4/45 + 4*s**3/45 - 29*s + 2. Factor g(b).
2*b*(b + 1)*(15*b - 2)**2/15
Let f(p) be the second derivative of -2*p**6/15 + 11*p**5/5 - 35*p**4/3 + 50*p**3/3 - 27*p + 1. Let f(l) = 0. Calculate l.
0, 1, 5
Solve 68 + 3198*o**3 + 60*o**2 + 105*o - 18 - 3193*o**3 = 0.
-10, -1
Factor -3/5*q**3 - 4*q + 8/5 + 14/5*q**2.
-(q - 2)**2*(3*q - 2)/5
Let g be 357/(-2040)*(-2)/14. Let p(u) be the third derivative of 1/6*u**3 + 0*u - 1/16*u**4 + 0 + 3*u**2 - g*u**5 + 1/120*u**6. Factor p(s).
(s - 2)*(s + 1)*(2*s - 1)/2
Let d(z) = 3*z**3 + z**2 - z. Let s be d(1). Factor s*c**3 - 3*c**2 + 52 - 52.
3*c**2*(c - 1)
Let g = 14 + -12. Suppose 1 = g*w - w. Factor 0 + 3 + 4*z + 2*z**2 - w.
2*(z + 1)**2
Let n(v) be the second derivative of 5*v**4/12 + 300*v**3 + 81000*v**2 + 592*v. Factor n(a).
5*(a + 180)**2
Let g be (-36)/(-234) - 27/(-78). Let t(b) be the first derivative of -8 + 1/4*b**2 + g*b - 1/3*b**3. Determine j, given that t(j) = 0.
-1/2, 1
Let l be (2/3)/((-6)/(-216)). Let c be (3 + l/(-4))/(-1). Solve -c*n**3 - 2*n - 3 + 2*n + 3*n + 0*n**2 + 3*n**2 = 0 for n.
-1, 1
Let m(b) be the third derivative of 7*b**2 + 0*b + 1/12*b**4 + 0 - 1/6*b**3 - 1/60*b**6 + 1/60*b**5. Let m(x) = 0. What is x?
-1, 1/2, 1
Let l(d) be the first derivative of 2*d**6/3 + 304*d**5/5 + 581. Factor l(q).
4*q**4*(q + 76)
Let l be (72/150)/(13 - (-630)/(-50)). Suppose -9/5*c - 3/5*c**5 - 6/5 + 0*c**4 + 12/5*c**3 + l*c**2 = 0. What is c?
-1, 1, 2
Suppose -3*o + 133*m = 129*m - 9, 3*o + 2*m = 9. Let c(a) be the first derivative of 0*a**3 + 1/2*a**4 - o - a**2 + 0*a. Factor c(s).
2*s*(s - 1)*(s + 1)
Factor 2/3*b**2 + 0 + 58/3*b.
2*b*(b + 29)/3
Let a(y) be the second derivative of -5*y**4/12 - 445*y**3 - 356445*y**2/2 - 788*y. Factor a(u).
-5*(u + 267)**2
Suppose 4*o - 20 + 0 = 0. Suppose -4*g = -3 - o. Determine f so that -4*f**4 - 37*f + 8*f**2 - g + 37*f - 2 = 0.
-1, 1
Suppose -p = -4, -5*c + 7*p = 3*p + 21. Let m be (-5 - 1*(c - 0))/(-7). Factor 1/7*i**3 + 0 + m*i**2 - 1/7*i**4 - 4/7*i.
-i*(i - 2)*(i - 1)*(i + 2)/7
Let y(k) be the third derivative of -k**9/12096 + k**8/4032 + k**7/1008 - k**6/144 + k**5/6 - 14*k**2. Let c(a) be the third derivative of y(a). Solve c(x) = 0.
-1, 1
Suppose 24 = 2*u - 6*u. Let w(m) = 5*m**5 + 10*m**4 - 5*m**3 + m**2 + 11. Let y(x) = -x**5 - 2*x**4 + x**3 - 2. Let r(z) = u*w(z) - 33*y(z). Factor r(g).
3*g**2*(g - 1)*(g + 1)*(g + 2)
What is z in 26/3*z + 20/3 + 8/3*z**2 = 0?
-2, -5/4
Let u be 16/6 + (-2)/3. Factor -16*j + 33*j**3 - 29*j**3 + j**2 - j**u.
4*j*(j - 2)*(j + 2)
Solve 21*j + 9*j**2 + 303 - 12*j**2 - 312 + 3*j**3 - 12*j**2 = 0.
1, 3
Let m(c) be the first derivative of c**5/25 - 3*c**4/20 - 3*c**3/5 - c**2/2 + 63. Suppose m(l) = 0. What is l?
-1, 0, 5
Let d(r) be the first derivative of 11/6*r**3 - 1/2*r**2 + 22 + 0*r - 5/8*r**4. Factor d(b).
-b*(b - 2)*(5*b - 1)/2
What is l in -1346 - 32*l**2 + 1346 + 2*l**3 = 0?
0, 16
Let d(y) = -10*y**3 - 83*y**2 + 60*y - 27. Let v be d(-9). Let 2/5*n**2 + v*n - 2/5 = 0. What is n?
-1, 1
Let q(i) be the second derivative of -i**7/630 + i**6/60 - i**5/15 + i**4/9 - 11*i**2/2 + 15*i. Let m(o) be the first derivative of q(o). Factor m(g).
-g*(g - 2)**3/3
Let 1/8*j**2 - 1/2*j**3 + 3/2 + 2*j - 1/8*j**4 = 0. What is j?
-3, -2, -1, 2
Factor 3*d + 48*d**3 - d + 9*d - 7*d + 52*d**2.
4*d*(d + 1)*(12*d + 1)
Let l(k) be the third derivative of -5*k**8/336 + k**7/21 + k**6/6 - 2*k**5/3 + 12*k**2 - 11. Solve l(j) = 0 for j.
-2, 0, 2
Let n(m) be the first derivative of -2*m**5/25 + 3*m**4/10 - 2*m**3/5 + m**2/5 + 386. Factor n(y).
-2*y*(y - 1)**3/5
Let x(y) be the first derivative of y**4/3 + 4*y**3/9 - 4*y**2/3 - 139. Factor x(q).
4*q*(q - 1)*(q + 2)/3
Let r(g) = 9*g + 43. Let q be r(11). Let t = q + -139. Factor -6/5*v - 2/5*v**t + 2/5 + 6/5*v**2.
-2*(v - 1)**3/5
Let z = -309 - -309. Let x(b) be the third derivative of -1/120*b**5 + z + 2*b**2 - 1/24*b**4 + 0*b**3 + 0*b + 1/240*b**6. Factor x(y).
y*(y - 2)*(y + 1)/2
Let g(t) be the first derivative of -t**4/22 - 4*t**3/33 + 82. Find b such that g(b) = 0.
-2, 0
Let p be (-5)/25*-2 + (-34)/(-15). Factor -2*t + p - 14/3*t**2.
-2*(t + 1)*(7*t - 4)/3
Suppose 0 = -11*z + 349 + 113. Let h be 7/(z/(-4)) + 416/264. Factor 4/11*o + 0 - h*o**2 - 6/11*o**3.
-2*o*(o + 2)*(3*o - 1)/11
Let t = 274 + -269. Let m be 2*t/(55/2). Factor 0 + m*y**3 - 2/11*y**4 - 2/11*y**2 + 0*y.
-2*y**2*(y - 1)**2/11
Let z be (-16)/8 + 10*15/75. Factor z + 2/3*n**3 + 4/3*n**2 - 8/3*n - 1/3*n**4.
-n*(n - 2)**2*(n + 2)/3
Let t = -1528/7 - -3077/14. Solve -3*r - 3/4 - t*r**2 + 9/4*r**4 + 3*r**3 = 0 for r.
-1, -1/3, 1
Let b(s) be the second derivative of s**7/28 + s**6/4 + 3*s**5/10 - 2*s**4 - 8*s**3 - 12*s**2 - 38*s + 2. Determine o, given that b(o) = 0.
-2, -1, 2
Let x(r) = -7*r**2 + 78*r - 511. Let o(p) = 13*p**2 - 156*p + 1021. Let d(t) = -4*o(t) - 7*x(t). Solve d(a) = 0.
13
Suppose 6*y = -2*y. Let v(c) be the second derivative of 1/10*c**6 - 3/20*c**5 - 1/56*c**7 + y*c**4 + 0*c**2 - c + 0 + 0*c**3. Factor v(o).
-3*o**3*(o - 2)**2/4
Let r(f) be the first derivative of -3*f**4/4 - 20*f**3 - 231*f**2/2 + 726*f + 95. Factor r(z).
-3*(z - 2)*(z + 11)**2
Let q(m) be the second derivative of 4*m**2 + 0 - 2/3*m**4 + 2*m**3 + 4*m. Factor q(r).
-4*(r - 2)*(2*r + 1)
Let q = -23 + 21. Let d = 8/3 + q. Solve -d + 2/3*n**2 + 0*n = 0 for n.
-1, 1
Let c be -4 - (-2 - 49/21). Let y(r) be the second derivative of -5*r - 1/6*r**4 + c*r**3 + 2*r**2 + 0. Let y(n) = 0. Calculate n.
-1, 2
Factor -20*i**2 - 18*i**2 - 25 + i + 19*i + 43*i**2.
5*(i - 1)*(i + 5)
Let a(w) be the first derivative of -3*w**5/40 - 3*w**4/16 + w**3 + 136. Solve a(g) = 0.
-4, 0, 2
Let q = 694 - 687. Let j(o) be the first derivative of 1/8*o**4 + 0*o**3 + q + 0*o - 1/4*o**2. Let j(n) = 0. Calculate n.
-1, 0, 1
Let h(c) be the second derivative of -2/3*c**3 - 3*c**2 + 44*c - 1/5*c**5 + 0 + 7/6*c**4. Factor h(a).
-2*(a - 3)*(a - 1)*(2*a + 1)
Factor -18 + 8 + 6*i**4 - 14 + 19*i**4 - 124*i - 166*i**2 - 5*i**3.
(i - 3)*(i + 2)*(5*i + 2)**2
Let t(d) be the second derivative of 88*d**7/105 + d**6/3 - 91*d**5/50 - 5*d**4/6 + d**3/5 + d - 158. Find x such that t(x) = 0.
-1, -3/8, 0, 1/11, 1
Let h = 3515 + -24599/7. Factor 15/7*b - 6/7*b**2 - h.
-3*(b - 2)*(2*b - 1)/7
Let n be 2 + (-2*2)/(14/(-7)). Suppose 16 - 16 = -n*s. Determine u so that -2/5*u**2 + s*u + 0 = 0.
0
Let w(y) = -5*y**3 - 42*y**2 - 2*y. Let q(m) = -66*m**3 - 546*m**2 - 27*m. Let b(i) = -2*q(i) + 27*w(i). Suppose b(o) = 0. Calculate o.
-14, 0
Let z(b) be the second derivative of -b**5/50 - b**4/3 + 23*b*