1, 1
Let b(q) be the second derivative of -q**6/14 - 13*q**5/70 - 2*q**4/21 - q - 599. Solve b(d) = 0.
-4/3, -2/5, 0
Suppose -117 = -4*t + 79. Factor 98*m**3 - 101*m + 62 - 98 - 112*m**2 - t*m.
2*(m - 2)*(7*m + 3)**2
Suppose 2*b + 9 = 15. Suppose 0 = l + m + 2, -28 = -l - b*m + 8*m. Factor 0 + 36/7*n**2 + 24/7*n + 3/7*n**4 + 18/7*n**l.
3*n*(n + 2)**3/7
Let c(j) be the second derivative of -2*j**7/21 - 43*j**6/90 - 2*j**5/15 + 2*j**4/3 + 5*j**3/6 + 6*j. Let d(v) be the second derivative of c(v). Factor d(q).
-4*(q + 2)*(4*q - 1)*(5*q + 2)
Let r(x) = -x**3 + 4*x**2 - 2*x + 2. Let q(s) = -s + 1. Suppose -4*m = -3 - 5. Let a(k) = m*q(k) - r(k). Suppose a(o) = 0. Calculate o.
0, 4
Let y be (-36)/132 + (-108)/(-44) + -2. Let b be (4/(-10))/(1/(-5)). Factor y*w**b + 2/11 + 4/11*w.
2*(w + 1)**2/11
Suppose 6*z + 65 = -65 + 142. Factor -12/7*f**3 + 24/7*f - 4*f**z + 0.
-4*f*(f + 3)*(3*f - 2)/7
Let o(q) be the first derivative of 2*q**3/33 + 380*q**2/11 + 72200*q/11 - 686. Find l, given that o(l) = 0.
-190
Let s = -4 + 21. Let w = 50 - 50. Find f such that w*f**2 - 3*f**2 + s*f - 26*f = 0.
-3, 0
Let v(g) be the second derivative of -1/18*g**4 + 30*g + 0*g**2 + 0 + 10/9*g**3. Solve v(f) = 0 for f.
0, 10
Suppose 2*q + g - 3 = 0, 0*q - 5*g - 45 = -5*q. Suppose 3*t + 7 = 4*v, t - q*v + 10 = -3. What is z in -3*z**2 + 2*z**2 - 3*z**t + 10*z**2 + 0*z**2 = 0?
0, 3
Let a(l) be the second derivative of l**7/168 + l**6/72 - 14*l**3/3 + 26*l. Let r(c) be the second derivative of a(c). Factor r(x).
5*x**2*(x + 1)
Let w(d) be the second derivative of 1/40*d**5 + 0 - 5/12*d**3 + 1/12*d**4 - 3/2*d**2 + 27*d. Find o, given that w(o) = 0.
-3, -1, 2
Let p(z) be the second derivative of z**5/5 + 3*z**4 - 44*z**3/3 - 22*z + 1. Suppose p(g) = 0. What is g?
-11, 0, 2
Let o(r) = -r**2 + r + 1. Let q(g) = 5*g**2 + g - 2. Let j(s) = -2*o(s) - q(s). Factor j(w).
-3*w*(w + 1)
Let k = 59 + -56. Let d(t) = -3*t + 1. Let o be d(-1). Factor x**2 + 3*x**k + 213 - 213 + x**5 + 3*x**o.
x**2*(x + 1)**3
Let u be 494/169 + (-2)/(-26). Let h(l) be the first derivative of 0*l**2 + 5 - 1/3*l**u + 0*l. Factor h(s).
-s**2
Let s(o) = -o**3 + 4*o**2 + o + 2. Let z(q) = q**3 - 6*q**2 - 2. Let w(v) = 3*s(v) + 2*z(v). Factor w(l).
-(l - 2)*(l + 1)**2
Factor 12*d**2 + 16/3*d**3 + 0 + 20/3*d.
4*d*(d + 1)*(4*d + 5)/3
Let y(p) be the first derivative of 23*p**3/3 - 29*p**2/2 + 23*p + 2. Let l(u) = -4*u**2 + 5*u - 4. Let q(v) = 34*l(v) + 6*y(v). Factor q(n).
2*(n - 1)**2
Suppose -216 = -14*v + 5*v. Factor k**4 - v*k**3 + 7*k + k - 7*k**4 + 10*k**3.
-2*k*(k + 1)*(k + 2)*(3*k - 2)
Suppose n + 0 - 4 = 0. Let v be (196/35)/(3/15). Factor 6*u**4 - 10*u**4 - 20*u**2 + 2*u**4 - 4*u - v*u**3 - 10*u**n.
-4*u*(u + 1)**2*(3*u + 1)
Let l = 7 - 5. Suppose -l*h = -3*h - 2, -2*h - 6 = -r. Factor 13*s**2 - 2*s**3 - 5*s**2 - r*s**3.
-4*s**2*(s - 2)
Let l(p) be the third derivative of p**6/24 + 7*p**5 + 347*p**2. Let l(s) = 0. What is s?
-84, 0
Let r(p) be the first derivative of -p**5/240 + p**4/48 + p**3/8 - 5*p**2 - 9. Let f(a) be the second derivative of r(a). Suppose f(c) = 0. What is c?
-1, 3
Let y(r) be the first derivative of -4*r**3/3 - 6*r**2 + 72*r + 75. Factor y(a).
-4*(a - 3)*(a + 6)
Factor 45/2 + 1/4*b**2 - 91/4*b.
(b - 90)*(b - 1)/4
Factor -824 - 4*d**3 - 52*d**2 - 816*d + 6*d**3 - 153*d**2 + 0*d**3 + 7*d**2.
2*(d - 103)*(d + 2)**2
Suppose 0 = 4*c - 38 - 18. Suppose -3*x - c = 2*s + 2*x, -s - 2*x - 5 = 0. Let 2*w + 6*w**s - 9*w**2 + 0*w + w = 0. What is w?
0, 1/2, 1
Let s(k) = 3*k**4 - 35*k**3 - 48*k**2 + 251*k + 251. Let l(v) = 4*v**4 - 52*v**3 - 72*v**2 + 376*v + 376. Let p(n) = -5*l(n) + 8*s(n). Factor p(f).
4*(f - 4)**2*(f + 1)*(f + 2)
Let i(s) be the second derivative of -2*s**7/21 - 4*s**6/15 + 4*s**5 - 8*s**4 + 62*s. Factor i(g).
-4*g**2*(g - 2)**2*(g + 6)
Let f = 29 - 26. Factor 11*z - 3*z + 19*z**f - 10*z**2 - 17*z**3.
2*z*(z - 4)*(z - 1)
Let z(h) be the second derivative of -h**6/165 + 114*h**5/55 - 3249*h**4/11 + 246924*h**3/11 - 10556001*h**2/11 + h + 40. Factor z(i).
-2*(i - 57)**4/11
Let m = -390 + 1968/5. Let d(x) be the first derivative of -1 - 3*x**2 + m*x + 14/15*x**3 - 1/10*x**4. Factor d(k).
-2*(k - 3)**2*(k - 1)/5
Let x(s) be the first derivative of 0*s**4 + 0*s - 11 - 2/15*s**5 + 2/9*s**3 + 0*s**2. Factor x(g).
-2*g**2*(g - 1)*(g + 1)/3
Let s(w) be the second derivative of 0 - 5/2*w**2 + 1/20*w**5 - w**3 - 4*w + 1/8*w**4. Let j(x) be the first derivative of s(x). Solve j(v) = 0.
-2, 1
Find n such that 0 + 8/3*n - 4/9*n**2 = 0.
0, 6
Suppose 4*w - 5*g + 15 = 6*w, 23 = 4*w + 3*g. Suppose -3*c = 3*a + 3, -2*c + 2 = 2*c + 2*a. Suppose -4*n + 0*n**2 + 1 - n - w - n**c = 0. Calculate n.
-4, -1
Let p = -381 - -385. Let a(w) be the third derivative of -49/30*w**5 + 3*w**2 + 0 - 4/3*w**3 + 0*w - 7/3*w**p. Factor a(r).
-2*(7*r + 2)**2
Suppose 4*j = 2*w - 10, -6 = 3*j - 5*w + 4*w. Let y be j/(-3) - (1 + (-14)/12). Factor 2*n + y*n**3 - 2*n**2 + 0.
n*(n - 2)**2/2
Let q(g) be the second derivative of -7/80*g**5 - 1/120*g**6 + 0 - 13/24*g**3 + 13*g - 5/16*g**4 - 1/2*g**2. Suppose q(v) = 0. Calculate v.
-4, -1
Let f(i) be the first derivative of -i**8/840 - i**7/84 - 2*i**6/45 - i**5/15 - 6*i**3 + 26. Let a(m) be the third derivative of f(m). Factor a(s).
-2*s*(s + 1)*(s + 2)**2
Let y(v) be the first derivative of v**3/3 + 3*v**2 + 5*v + 26. Suppose y(z) = 0. What is z?
-5, -1
Suppose 2*d - 4 = 4*m - 0, -5*m - 5 = -4*d. Suppose 0 = -p - d*p. Determine r, given that r**2 + 2*r**2 + 2*r - 3 - 3*r**3 + p*r + r = 0.
-1, 1
Let c(m) = -4*m**2 - 1. Let f be c(1). Let s(q) = -10*q**2 - 18*q + 22. Let y(v) = 9*v**2 + 17*v - 21. Let t(u) = f*s(u) - 6*y(u). Factor t(d).
-4*(d - 1)*(d + 4)
Let g(l) = -l + 11. Let z be g(8). Suppose 5*y = -z*p + 11, -p + 0*y + 2*y = 0. Factor -6*v - 3*v**p + 8*v + v.
-3*v*(v - 1)
Let h(j) = -6*j**2 + 12*j - 15. Let s(q) = -q**2. Let w(b) = -h(b) + 9*s(b). What is l in w(l) = 0?
-5, 1
Let n = -20/7 + 846/301. Let d = n - -49/129. Factor 2/3*h**2 + 0*h**3 - d*h + 0 - 2/3*h**4 + 1/3*h**5.
h*(h - 1)**3*(h + 1)/3
Suppose -2*k - 7 = -h - 15, 5*h + 5*k = -85. Let m be 2 + h/6 + (-182)/(-294). Let m + 8/7*g**2 - 10/7*g = 0. Calculate g.
1/4, 1
Let s be (-20)/(-6)*18/30. Let o(x) be the second derivative of -9/4*x**4 + 0*x**s - 1/2*x**6 + 5*x + x**3 + 0 + 9/5*x**5. Solve o(l) = 0 for l.
0, 2/5, 1
Let t(y) be the first derivative of y**4/8 - 13*y**3/3 + 56*y**2 - 320*y - 75. Let t(c) = 0. Calculate c.
8, 10
Let i(y) be the second derivative of -y**7/63 - 11*y**6/45 - 23*y**5/30 + 11*y**4/18 + 8*y**3/3 + 139*y. Determine s so that i(s) = 0.
-8, -3, -1, 0, 1
Let o(i) be the third derivative of 25*i**9/756 - 3*i**8/28 + 4*i**7/35 - 2*i**6/45 + 7*i**3/6 - 19*i**2. Let w(p) be the first derivative of o(p). Factor w(b).
4*b**2*(b - 1)*(5*b - 2)**2
Let o(n) be the third derivative of 0 - 5/12*n**4 + 1/12*n**6 - 1/12*n**5 + 0*n + 0*n**3 + 41*n**2 + 1/42*n**7. Factor o(q).
5*q*(q - 1)*(q + 1)*(q + 2)
Solve 28/3 - 14/3*d**5 + 268/3*d**3 + 178/3*d + 352/3*d**2 + 52/3*d**4 = 0.
-1, -2/7, 7
Suppose -s = -5*s - 4. Let b be (-65)/(-75) + ((-6)/(-9))/s. Let 0 + 2/5*x - 3/5*x**4 - b*x**3 + 3/5*x**2 - 1/5*x**5 = 0. What is x?
-2, -1, 0, 1
Let v(q) be the second derivative of -q**6/6 + 13*q**5/4 - 95*q**4/4 + 475*q**3/6 - 125*q**2 - 4*q + 48. Solve v(p) = 0.
1, 2, 5
Let u(x) be the third derivative of -x**6/240 + x**5/60 + x**4/12 - 2*x**3/3 - 121*x**2. Find j such that u(j) = 0.
-2, 2
Let r = -254 + 268. Let q(j) be the second derivative of 1/4*j**4 - r*j + 2*j**3 + 9/2*j**2 + 0. Factor q(p).
3*(p + 1)*(p + 3)
Let v(d) = d**2 + 5*d - 6. Let s(o) = -5*o - o - 3 + 8*o + o**2. Let c(n) = -7*s(n) + 4*v(n). Suppose c(h) = 0. Calculate h.
1
Let v(n) = -450*n**3 - 235*n**2 + 413*n - 106. Let u(q) = -1125*q**3 - 588*q**2 + 1032*q - 264. Let a(k) = 5*u(k) - 12*v(k). Factor a(m).
-3*(3*m + 4)*(5*m - 2)**2
Let l be ((-2)/8)/((-8)/64). Find q such that -15*q**4 - 8*q - 15*q**4 + 8*q**3 + 10*q**4 + 20*q**l = 0.
-1, 0, 2/5, 1
Let m = -54 + 92. Let h be 6/(-40)*4 + m/30. Factor 0*p + 0 + 0*p**3 + h*p**2 - 2/3*p**4.
-2*p**2*(p - 1)*(p + 1)/3
Let a(n) = n**5 - n**4 - n**3 - n. Let k(l) be the second derivative of -l**7/14 + 3*l**5/10 + l**4/2 + l**3/2 + 6*l. Let d(y) = -6*a(y) - k(y). Factor d(g).
-3*g*(g - 1)**3*(g + 1)