+ w - 3/4*f**4 + 3/4*f**5 + 0*f = 0.
0, 1
Let l = -82 + 84. Factor 57*k + 12 - 40*k**3 + 80*k**l - 117*k + 4 + 4*k**5.
4*(k - 1)**4*(k + 4)
Let l be (-14)/217 + (-984)/(-9486). Let i(w) be the first derivative of -l*w**3 + 6 + 0*w - 2/17*w**2. Factor i(c).
-2*c*(c + 2)/17
Let y(h) be the first derivative of h**6/24 - 3*h**5/20 - h**4/16 + h**3/4 - 636. Factor y(m).
m**2*(m - 3)*(m - 1)*(m + 1)/4
Let x be 2/5*(-2 + 97). Determine t so that 38 - x - t**3 = 0.
0
Suppose 2*x - 12 = -f + 3*f, 0 = 4*x - 3*f - 22. Factor 16/7*u**x + 0*u + 0 - 4/7*u**5 + 8/7*u**2 - 20/7*u**3.
-4*u**2*(u - 2)*(u - 1)**2/7
Let c(i) = 21*i - 1216. Let g be c(58). Factor -1/3*z + 0 - 1/6*z**g.
-z*(z + 2)/6
Let f(s) be the second derivative of -3*s**4/16 - 29*s**3/24 - 3*s**2/4 + 377*s. Determine x so that f(x) = 0.
-3, -2/9
Suppose 56*b - 37*b = -22*b - 50*b. Let 2/9*w**3 - 2/9*w**4 + 4/9*w**2 + 0 + b*w = 0. What is w?
-1, 0, 2
Let n(x) be the first derivative of -1/15*x**5 - 6 + 0*x + 1/60*x**6 + 0*x**3 + 5*x**2 + 1/12*x**4. Let z(g) be the second derivative of n(g). Factor z(i).
2*i*(i - 1)**2
Solve 5*o**3 - 2*o**4 - 2*o**4 + o**2 + 7*o**3 + 4*o - 11*o**2 - 2*o**2 = 0 for o.
0, 1
Let t(q) be the third derivative of -q**5/270 + 11*q**4/36 + 204*q**2. Factor t(i).
-2*i*(i - 33)/9
Suppose 0*d - 17 = d. Let w = 19 + d. Factor -8*i + w*i**2 - 6*i**2 + 8*i**2.
4*i*(i - 2)
Let b = -2558 - -2561. Let w(t) be the first derivative of 2/55*t**5 + 1/33*t**6 - 8 + 0*t**b + 0*t**2 - 1/11*t**4 + 0*t. Suppose w(h) = 0. What is h?
-2, 0, 1
Let x(c) be the third derivative of 0*c - 2/15*c**5 + 0*c**3 + 0 - 1/60*c**6 - 1/3*c**4 - 6*c**2. Factor x(l).
-2*l*(l + 2)**2
Let a(g) be the first derivative of g**6/18 + 2*g**5/15 - 3*g**4/2 + 32*g**3/9 - 23*g**2/6 + 2*g - 26. Find j such that a(j) = 0.
-6, 1
Let j(f) be the second derivative of 27/2*f**2 - 5/4*f**4 + 3/2*f**3 + 8*f + 0 + 3/20*f**5. Factor j(i).
3*(i - 3)**2*(i + 1)
Suppose 0 + 9/2*d**2 + 1/4*d**5 + 0*d - 1/4*d**3 - 9/2*d**4 = 0. What is d?
-1, 0, 1, 18
Let g(o) be the third derivative of -o**5/75 + 8*o**4/5 - 384*o**3/5 - 27*o**2. Factor g(j).
-4*(j - 24)**2/5
Let a = -17 - -18. Let g(t) = -3*t - 4. Let l(s) = -s**2 + s + 1. Let u(n) = a*g(n) - l(n). What is k in u(k) = 0?
-1, 5
Suppose m + 12 = 15. Find j, given that 17*j**3 - 36*j**m + 18*j**3 = 0.
0
Let r(u) be the third derivative of u**7/3780 + u**6/216 - u**5/30 + 35*u**4/24 + 26*u**2. Let j(b) be the second derivative of r(b). Factor j(k).
2*(k - 1)*(k + 6)/3
Let -17 - 9*x - 16*x**2 - 16*x**2 - 13 + 35*x**2 = 0. What is x?
-2, 5
Suppose 9*j = 164 + 16. Let q be (-2)/(j*3/(-6)). Solve 0*w - q*w**3 - 3/5*w**5 + 1/5*w**2 - w**4 + 0 = 0.
-1, 0, 1/3
Let b be (2/(-3))/((-6)/(-171)). Let c = b - -22. Factor -13*q**3 - 4*q**2 + 4*q**4 + 13*q**c.
4*q**2*(q - 1)*(q + 1)
Let x(g) be the first derivative of 0*g + 3*g**2 - 1/32*g**4 + 0*g**5 - 1/24*g**3 - 3 + 1/120*g**6. Let j(z) be the second derivative of x(z). Factor j(y).
(y - 1)*(2*y + 1)**2/4
Let f(u) = u**2 - 28*u - 36. Let x be f(30). Suppose x = 4*l + 4*l. Factor 1/4*j**l + 0 - 1/4*j**2 + 0*j.
j**2*(j - 1)/4
Suppose -2*r - 85 = -7*r. Find d such that r*d + 4*d + 24 - 15*d**2 + 47*d - 14*d = 0.
-2/5, 4
Let y = -279 + 283. Let m(j) be the second derivative of 8*j + 0 + 1/60*j**5 + 0*j**3 + 0*j**2 - 1/36*j**y. Factor m(i).
i**2*(i - 1)/3
Suppose 5 = -5*q, -4*z - 105*q = -103*q + 2. Solve -1/8*o**3 + z - 1/4*o**2 + 0*o = 0 for o.
-2, 0
Factor 51/4*l + 0 + 3/4*l**2.
3*l*(l + 17)/4
Let h(r) = -5*r**4 - 87*r**3 - 311*r**2 - 321*r - 108. Let s(p) = 2*p**4 - 3*p**3 - p**2. Let x(g) = -h(g) - 4*s(g). Let x(w) = 0. What is w?
-1, 36
Let z = -214 + 216. Suppose -5*l - z = -12. Let 45/2*i**l + 25/2*i**3 - 5 - 35/2*i**4 - 25/2*i = 0. Calculate i.
-1, -2/7, 1
Let v(g) be the third derivative of g**7/420 - g**6/90 - g**5/60 + g**4/6 + g**3 + 11*g**2. Let h(n) be the first derivative of v(n). Factor h(r).
2*(r - 2)*(r - 1)*(r + 1)
Let i(l) = -l**3 + 2*l**2 + 10*l - 5. Let x be i(4). Factor 19*v**5 - 5*v + 15*v**2 - 14*v**5 - 15*v**4 + 5*v**x - 5*v.
5*v*(v - 2)*(v - 1)**2*(v + 1)
Let j = 437/2 - 217. Suppose 3*l + 5*a = -14 - 2, 3*a + 27 = 4*l. Factor -9/2*z + j*z**2 + 3/2*z**4 + 9/2*z**l - 3.
3*(z - 1)*(z + 1)**2*(z + 2)/2
Let d(a) be the third derivative of -a**6/80 + a**5/20 - a**4/16 - 2*a**2 - 3. Factor d(z).
-3*z*(z - 1)**2/2
Determine h, given that -18/7*h**4 - 122/7*h**3 + 36/7 - 242/7*h**2 - 102/7*h = 0.
-3, -1, 2/9
Let v = -9488 - -9509. Factor 108/7*h - 12/7 - v*h**4 - 327/7*h**2 + 54*h**3.
-3*(h - 1)**2*(7*h - 2)**2/7
Let t(v) be the second derivative of 0 + 22*v + 2/21*v**3 - 12/7*v**2 + 1/21*v**4. Determine f, given that t(f) = 0.
-3, 2
Let s = -1270 - -12709/10. Let z(h) be the second derivative of 1/2*h**3 + 1/14*h**7 + 0*h**2 + 0 + h**4 + s*h**5 + 2/5*h**6 - 3*h. Factor z(x).
3*x*(x + 1)**4
Let u = -3881/330 - 4/55. Let a = u - -12. What is w in a*w + 0*w**2 + 0*w**4 + 1/6*w**5 - 1/3*w**3 + 0 = 0?
-1, 0, 1
Suppose y - 3*y - 8 = 0. Let j = y + 6. Factor -1/3*g**j + 1/3 + 0*g.
-(g - 1)*(g + 1)/3
Factor 8 - 74/11*w + 2/11*w**3 - 16/11*w**2.
2*(w - 11)*(w - 1)*(w + 4)/11
Suppose 4*a + 5*j - 8 = 0, 4*j + 10 = 5*a + 3*j. Let 8/7*h - 16/7 - 1/7*h**a = 0. What is h?
4
Let v(y) be the second derivative of y**7/4620 + y**6/165 + 3*y**5/55 + 5*y**3/3 - 29*y. Let a(p) be the second derivative of v(p). Factor a(c).
2*c*(c + 6)**2/11
Suppose -7*m = -12*m + 20. Suppose -v = -m + 1. Factor -1 - 3*r + r + 4*r + v*r**2 - 4*r**2.
-(r - 1)**2
Let u(b) be the third derivative of -b**8/336 + b**7/84 - b**5/12 + 5*b**4/24 + 16*b**3/3 + 36*b**2. Let j(z) be the first derivative of u(z). Factor j(r).
-5*(r - 1)**3*(r + 1)
Let n be (-1)/22*-18*(-40)/(-60). Factor 0*b + 4/11*b**3 + n*b**4 + 0*b**2 + 0.
2*b**3*(3*b + 2)/11
Let f(l) be the second derivative of 2*l + 0*l**3 - 1/80*l**5 - 1/48*l**4 + 0 - l**2. Let o(v) be the first derivative of f(v). Factor o(q).
-q*(3*q + 2)/4
Let s(o) = o**2 - 96*o - 1919. Let c be s(113). Factor 14/11*f + 12/11 + 2/11*f**c.
2*(f + 1)*(f + 6)/11
Let s = 463 + -463. Let k(a) be the second derivative of 0*a**3 + 0 + 0*a**2 + s*a**5 + 1/15*a**6 - 1/6*a**4 - 7*a. Factor k(c).
2*c**2*(c - 1)*(c + 1)
Factor -9*g**3 + 50*g**2 - 30*g**4 + 33*g**4 - 50*g**2.
3*g**3*(g - 3)
Let k(f) be the first derivative of -9 - 2/11*f**3 - 16/11*f + 14/11*f**2. Factor k(n).
-2*(n - 4)*(3*n - 2)/11
Let w(g) = -368*g**3 - 464*g**2 - 180*g - 24. Let q(k) = -123*k**3 - 154*k**2 - 60*k - 8. Let h(y) = -21*q(y) + 6*w(y). Factor h(p).
3*(5*p + 2)**3
Let q(g) be the second derivative of -g**7/630 - g**6/9 - 10*g**5/3 + 15*g**4/4 - 12*g. Let k(y) be the third derivative of q(y). Suppose k(n) = 0. What is n?
-10
Suppose 2*b + 2*b = 0. Factor 4*j**2 - 8 + 4*j + b*j + 2*j - 2*j.
4*(j - 1)*(j + 2)
Let c(i) be the second derivative of i**7/490 + i**6/280 - i**5/70 - 7*i**2/2 + 12*i. Let t(b) be the first derivative of c(b). What is g in t(g) = 0?
-2, 0, 1
What is k in -12 + 2876*k - 10*k**3 + 14*k**2 - 2866*k + 2*k**4 - 4*k**2 = 0?
-1, 1, 2, 3
Let i(r) = -3*r**2 - 12*r + 11. Let s(c) = c**2 + 1. Let v(u) = i(u) + 2*s(u). Factor v(d).
-(d - 1)*(d + 13)
Let h(o) be the third derivative of -o**5/60 + 5*o**4/24 + 4*o**3 + 96*o**2. Factor h(d).
-(d - 8)*(d + 3)
Let c(g) be the second derivative of -g**6/540 + g**5/60 - g**4/18 - 8*g**3/3 + 6*g. Let j(f) be the second derivative of c(f). Find a, given that j(a) = 0.
1, 2
Let t be (-3 + (-39)/(-12))*65/741. Let a(k) be the third derivative of 0 + 9*k**2 - 7/570*k**5 + 2/57*k**3 - t*k**4 + 0*k. Factor a(i).
-2*(i + 1)*(7*i - 2)/19
Suppose -376/7*a**2 - 150*a**4 + 0 + 250/7*a**5 + 1020/7*a**3 + 48/7*a = 0. What is a?
0, 2/5, 3
Let w be (6/5)/((-3)/(-10)). Let n = -521 - -523. Factor w*q**n + q + 4 + 0*q - q - 8*q.
4*(q - 1)**2
Let p(c) be the first derivative of -c**6/540 + c**5/270 + c**4/108 - c**3/27 + 15*c**2/2 - 8. Let m(x) be the second derivative of p(x). Factor m(s).
-2*(s - 1)**2*(s + 1)/9
Let m(g) be the first derivative of -16 - 3/8*g**4 + 4/3*g**3 + 0*g - g**2. Factor m(n).
-n*(n - 2)*(3*n - 2)/2
Let c be (-2)/(-3)*54/12. Factor -t - 12*t**c + 4*t + 3*t + 10*t**2 - 4.
-2*(t - 1)*(2*t - 1)*(3*t + 2)
Let h(o) be the second derivative of -1/20*o**4 + 0 - 1/10*o**2 + 1/100*o**5 - 7*o + 1/10*o**3. Suppose h