2 + 0 + 0*u**3 - 1/9*u**5 + 0*u**4. Factor c(f).
-2*f**2*(f + 10)/3
Let s = 2716 - 2716. Let a(f) be the first derivative of -1/12*f**3 + s*f + 7 + 0*f**2. Factor a(d).
-d**2/4
Let v(k) be the first derivative of 5*k**3/36 - 67*k**2/12 - 9*k/4 - 464. Find n, given that v(n) = 0.
-1/5, 27
Let c(x) be the second derivative of -x**8/168 + 3*x**7/140 - x**6/40 + x**5/120 - 6*x**2 + 11*x. Let m(z) be the first derivative of c(z). Factor m(j).
-j**2*(j - 1)**2*(4*j - 1)/2
Let n(j) be the third derivative of 12*j**2 + 0*j + 0 - 1/9*j**3 + 1/180*j**5 + 1/72*j**4. Solve n(x) = 0.
-2, 1
Let a(w) be the first derivative of 5*w**3/3 - 65*w**2/2 - 150*w + 36. Suppose a(q) = 0. Calculate q.
-2, 15
Let b = 4 + 1. Suppose b*h - l = 9, 6*h + 3*l = h + 13. Determine u so that -2*u - 4*u + 12*u**2 - 14*u**h = 0.
-3, 0
Let f be 67 + (-5 + 2 - 0). Find r, given that r**4 + 3*r**4 - 60 + f - 8*r**2 = 0.
-1, 1
Let f(c) be the first derivative of -c**4/2 + 8*c**3 + c**2 - 24*c + 28. Determine v, given that f(v) = 0.
-1, 1, 12
Let b = 13 + -11. Factor 4*h**b + 14 - 22*h + 6*h + 2.
4*(h - 2)**2
Let f = 39606/19 + -2084. Factor 2/19*c**3 - 6/19*c**2 - f*c - 4/19 + 2/19*c**4.
2*(c - 2)*(c + 1)**3/19
Let h(m) be the third derivative of 10*m**2 + 0*m - 1/6*m**3 + 5/48*m**4 + 0 - 1/60*m**5. Find y, given that h(y) = 0.
1/2, 2
Determine x so that -1/9*x**2 + 14/9 + 13/9*x = 0.
-1, 14
Let u(c) be the third derivative of -3*c**6/40 - 19*c**5/60 - 11*c**4/24 - c**3/6 - 42*c**2 - 2*c. Factor u(s).
-(s + 1)**2*(9*s + 1)
Suppose -2*o - b = -16, -5*o + 2*o + 3*b + 33 = 0. Factor -12*x - o*x**3 - 6*x**4 + 266 + 3*x**5 - 266 + 24*x**2.
3*x*(x - 2)*(x - 1)**2*(x + 2)
Let k = -274 + 274. Let y(i) be the second derivative of 0*i**5 + k + 9*i - 1/9*i**4 + 0*i**2 + 1/30*i**6 + 1/126*i**7 + 0*i**3. Solve y(a) = 0.
-2, 0, 1
Let m(l) be the first derivative of -1/33*l**6 - 8/11*l + 41 - 2/55*l**5 + 5/22*l**4 - 4/11*l**2 + 10/33*l**3. Find y, given that m(y) = 0.
-2, -1, 1, 2
Let z = -175 - -177. Let t be 141/63 - z/(-6). Solve 8/7*p**2 + 4/7 + t*p = 0 for p.
-2, -1/4
Let q(w) be the first derivative of 0*w**2 + 12 + 1/3*w**4 - 2/5*w**5 + 0*w + 2/9*w**3. Let q(d) = 0. Calculate d.
-1/3, 0, 1
Let v(k) be the first derivative of -k**6/105 - 3*k**5/70 + k**4/42 + k**3/7 + 22*k - 32. Let y(t) be the first derivative of v(t). Let y(i) = 0. What is i?
-3, -1, 0, 1
Let w = 51/8 + -45/8. Factor 3*g**4 + 3/4*g**5 + 9/2*g**3 + 0 + w*g + 3*g**2.
3*g*(g + 1)**4/4
Let s(v) = -3*v**3 + 10*v**2 + 12*v. Let a(d) = -6*d**3 + 20*d**2 + 23*d. Let x = -152 - -148. Let j(u) = x*a(u) + 7*s(u). Factor j(n).
n*(n - 4)*(3*n + 2)
Let p(q) be the second derivative of 0 - 8*q + 1/60*q**6 + 0*q**2 + 1/30*q**5 + 0*q**3 + 0*q**4 - 1/252*q**7. Find t such that p(t) = 0.
-1, 0, 4
Let d(l) = -27*l - 2214. Let j be d(-82). Factor 2/15*m - 2/15*m**3 + j + 0*m**2.
-2*m*(m - 1)*(m + 1)/15
Factor -284*p**2 + 4*p + 564*p**2 - 2 - 282*p**2.
-2*(p - 1)**2
Suppose -40 = -4*x + 12. Factor 27*m + 45*m**5 + 35*m**4 + x*m + 100*m**2 + 90*m**3 - 40*m**5.
5*m*(m + 1)*(m + 2)**3
Let k(j) be the third derivative of j**6/480 + 307*j**5/240 + 1463*j**4/6 - 5929*j**3/6 - 7*j**2 + 25*j. Factor k(q).
(q - 1)*(q + 154)**2/4
Suppose 0 = w + 3*w - 12. Determine d so that -16*d**3 - 2*d**5 + 18*d + 0*d**5 - 12*d**2 + 0*d**w + 12*d**4 = 0.
-1, 0, 1, 3
Let d(h) be the first derivative of -h**3/33 - 15*h**2/22 + 16*h/11 - 582. Solve d(z) = 0.
-16, 1
Determine k so that 78*k**2 - 43*k + 54 - 3*k**3 - k**4 + 0*k**3 - 6*k**3 + 66 - 129*k = 0.
-15, 2
Let y(z) be the first derivative of -2*z**7/75 - 8*z**6/75 - 11*z**5/75 - z**4/15 + 11*z**2/2 + z - 15. Let f(a) be the second derivative of y(a). Factor f(m).
-4*m*(m + 1)**2*(7*m + 2)/5
Factor 34*l**3 - 35*l**3 + 5*l**3 + 384*l - 88*l**2 + 1152.
4*(l - 12)**2*(l + 2)
Let m(x) be the first derivative of x**6/6 + 3*x**5/5 + x**4/2 - 126. Factor m(l).
l**3*(l + 1)*(l + 2)
Solve 5/2*v**2 + 0*v - 5/4*v**4 + 5/4*v**3 + 0 = 0 for v.
-1, 0, 2
Suppose 5*h = -g + 10, -5*g - 2*h - 106 = -9*g. Suppose 5*y - g = -2*r - 2*r, 0 = -r. Solve -22/9*v**3 + 0 - 4/9*v**2 - 14/9*v**y + 0*v - 32/9*v**4 = 0 for v.
-1, -2/7, 0
Determine x, given that -55 + 54 - 167*x - 159 - 47*x**2 - 105*x**2 - 12*x**3 - 169*x = 0.
-10, -2, -2/3
Let d(o) = o**3 + 11*o**2 - 14*o - 18. Let i be d(-12). Let l(b) = -4*b**3 - b**2 - 5. Let r(g) = -5*g**3 - g**2 - 6. Let z(t) = i*l(t) - 5*r(t). Factor z(n).
n**2*(n - 1)
Let u(r) be the third derivative of r**5/105 + 19*r**4/84 - r**3 - 205*r**2. Factor u(m).
2*(m - 1)*(2*m + 21)/7
Let m(x) be the second derivative of 2/3*x**3 + 5*x**2 + 1/30*x**4 - 7*x + 0. Determine r, given that m(r) = 0.
-5
Let g = -50 + 36. Let h be (-3)/((-42)/5) + g/(-98). Factor 0 + h*k**5 - 1/2*k**4 + 0*k**2 + 0*k + 0*k**3.
k**4*(k - 1)/2
Let v = 3 + -19. Let f be 8/v*21/(-2). Factor -f*z**3 - 33/4*z + 12*z**2 + 3/2.
-3*(z - 1)**2*(7*z - 2)/4
Let q(b) = 10*b**2 + 4*b + 12. Let d(z) be the third derivative of -z**5/60 - z**3/6 - 23*z**2. Let x(i) = 18*d(i) + 2*q(i). What is o in x(o) = 0?
-3, -1
Let l = 139 - 207. Let x = -474/7 - l. Find w, given that -x*w**4 + 4/7*w**3 - 16/7*w + 6/7*w**2 + 8/7 = 0.
-2, 1, 2
Let j be (-356)/(-1335)*(24/(-9))/(-4)*9. Factor 8/5*n - 2/5*n**2 - j.
-2*(n - 2)**2/5
Let n(h) be the second derivative of h**7/42 - h**5/6 + 5*h**3/6 + 25*h**2/2 - 2*h. Let u(v) be the first derivative of n(v). Suppose u(x) = 0. Calculate x.
-1, 1
Suppose -2*w = 0, 4 = r - w - 4*w. Find a such that -3*a**5 - 31 + 31 + 8*a**5 + 5*a**r = 0.
-1, 0
Let t(w) be the third derivative of -1/21*w**5 - 1/84*w**4 + 0 - 4*w**2 + 0*w + 10/21*w**3 + 1/420*w**6. Factor t(f).
2*(f - 10)*(f - 1)*(f + 1)/7
Factor 0*r + 7/4*r**2 + 0 - 1/4*r**4 - 3/2*r**3.
-r**2*(r - 1)*(r + 7)/4
Let u(f) = 173*f + 867. Let j be u(-5). Factor 0 + 1/2*z**j - 1/4*z**3 - 1/4*z.
-z*(z - 1)**2/4
Find m such that -22*m**2 + 3484*m**3 + 3482*m**3 - 6968*m**3 = 0.
-11, 0
Suppose -11 = -2*o + 5*i, -4*i + 6*i = -o + 1. Let b(d) be the third derivative of 0 + 2*d**4 - 4*d**2 + 2*d**o + 7/20*d**5 + 0*d. Factor b(r).
3*(r + 2)*(7*r + 2)
Let h = 1957/2151 - 5/239. Suppose 0 - 16/9*r**2 - 2/9*r**3 - h*r + 2/3*r**4 = 0. What is r?
-1, -2/3, 0, 2
Find d such that 15 - 74/5*d - 1/5*d**2 = 0.
-75, 1
Let c(o) be the second derivative of -5*o**4/28 + 47*o**3/42 - 3*o**2/7 + 43*o - 1. Determine d, given that c(d) = 0.
2/15, 3
Let o(t) be the second derivative of 1/30*t**6 + 1/6*t**3 - 20*t + 0*t**2 - 1/12*t**4 - 1/20*t**5 + 0. Let o(l) = 0. Calculate l.
-1, 0, 1
Suppose 0 = 2*w - 6 - 2. Factor -10*d**2 - w*d - 298 + 298 - 4*d**2.
-2*d*(7*d + 2)
Factor -l**2 - 534 + 678*l - 772*l - 1675.
-(l + 47)**2
Let c(g) = -g**4 - 6*g**2 - 4*g + 3. Let z(a) = -17*a - 23 + 54*a**2 - 3 - a**4 + 53*a + 9*a**4. Let u(f) = 52*c(f) + 6*z(f). Factor u(q).
-4*q*(q - 2)*(q + 1)**2
Suppose 2*v - 32 + 22 = 0. Suppose -v*d - 5*f + 8*f + 9 = 0, -3*d - 2*f - 6 = 0. Factor -3/8*u + d + 3/8*u**3 - 3/8*u**4 + 3/8*u**2.
-3*u*(u - 1)**2*(u + 1)/8
Let k(s) = -7*s**3 - 20*s**2 + 14*s. Let t(d) = -16*d**3 - 40*d**2 + 27*d. Let o(n) = -13*k(n) + 6*t(n). Factor o(b).
-5*b*(b - 2)**2
Let b(t) = 3*t + 11. Let c be b(-3). Determine l so that -l - 3*l + 6 + 5*l - 3*l**c - 4*l = 0.
-2, 1
Let p = 32294417/856791 + 1/65907. Let 524/13*n**2 - p*n**5 + 152/13*n - 1062/13*n**3 - 48/13 - 1876/13*n**4 = 0. Calculate n.
-3, -1, -2/5, 2/7
Let g(k) be the third derivative of -k**6/180 - k**5/10 - k**4/2 - 115*k**2. Factor g(z).
-2*z*(z + 3)*(z + 6)/3
Let p(i) be the first derivative of 5*i**3/3 + 5*i**2/2 - 10*i - 58. Solve p(n) = 0 for n.
-2, 1
Let z(o) be the first derivative of 6/7*o**2 - 10 - 2/21*o**3 - 10/7*o. Factor z(a).
-2*(a - 5)*(a - 1)/7
Let f = 23 + -21. Let z be (1 + f/8)*56/20. Solve 3/2*k + 0 - z*k**2 + k**3 = 0 for k.
0, 1/2, 3
Let r(d) = d + 20. Let h be r(-4). What is v in -22 + 39 - 4*v**2 - 17 - h*v = 0?
-4, 0
Factor 22*u**2 - 12*u - 2*u**4 + 9*u**2 - 8*u**3 + 10*u**2 - 26*u**2 + 7*u**2.
-2*u*(u - 1)**2*(u + 6)
Let d(t) be the second derivative of t**4/3 + 4*t**3 + 18*t**2 + 5*t - 65. Determine k so that d(k) = 0.
-3
Suppose -4*w - 5*v = -2 - 21, w + 5*v = 17. Factor -m**4 + m**5 + 21*m**w - 37*m**2 - m**3 + 17*m**2.
m**2*(m - 1)**2*(m + 1)
Let y(c) = -4*c**4 + 4*c**3 + 31*c**2 + 32*c - 3. Let d(j) = j**4 - 