2/5*a**3 + g*a**5 - 4/5*a**4 + 0*a = 0.
0, 1
Let l(m) be the second derivative of -m**7/231 + m**6/33 - 3*m**5/55 - m - 3. Factor l(c).
-2*c**3*(c - 3)*(c - 2)/11
Let u(b) = -3*b**2 - 6*b + 16. Let d(t) be the first derivative of -t**3/3 - t**2 + 5*t + 8. Let z(v) = -8*d(v) + 3*u(v). Factor z(q).
-(q - 2)*(q + 4)
Let g(q) be the first derivative of -q**3/3 + 69*q**2 - 4761*q - 265. Factor g(j).
-(j - 69)**2
Determine y so that -y**3 - 10*y**2 - 20*y**2 - 23*y**2 + 22*y**2 = 0.
-31, 0
Let p be 720/50 + (-6)/(-10). Let v be (p/(-10))/(-3)*2. Let -3 - 5*r + v + 4 + 2*r**2 = 0. What is r?
1/2, 2
Let w(t) be the third derivative of -t**5/450 - 4*t**4/15 + 17*t**3/5 + 689*t**2. Determine d so that w(d) = 0.
-51, 3
Let t(v) be the first derivative of -v**4/20 + 2*v**3/15 + 93. Factor t(w).
-w**2*(w - 2)/5
Factor -132*b**2 - 198321 - 6*b**3 - 256*b + 198321 + 4*b**3.
-2*b*(b + 2)*(b + 64)
Let l = 21841 - 43675/2. Determine b, given that l*b + 1/2*b**2 + 5 = 0.
-5, -2
Let r(d) be the second derivative of -d**6/6 + 5*d**5/4 - 10*d**4/3 + 10*d**3/3 - 7*d + 1. Factor r(x).
-5*x*(x - 2)**2*(x - 1)
Factor -86/13*u**2 + 348/13*u - 16/13.
-2*(u - 4)*(43*u - 2)/13
Let b(i) = 3*i + 4*i**2 - 6 - 3*i**2 - 7*i**2 - i**3 + 2*i**2. Let t be b(-5). Suppose 2/3*m**t - 8/9*m**2 + 0*m + 0 - 8/9*m**3 = 0. What is m?
-2/3, 0, 2
Suppose 0 = -7*b - 70 + 84. Let j(w) be the third derivative of 1/60*w**5 + 1/24*w**4 + 0 + 0*w**3 + 0*w + 8*w**b. Let j(p) = 0. What is p?
-1, 0
Suppose 5 = -4*b + 37. Suppose b = 5*y + 3*x, 0*y - y - 16 = 5*x. Let -1/2*k + 0 + 1/2*k**3 + 1/4*k**y - 1/4*k**2 = 0. Calculate k.
-2, -1, 0, 1
Let t = -31 + 37. Let l(u) = 4*u**3 + 26*u**2 + 32*u + 16. Let d(o) = -12*o**3 - 77*o**2 - 96*o - 48. Let f(w) = t*d(w) + 17*l(w). Factor f(g).
-4*(g + 1)*(g + 2)**2
Let t(r) be the second derivative of r**7/6 - 22*r**6/15 - 39*r**5/5 - 67*r**4/6 - 11*r**3/6 + 9*r**2 - 236*r. Let t(f) = 0. Calculate f.
-1, 2/7, 9
Let o be ((-1)/(-4))/((-1)/(-2)). Suppose 12 - 96 = -21*b. Factor -3/2*s + 3/2*s**3 + o*s**b + 1/2*s**2 - 1.
(s - 1)*(s + 1)**2*(s + 2)/2
Let l be (625/(-20))/((-9)/(-12)). Let h = 42 + l. Factor 1/6 + h*f + 1/6*f**2.
(f + 1)**2/6
Let o(h) be the first derivative of 0*h + 1/360*h**6 + 1/24*h**4 + 0*h**2 + 2/3*h**3 + 1/60*h**5 + 3. Let z(j) be the third derivative of o(j). Factor z(a).
(a + 1)**2
Let 200/13*q**3 + 1204*q + 3698/13 + 3490/13*q**2 = 0. Calculate q.
-43/5, -1/4
Let b(v) be the first derivative of -v**5/120 + v**4/48 + v**3/6 - 2*v**2 + 8. Let z(t) be the second derivative of b(t). Factor z(x).
-(x - 2)*(x + 1)/2
Let d(t) be the second derivative of 14*t + 1/3*t**4 + 0 + 0*t**2 - 1/10*t**5 - 1/3*t**3 + 1/90*t**6. Let z(w) be the second derivative of d(w). Factor z(h).
4*(h - 2)*(h - 1)
Let j = 33 + -31. Let h(g) be the first derivative of -6/7*g - 8/7*g**3 + 3/7*g**4 - 2 + 10/7*g**j - 2/35*g**5. Solve h(y) = 0 for y.
1, 3
Let d(q) be the second derivative of -q**9/3780 + q**8/1680 + q**7/315 + 3*q**4/2 + 9*q. Let x(s) be the third derivative of d(s). What is w in x(w) = 0?
-1, 0, 2
Let y = -5649 - -5661. Factor -18 + 2/3*x**4 + y*x**2 + 0*x - 16/3*x**3.
2*(x - 3)**3*(x + 1)/3
Let q(x) be the second derivative of -x**7/56 - x**6/40 + 3*x**5/80 + x**4/16 + 5*x + 59. Factor q(l).
-3*l**2*(l - 1)*(l + 1)**2/4
Let j(m) be the second derivative of m**7/840 + m**6/72 + 7*m**3/2 + 16*m. Let b(i) be the second derivative of j(i). Factor b(v).
v**2*(v + 5)
Let n(p) be the second derivative of 2*p**7/21 + 152*p**6/15 + 1444*p**5/5 - 56*p + 3. Determine m so that n(m) = 0.
-38, 0
Determine c so that 51/2*c**3 - 375 + 825/2*c - 315/2*c**2 - 3/2*c**4 = 0.
2, 5
Let q = -23 + 32. What is w in q*w**3 + 118*w**2 + 38*w**3 + 7*w**3 - 56*w**4 - 8 = 0?
-1, -2/7, 1/4, 2
Let k = 7/19 + 136/95. Suppose -k*u**3 + 9/5*u - 3/5*u**2 + 3/5 = 0. Calculate u.
-1, -1/3, 1
Let u(g) = -g**2 - 12*g + 3. Let k be u(-12). Suppose 5*h + 8 = 2*i - 3, i = -k*h. Factor 0*y**3 - i*y**3 + 0*y**4 - 4*y**4 + 7*y**3 + 8*y**2.
-4*y**2*(y - 2)*(y + 1)
Let a(r) be the first derivative of r**6/80 - 3*r**5/160 - r**4/32 + r**3/16 + 8*r - 22. Let h(c) be the first derivative of a(c). Let h(b) = 0. Calculate b.
-1, 0, 1
Suppose 4*d - 6 = 2. Let x = 6 - 10/3. Factor -2*i**d + 0*i + x - 2/3*i**3.
-2*(i - 1)*(i + 2)**2/3
Suppose 21*v - 12 = 18*v. Let g(s) be the second derivative of 0*s**5 + s + 0*s**2 + 1/2*s**v - 1/2*s**3 - 1/5*s**6 + 1/14*s**7 + 0. Find j such that g(j) = 0.
-1, 0, 1
Suppose 0 = -18*m + 21*m + 42. Let y be (-4)/m + (-99)/(-21) + -5. Determine w so that -2/3 + y*w + 2/3*w**2 = 0.
-1, 1
Let y(f) be the first derivative of -3 - 2/27*f**3 + 0*f + 0*f**2. Find i such that y(i) = 0.
0
Let t(s) be the first derivative of -s**4/38 + 20*s**3/57 - 27*s**2/19 + 36*s/19 + 145. Suppose t(l) = 0. Calculate l.
1, 3, 6
Let w be 4 - (0 + (-910)/(-231)). Let i(r) be the second derivative of 6*r + 1/110*r**5 - 1/22*r**4 + w*r**3 + 0 + 0*r**2. Factor i(n).
2*n*(n - 2)*(n - 1)/11
Let m be ((-6)/7)/3 - (-2727)/63. Let s = 40 - 28. Find j, given that -24*j**2 + m*j**3 - 47*j**3 - 21*j - 3*j - s*j = 0.
-3, 0
Determine n so that -4*n - 5 - n**2 + 5 - 4 = 0.
-2
Suppose -g = -4*w - 21 + 37, 12 = -3*g. Let r be ((-12)/(-18))/(8/6). Solve 0*u**2 + 0*u + 0 - r*u**w = 0.
0
Factor 7*s**4 - 2642*s**3 + 13*s**2 + s**5 + 5308*s**3 + 4*s - 2651*s**3.
s*(s + 1)**3*(s + 4)
Let m(q) be the first derivative of -q**8/336 - q**7/60 - 7*q**6/240 - q**5/60 - 6*q**2 - 5. Let c(v) be the second derivative of m(v). Let c(w) = 0. What is w?
-2, -1, -1/2, 0
Let d(y) be the first derivative of -y**6/14 - 9*y**5/35 + 3*y**4/28 + 3*y**3/7 + 2. Find a, given that d(a) = 0.
-3, -1, 0, 1
Let q(g) be the second derivative of g**5/120 - 11*g**4/36 - 47*g**3/36 - 2*g**2 + 9*g. Suppose q(y) = 0. What is y?
-1, 24
Let f(w) = -w**3 - 9*w**2 - 10*w - 13. Suppose 0 = -3*i + 12*i + 72. Let k be f(i). Factor 3/5*p**2 + 7/5*p**4 - 2/5*p + 12/5*p**k + 0.
p*(p + 1)**2*(7*p - 2)/5
Let 272*i + 0*i**3 + 40 + 17*i**2 + 15*i**2 + 52*i**3 - 396*i = 0. Calculate i.
-2, 5/13, 1
Let r be 12/40*1/12. Let x(b) be the third derivative of -1/6*b**4 - 4*b**2 + 0*b**5 + 0 + 0*b + 0*b**3 - 1/210*b**7 + r*b**6. Let x(o) = 0. What is o?
-1, 0, 2
Let b(o) be the third derivative of 0*o - 1/6*o**4 + 0 + 1/9*o**3 - 23*o**2 + 1/18*o**5. Find m such that b(m) = 0.
1/5, 1
Let d(k) be the third derivative of k**5/4 - 35*k**4/6 + 5*k**3/2 + 6*k**2. Let b(t) = -t**2 + 10*t - 1. Let w(y) = 55*b(y) + 4*d(y). Factor w(o).
5*(o - 1)**2
Let o(y) be the second derivative of 1/2*y**3 - 6*y + y**4 + 1/14*y**7 + 0 + 0*y**2 + 2/5*y**6 + 9/10*y**5. Factor o(n).
3*n*(n + 1)**4
Let l(t) = -8*t**3 - 161*t**2 - 3*t + 3. Let v(r) = -9*r**3 - 163*r**2 - 4*r + 4. Let u(d) = -4*l(d) + 3*v(d). Determine k so that u(k) = 0.
-31, 0
Suppose -3*h = 15, 3*v + v = -2*h - 6. Let q be (-45)/(-10) + v/(-2). Suppose -2*f - 5*f**3 + q*f**3 + 0*f - 4*f**2 - f**3 = 0. What is f?
-1, 0
Let w(p) be the third derivative of -11*p**5/120 + 13*p**4/48 - p**3/6 + 20*p**2. Factor w(d).
-(d - 1)*(11*d - 2)/2
Suppose 11/2*j**4 - j + 6*j**3 + 0 - 21/2*j**2 = 0. What is j?
-2, -1/11, 0, 1
Let l(f) be the second derivative of -f**4 + 5*f + 0 + 4/3*f**3 + 0*f**2. Solve l(u) = 0.
0, 2/3
Suppose 0 = -2*c + 2*f - 60, -4*c = 2*f - 5*f + 122. Let r = -158/5 - c. Factor -r*g - 1/5*g**2 - 1/5.
-(g + 1)**2/5
Factor 279841/2 + 1587*y**2 + 24334*y + 46*y**3 + 1/2*y**4.
(y + 23)**4/2
Factor 2604*h**2 - 2603*h**2 + h + h.
h*(h + 2)
Suppose 7 = 4*a - 3*u, 8*a - 3*a + u - 23 = 0. Suppose -a*q + 24 = -5*m, -9*m - 18 = -3*q - 5*m. Solve 4/3 + 6*w + 4/3*w**4 + 28/3*w**2 + q*w**3 = 0 for w.
-2, -1, -1/2
What is h in -39/7*h**2 + 156/7*h - 12 - 9/7*h**3 = 0?
-7, 2/3, 2
Let g(a) = a + 8. Let x be g(4). Let b be 13/x + -1 - 7/(-28). Factor -b - n + 1/3*n**2 + n**3.
(n - 1)*(n + 1)*(3*n + 1)/3
Let p(x) = -x**2 + 14*x - 25. Let j be p(11). Let y be (j - 5)*-2*(-2)/18. Suppose -2/3*u + y*u**3 - 2/3*u**4 + 0 + 2/3*u**2 = 0. What is u?
-1, 0, 1
Suppose 191*a - 1780 = -367*a + 113*a. Factor -2*m**2 - 1/4*m**4 + 0 + 7/4*m**3 - a*m.
-m*(m - 4)**2*(m + 1)/4
Let r(x) be the first derivative of -x**3 + 1/30*x**5 + 2 + 0*x - 2*x**2 - 1/6*x**4. Let i(m) be the second derivative of r(m). Factor i(s).
2*(s - 3)*(s + 1)
Let s(r) be the second deriv