
Let l(n) be the first derivative of -n**6/150 + 3*n**5/100 - n**4/20 + n**3/30 - 3*n + 2. Let j(z) be the first derivative of l(z). What is g in j(g) = 0?
0, 1
Suppose -s - 4*x = -2*s - 5, -s - 4*x + 11 = 0. Factor 2*i**3 + 2*i + i - 5*i**s.
-3*i*(i - 1)*(i + 1)
Let j = 2362/9 - 262. Let j*q**3 - 4/9*q - 2/9*q**2 + 2/9 = 0. What is q?
-1, 1/2, 1
Factor -4 + 19*x**3 - 30*x**2 - 77*x**3 - 36*x**2 + 34*x**4 - 30*x - 52*x**4.
-2*(x + 1)**3*(9*x + 2)
Let b = -11 - -14. Suppose 4*o - 2*o = 0. Factor -d**3 - 1 - 1 + o*d**3 + 0*d**3 + b*d.
-(d - 1)**2*(d + 2)
Let y = 3 - -1. Determine r, given that 2*r**5 + 2*r**2 + r**2 - y*r**4 - 3*r**2 = 0.
0, 2
Let g(i) = -i**2 - i - 1. Let m(f) = -6*f**2 - 11*f - 3. Let z(y) = 14*g(y) - 2*m(y). Find w such that z(w) = 0.
2
Factor 0 - 4/9*y - 2/9*y**2.
-2*y*(y + 2)/9
Let c(m) be the second derivative of -m**5/60 + m**4/18 - m**3/18 + 2*m + 12. Factor c(o).
-o*(o - 1)**2/3
Let s(c) be the third derivative of c**7/5040 - c**6/1440 + c**4/24 + 2*c**2. Let y(j) be the second derivative of s(j). Factor y(i).
i*(i - 1)/2
Let c(k) be the first derivative of k**7/168 - k**6/40 + 3*k**5/80 - k**4/48 + k - 5. Let w(t) be the first derivative of c(t). Let w(y) = 0. Calculate y.
0, 1
Let d(v) = -18*v**2 + 9*v. Let g(w) = 19*w**2 - 10*w. Let z(t) = -4*d(t) - 3*g(t). Factor z(p).
3*p*(5*p - 2)
Let h be 4 + -3 - (3 - 1). Let g(c) = -4*c**3 - 6*c**2 - 8*c + 6. Let i(f) = f**3 + f. Let w(q) = h*g(q) - 6*i(q). Determine a so that w(a) = 0.
-1, 1, 3
Factor -3/2*q**3 - 9/2*q + 3/2 + 9/2*q**2.
-3*(q - 1)**3/2
Let h = 0 - 0. Let s = 44 - 41. Factor 0*i - 2/7*i**5 + 2/7*i**4 + 0 + h*i**s + 0*i**2.
-2*i**4*(i - 1)/7
Let u(t) be the second derivative of t**4/48 + 11*t**3/24 + 5*t**2/4 - 71*t. Find d, given that u(d) = 0.
-10, -1
Let y(z) be the second derivative of 1/2*z**3 + z + 0 - 3/20*z**5 - 3/4*z**4 + 0*z**2 + 3/10*z**6. Factor y(a).
3*a*(a - 1)*(a + 1)*(3*a - 1)
Let x(j) be the second derivative of -j**7/3780 + j**6/1620 - 3*j**3/2 - 6*j. Let i(w) be the second derivative of x(w). Factor i(m).
-2*m**2*(m - 1)/9
Let i(h) be the second derivative of h**4/6 + h**3/3 - 6*h**2 + 13*h. Factor i(b).
2*(b - 2)*(b + 3)
Let d = 157 - 157. Solve d - 1/3*j - 1/3*j**3 + 2/3*j**2 = 0 for j.
0, 1
Let b(z) be the first derivative of -2*z**5/15 - z**4/2 + 2*z**3/3 + 7*z**2/3 - 4*z + 2. Let b(x) = 0. Calculate x.
-3, -2, 1
Let f(b) = -b**2 + 4*b + 7. Let n be f(5). Suppose 3*d**2 - 4*d**3 + 2*d**4 - 3*d**2 + 2*d**n + 0*d**4 = 0. What is d?
0, 1
Let l(w) be the third derivative of w**11/285120 - w**10/181440 - w**9/181440 + 7*w**5/60 - 4*w**2. Let v(y) be the third derivative of l(y). Factor v(s).
s**3*(s - 1)*(7*s + 2)/6
Let y be (-1 - 2)*2/(-3). Suppose q + u = 0, y = -u - 1. Find w such that -w**q + 1/2*w**5 - 2*w**2 + w**4 + 1 + 1/2*w = 0.
-2, -1, 1
Let b(l) = l + 21. Let q be b(-18). Factor -7*w**2 - 28*w**3 + 20*w**3 + q*w**2.
-4*w**2*(2*w + 1)
Let c(u) be the second derivative of 1/6*u**4 + 0*u**3 + 1/30*u**6 + 0*u**2 - 5*u + 0 - 3/20*u**5. Factor c(v).
v**2*(v - 2)*(v - 1)
Let w be 1 - 3/(9/(-6)). Let a be 1 - (-2 + w)*-1. Determine p, given that -p**5 - p**2 + a*p**4 - p - p**2 + 2*p**5 = 0.
-1, 0, 1
Let x be (1 - 0)*(-6)/(-3). Factor -4*u + 4*u**2 + 4 - 2 - 2*u**x.
2*(u - 1)**2
Suppose -5*b + x + 15 = 0, 0*x = -3*b + 3*x + 21. Let g(d) be the first derivative of d + 20/3*d**3 - 9/2*d**b - 2. Factor g(y).
(4*y - 1)*(5*y - 1)
Factor 40*v - 30*v + 5*v**4 - 3*v**2 - 5 - 10*v**3 + 3*v**2.
5*(v - 1)**3*(v + 1)
Let q(p) = -p**2 + 3*p + 3. Let i(w) = w**2 - 4*w - 4. Let c be -3*(2 + (-14)/3). Let y be (-1 + 3)*12/c. Let t(h) = y*i(h) + 4*q(h). Solve t(x) = 0 for x.
0
Factor -128/15*i - 8/15 - 30*i**3 - 38*i**2.
-2*(i + 1)*(15*i + 2)**2/15
Suppose 0*s + 5*s + 3*n + 26 = 0, 12 = -s - 4*n. Let p be 21/12 + 3 + s. What is i in 1/2*i + p*i**2 + 0 + 7/4*i**4 - 3*i**3 = 0?
-2/7, 0, 1
Let q = 2932/5 - 586. Find d, given that 0 + q*d**2 + 0*d = 0.
0
Let w = -85 + 85. What is l in -2/7*l**2 + w + 4/7*l = 0?
0, 2
Let l(f) be the third derivative of -f**9/30240 - f**8/13440 + f**7/2520 - f**4/6 - 3*f**2. Let x(b) be the second derivative of l(b). Factor x(d).
-d**2*(d - 1)*(d + 2)/2
Let m be (-1 - -2)/((-4)/(-8)). Let c(o) be the second derivative of -1/12*o**4 + 0 - 1/6*o**3 + 0*o**2 + m*o. Factor c(u).
-u*(u + 1)
Factor 8 - 5 + 9 - 3*r**2.
-3*(r - 2)*(r + 2)
What is j in -1/7*j + 2/7 - 2/7*j**2 + 1/7*j**3 = 0?
-1, 1, 2
Suppose -305 + 296 = -3*g. Factor 0 + 1/2*t**g + t - 3/2*t**2.
t*(t - 2)*(t - 1)/2
Let g(d) = 27*d**3 - 30*d**2 + 3*d + 6. Let b(o) = -1. Let u(i) = 6*b(i) + g(i). Solve u(h) = 0.
0, 1/9, 1
Suppose -2 + 26 = 3*o. Factor 72*k**3 - 20*k**3 + 8 - 17*k - 36*k**4 - 20*k**2 + 5*k + o*k**5.
4*(k - 2)*(k - 1)**3*(2*k + 1)
Let x be 3/3 + 12/12. Suppose 0*a - 2/5*a**x + 2/5 = 0. What is a?
-1, 1
Let y = 10 + -5. Factor j**3 - 3*j**2 + 3*j**5 + 3*j**4 + 3*j**3 - 2*j**3 - y*j**3.
3*j**2*(j - 1)*(j + 1)**2
What is h in -22/5*h**3 + 8/5*h + 8/5*h**2 - 12/5*h**4 + 0 + 18/5*h**5 = 0?
-2/3, 0, 1
Let q(p) = p**3 - 8*p**2 + 5*p - 2. Let s be q(7). Let w be s/(-20) + 1/5. Factor 1/4*o**2 + w - o.
(o - 2)**2/4
Let z(m) be the first derivative of -m**7/2520 - m**6/1080 + m**3 - 1. Let i(j) be the third derivative of z(j). Factor i(g).
-g**2*(g + 1)/3
Let v(b) be the third derivative of -b**3 - 1/20*b**5 + 0 + 0*b - 3/8*b**4 - 2*b**2. Suppose v(u) = 0. Calculate u.
-2, -1
Let s(b) = -b**4 + b**3 + b**2 - b. Let g(q) = -q**3 + q**2 + q - 1. Let c(u) = -3*g(u) - 3*s(u). What is n in c(n) = 0?
-1, 1
Let h be ((-2)/6)/((-4)/6). Suppose -3*s - 2*s - 5*p = -15, s = -3*p + 5. Factor h*u**s + 0 + u.
u*(u + 2)/2
Factor -4/5*c**4 + 2/5*c**5 + 16/5*c**2 - 4/5*c**3 + 4/5 - 14/5*c.
2*(c - 1)**4*(c + 2)/5
Let j(d) be the second derivative of 3*d**6/70 + 3*d**5/35 - d**4/28 - d**3/7 + 5*d. Factor j(x).
3*x*(x + 1)**2*(3*x - 2)/7
Let b(f) be the first derivative of 2*f**6/33 + 14*f**5/55 + 3*f**4/11 - 2*f**3/33 - 2*f**2/11 - 6. Find y, given that b(y) = 0.
-2, -1, 0, 1/2
Let x = 12 + -7. Suppose -2*g + 2*j = -20, -4*g = 4*j - j - 5. Determine c so that c**3 + 2*c**4 - 3*c**5 + 7*c**x - 3*c**g = 0.
-1, 0
Suppose 0 = 5*q + 6 - 66. Let r be (-9)/q - 6/(-8). Find l such that 1/2*l**2 + 1/2*l + r = 0.
-1, 0
Let w(p) be the third derivative of -7*p**6/60 - 19*p**5/30 - 2*p**4/3 + 4*p**3/3 - 50*p**2. Factor w(l).
-2*(l + 1)*(l + 2)*(7*l - 2)
Let t = -2 - -4. Factor 6*x**t - 2*x**4 - 2*x**5 - 6*x**2.
-2*x**4*(x + 1)
Let s be (-3 - -2)/(9/(-8)). Let y(u) be the first derivative of 2/27*u**3 + 4/9*u**2 + s*u + 1. Factor y(p).
2*(p + 2)**2/9
Let l(u) be the second derivative of u**7/210 + u**6/20 + 13*u**5/60 + u**4/2 + 2*u**3/3 + u**2 + u. Let o(f) be the first derivative of l(f). Factor o(b).
(b + 1)**2*(b + 2)**2
Let y(o) be the first derivative of -63*o**6/2 - 198*o**5/5 + 57*o**4/2 + 24*o**3 - 45*o**2/2 + 6*o + 39. Determine z so that y(z) = 0.
-1, 2/7, 1/3
Let g = -1/1036 + 10371/11396. Factor -4/11*k + 0 - g*k**2.
-2*k*(5*k + 2)/11
Solve 6*y - 4*y + y - 9 + 3*y - y**2 = 0 for y.
3
Let j(m) = -m**3. Let d(o) = -3*o**5 - 9*o**4 - 15*o**3 - 3*o**2. Let s(i) = -d(i) + 6*j(i). Solve s(q) = 0 for q.
-1, 0
Let y be (-9)/12 - (-46)/8. Suppose 4*r + 57 = y*v, 2*v + 3*r - 8 = 1. Factor z + 0*z - v*z**4 - z**5 + 7*z**4 + 2*z**2.
-z*(z - 1)*(z + 1)**3
Let f(v) be the second derivative of v**7/840 + v**6/120 - v**4/4 - 6*v. Let r(h) be the third derivative of f(h). Let r(j) = 0. Calculate j.
-2, 0
Let s(c) be the first derivative of -c**3/15 - c**2/10 + 2*c/5 + 19. Solve s(a) = 0 for a.
-2, 1
Factor -f**4 + 39*f**3 + 192 + 3*f**4 + 336*f + 180*f**2 + f**4.
3*(f + 1)*(f + 4)**3
Let n(t) be the second derivative of t**4/66 + 2*t**3/33 - 3*t**2/11 - 23*t. Factor n(i).
2*(i - 1)*(i + 3)/11
Let d be 10/24 - 2/(-8). Let t(y) = 3*y**2 - y - 2. Let m be t(-1). Determine v, given that 1/3*v**m + d*v + 1/3 = 0.
-1
Suppose 2*x - x = 8. Suppose -y - 2*d = -0 - 11, 0 = -2*d + x. Factor 0 - 4/7*t**2 + 2/7*t**y + 2/7*t.
2*t*(t - 1)**2/7
Suppose 0 = 5*a - a. Suppose a = s - 1 - 2. Factor k**s + 3*k**2 + 0 + 3*k - k + 1 + k.
(k + 1)**3
Factor 0 - 16/7*d - 2/7*d**5 + 2*d**4 - 36/7*d**3 + 40/7*d**2.
-2*d*(d - 2)**3*(d - 1)/7
Let p(a) be the second derivative of -3*a**7/56 + a**6/8 + 3*a**5/80 - 5*a**4/16 + a**3/