Let g(a) be the second derivative of a**4/66 - 2*a**3/33 + a**2/11 - 5*a. Suppose g(j) = 0. What is j?
1
Suppose -14 = j + 2*n, -4*n + 1 + 1 = -3*j. Let u be (-48)/(-18) + (-2)/j. Determine m, given that 1 - 2*m**2 + 3*m + 0*m + u*m**2 - 5*m = 0.
1
Factor -1/2*w + 1/2*w**3 + 1/2 - 1/2*w**2.
(w - 1)**2*(w + 1)/2
Let -48/7*b**4 - 914/7*b**3 + 72/7*b + 32*b**5 + 28*b**2 - 16/7 = 0. Calculate b.
-2, -2/7, 1/4, 2
Let y(h) be the first derivative of 3 - 2/3*h**2 - 2/3*h**3 + 0*h - 1/6*h**4. Factor y(r).
-2*r*(r + 1)*(r + 2)/3
Let n = -6 - -7. Let s(p) be the first derivative of p**2 - n - 1/2*p**4 - p + 0*p**3 + 1/5*p**5. Let s(g) = 0. What is g?
-1, 1
Let g(k) = 3*k**3 + 2*k**2 - k - 3. Let q = 11 + -7. Let r(a) = -3*a**3 - 2*a**2 + a + 4. Let h(j) = q*g(j) + 3*r(j). Factor h(n).
n*(n + 1)*(3*n - 1)
Factor 5 + u + 2*u**2 - 1 + 8*u - 3*u.
2*(u + 1)*(u + 2)
Let s(g) be the first derivative of -2*g**5/75 + g**4/20 + g**3/15 + g**2/2 + 2. Let k(u) be the second derivative of s(u). Factor k(w).
-2*(w - 1)*(4*w + 1)/5
Let f(y) be the third derivative of y**7/1260 + y**6/180 - y**4/12 - 3*y**2. Let t(a) be the second derivative of f(a). Factor t(g).
2*g*(g + 2)
Factor -6/17*c**4 + 2/17 - 6/17*c + 2/17*c**5 + 4/17*c**2 + 4/17*c**3.
2*(c - 1)**4*(c + 1)/17
Let v be (10/14 - 1) + 48/21. Let f(r) be the first derivative of 10/3*r**3 + 9/2*r**2 + 3/4*r**4 + 2 + v*r. Solve f(o) = 0 for o.
-2, -1, -1/3
Let p(u) be the first derivative of -u**6/3 - 24*u**5/35 + 2*u**4/7 + 4*u**3/3 + 3*u**2/7 - 4*u/7 + 6. Find g such that p(g) = 0.
-1, 2/7, 1
Factor 6*r**4 + 2*r**2 + 6*r**3 + 185*r + 2*r**5 - 185*r.
2*r**2*(r + 1)**3
Let f(t) be the first derivative of -t**6/360 - t**5/60 - t**4/24 + 2*t**3/3 - 3. Let z(i) be the third derivative of f(i). Factor z(p).
-(p + 1)**2
Let i be 2*1*66/(-4). Let a be -2*(-4 - 123/i). Factor -2/11*q**3 + 2/11 - 6/11*q + a*q**2.
-2*(q - 1)**3/11
Let y be 5/2*54/45. Find x such that -4*x**2 + 5*x + 3*x**y - 2*x + 0*x - 2*x**2 = 0.
0, 1
Let k(i) be the third derivative of -i**8/336 - i**7/70 + i**6/120 + 7*i**5/60 - 2*i**3/3 + 4*i**2. Factor k(g).
-(g - 1)**2*(g + 1)*(g + 2)**2
Let d(o) = o**3 + 18*o**2 + 15*o - 31. Let b be d(-17). Solve -21/4*j**2 + 11/4*j + 17/4*j**b - 1/2 - 5/4*j**4 = 0.
2/5, 1
Let t(l) be the third derivative of -l**5/12 - 5*l**4/12 - 5*l**3/6 + 7*l**2. Factor t(b).
-5*(b + 1)**2
Factor 90*s**5 + 8*s + 36*s**3 - 20*s**4 - 86*s**5 - 16*s**2 - 12*s**2.
4*s*(s - 2)*(s - 1)**3
Let a(i) be the first derivative of i**4 + 4*i**3/3 - 2*i**2 - 4*i - 17. Factor a(l).
4*(l - 1)*(l + 1)**2
Let z(r) = -14*r**4 - 41*r**3 - 13*r**2 + 5*r. Let p(c) = -7*c**4 - 20*c**3 - 7*c**2 + 2*c. Let g(h) = -9*p(h) + 4*z(h). What is b in g(b) = 0?
-1, -2/7, 0
Let r(m) = -m**2 + 8*m - 2. Let f be r(7). What is t in -t - 3*t**2 - t + 0*t + f*t**2 = 0?
0, 1
Let p(u) be the first derivative of 2*u**5/35 - 4*u**3/21 + 2*u/7 + 5. Determine w so that p(w) = 0.
-1, 1
Let g(o) be the first derivative of o**6/9 + 4*o**5/15 + o**4/6 - 1. Solve g(x) = 0 for x.
-1, 0
Let o = 2/23 + 3/230. Let g(c) be the second derivative of 0 - 1/3*c**3 + c + o*c**5 + 0*c**4 + 0*c**2. Factor g(j).
2*j*(j - 1)*(j + 1)
Let q(m) be the first derivative of -m**3/3 - 14*m**2 - 196*m - 24. Find a such that q(a) = 0.
-14
Let l(c) be the second derivative of 3*c**5/80 + c**4/2 + 2*c**3 + 13*c. Factor l(u).
3*u*(u + 4)**2/4
Suppose 0 = 3*z - z - 2. Let m(f) = 49*f**3 - 39*f**2 + 8*f - 1. Let q(l) = l**3 - l**2 + 1. Let g(w) = z*q(w) + m(w). Suppose g(v) = 0. Calculate v.
0, 2/5
Let q = 391 + -388. Suppose -2/5*d**q + 1/5*d**4 + 4/5 + 4/5*d - 3/5*d**2 = 0. What is d?
-1, 2
Factor 12*x**2 - 6*x**2 - 27*x + 2 + 3*x**5 + 4*x**3 + 20*x**3 - 18*x**4 + 10.
3*(x - 4)*(x - 1)**3*(x + 1)
Let 0*c**3 - 1/2*c**5 + 0 + 0*c**2 + 0*c + c**4 = 0. What is c?
0, 2
Let f(b) be the second derivative of 1/30*b**5 + 2/45*b**6 - 3*b + 0*b**2 + 1/63*b**7 + 0*b**3 + 0 + 0*b**4. Find q, given that f(q) = 0.
-1, 0
What is h in -8/11 + 32/11*h - 14/11*h**2 = 0?
2/7, 2
Let x(d) be the third derivative of -d**7/1260 + d**6/120 - d**5/30 + d**4/8 + 4*d**2. Let l(f) be the second derivative of x(f). Find y such that l(y) = 0.
1, 2
Let w(z) be the second derivative of -z**9/4200 - z**8/1400 - z**7/1575 + z**4/4 + 2*z. Let a(s) be the third derivative of w(s). Find h, given that a(h) = 0.
-2/3, 0
Let n(f) be the first derivative of -f**6/15 - 3*f**5/20 + f**4/12 + f**3/2 + f**2/2 + f - 4. Let y(k) be the first derivative of n(k). Solve y(r) = 0 for r.
-1, -1/2, 1
Suppose 0 = -4*x + 5*b - 8, 5*b - 35 = -4*x - x. Let d = 5 - x. Factor 0 + 0*f + 4/9*f**4 - 2/9*f**5 - 2/9*f**3 + 0*f**d.
-2*f**3*(f - 1)**2/9
Let x(b) be the first derivative of -b**6/90 + 4*b - 4. Let t(v) be the first derivative of x(v). Factor t(a).
-a**4/3
Let n(y) be the second derivative of 0*y**3 - y + 0*y**2 + 0*y**4 + 1/147*y**7 + 0 + 1/70*y**5 + 2/105*y**6. Factor n(m).
2*m**3*(m + 1)**2/7
Suppose -2*m = -6*m - 20. Let u be 2 + 2 + 4 + m. Solve 3/4*t**u - 5/4*t**2 - t + 1 = 0.
-1, 2/3, 2
Let l = -5 - -7. Suppose -16 = l*o - 4*o. Solve 8*u - o*u - u**2 + 1 = 0.
-1, 1
Let h be 5 - 6 - 1/1. Let v = h + 4. Factor 2/5*w**4 + 0*w + 2/5*w**v + 0 + 4/5*w**3.
2*w**2*(w + 1)**2/5
Let z(i) be the second derivative of -i**8/13440 + i**7/2520 + i**6/1440 - i**5/120 - i**4/6 + 2*i. Let a(m) be the third derivative of z(m). Factor a(v).
-(v - 2)*(v - 1)*(v + 1)/2
Let q(w) be the second derivative of w**6/75 - w**5/25 - w**4/30 + 2*w**3/15 + 30*w. Factor q(t).
2*t*(t - 2)*(t - 1)*(t + 1)/5
Let b(r) = r**3 + 7*r**2 + 7*r. Let x be b(-6). Let s(g) = 5*g**2 + 2*g - 7. Let i(m) = 6*m**2 + 2*m - 8. Let l(a) = x*i(a) + 7*s(a). Solve l(c) = 0.
1
Let b(g) be the first derivative of -g**3 - 2*g**2 - 6*g + 3. Let q(p) = 7*p**2 + 8*p + 13. Let d(m) = -5*b(m) - 2*q(m). Factor d(i).
(i + 2)**2
Let g = 164 - 164. Let 0*x + g - 32/3*x**4 + 8/3*x**3 + 10*x**5 + 0*x**2 = 0. What is x?
0, 2/5, 2/3
Let t be 9 + -14 - (-3 - 2). Find u such that 0*u**3 + 0*u**2 + 2/17*u**5 + 0*u + t - 2/17*u**4 = 0.
0, 1
Suppose -40/3*b - 8/3 - 6*b**2 = 0. Calculate b.
-2, -2/9
Let t = 6 + -3. Let x = t - 1. Determine w so that -2*w**3 - 14*w**4 + x*w**5 - 10*w**5 + 4*w**4 = 0.
-1, -1/4, 0
Let q = -104024025149/2340 + 44454710. Let k = -1/468 - q. Solve k*g**4 + 0 + 0*g - 2/5*g**2 - g**5 - 1/5*g**3 = 0 for g.
-2/5, 0, 1
Let n = 87 + -83. Let m(q) be the first derivative of 0*q + 3/2*q**2 + q**3 - n. Factor m(o).
3*o*(o + 1)
Let y(q) = -2*q**2 + 2*q. Let r(z) = -2*z**2 + 2*z. Let m(l) = 2*r(l) - 3*y(l). Suppose m(b) = 0. Calculate b.
0, 1
Factor -2/3 + 4/3*z - 2/3*z**2.
-2*(z - 1)**2/3
Let s = 227/315 + 5/63. Factor 2/5*u**2 + 2/5 + s*u.
2*(u + 1)**2/5
Let j(n) be the first derivative of -2*n**6/15 - n - 1. Let m(w) be the first derivative of j(w). Factor m(b).
-4*b**4
Let v be 2*(-4)/20 + (-288)/(-70). Suppose v*i**2 + 8/7 - 32/7*i + 10/7*i**5 + 22/7*i**3 - 34/7*i**4 = 0. Calculate i.
-1, 2/5, 1, 2
Let c(q) be the first derivative of -2*q**6/3 + 16*q**5/5 + 5*q**4 - 42. Determine i, given that c(i) = 0.
-1, 0, 5
Let s be 1 + -5 - 144/(-56) - -2. Solve -s*t**3 + 4/7*t + 0 - 2/7*t**4 + 2/7*t**2 = 0.
-2, -1, 0, 1
Suppose -3*l - 4 = -4*l. Factor 2*u**3 + u**2 + 1 + u**3 + 0*u**3 - 3*u + u**l - 3.
(u - 1)*(u + 1)**2*(u + 2)
Suppose -9*s**2 - 63/2*s**4 + 33/4*s**5 + 0 - 3*s + 141/4*s**3 = 0. Calculate s.
-2/11, 0, 1, 2
Let j = 7 - 4. Determine a, given that 11*a - j*a**3 - 8*a - 3*a**4 + 0*a**3 + 3*a**2 = 0.
-1, 0, 1
Let -2/5*t**2 + 22/5 + 4*t = 0. Calculate t.
-1, 11
Let j(p) be the second derivative of 1/40*p**6 - p - 9/80*p**5 - 1/8*p**3 + 0 + 3/16*p**4 + 0*p**2. Factor j(i).
3*i*(i - 1)**3/4
Let c(k) = -12*k**4 - 4*k**3 + 20*k**2 + 9*k - 13. Let m(p) = 12*p**4 + 4*p**3 - 20*p**2 - 8*p + 12. Let w(z) = 4*c(z) + 5*m(z). Let w(v) = 0. Calculate v.
-1, 2/3, 1
Factor 6*v**3 - 12 + 24*v - 3/4*v**4 - 18*v**2.
-3*(v - 2)**4/4
Suppose -4*i - 4 = 4*j, 7*j = 9*j - 4*i - 4. Find f, given that -4/3*f**3 + j*f - 2/3*f**2 - 2/3*f**4 + 0 = 0.
-1, 0
Let x be (-140)/(-147) - (-4)/(-14). Factor 8/9*c - x*c**3 + 98/9*c**5 + 140/9*c**4 + 0 - 40/9*c**2.
2*c*(c + 1)**2*(7*c - 2)**2/9
Let s = 220 - 94. Let h = 382/3 - s. Factor -h*g + 1/3 + g**2.
(g - 1)*(3*g - 1)/3
Let i = 76 + -207. Let t = 661/5 + i. What is r in -t*r**2