
Suppose 4*w + 3*a - 7 = 8, 5*w + 4*a = 19. Solve 2/19*g - 4/19*g**2 - 2/19*g**w + 4/19 = 0.
-2, -1, 1
Let q(n) be the third derivative of n**8/2240 - n**6/240 + 3*n**4/8 - n**2. Let g(h) be the second derivative of q(h). Solve g(b) = 0 for b.
-1, 0, 1
Let -13*h**3 + 20*h + 18*h**2 + 12*h**3 + 6*h - 2*h + 4*h**3 = 0. What is h?
-4, -2, 0
Factor 3 - 320*h**2 + 122*h**2 + 0 + 0 - 3*h + 3.
-3*(6*h - 1)*(11*h + 2)
Let n(v) = -v**2 - 34*v - 156. Let k be n(-28). Let h(w) be the second derivative of -1/8*w**3 + 1/12*w**4 + 0 + 0*w**2 - 1/80*w**5 - k*w. Factor h(q).
-q*(q - 3)*(q - 1)/4
Determine s, given that s**2 + 3*s**2 - 2*s - 9*s - 4*s**5 + 3*s + 12*s**3 - 4*s**4 = 0.
-2, -1, 0, 1
Let t(h) = 63*h + 317. Let m be t(-5). Determine d, given that -1/3*d + 1/3*d**3 - 1/6*d**4 + 1/6 + 0*d**m = 0.
-1, 1
Let m(k) be the first derivative of -1/2*k**4 + 0*k + 8/15*k**5 - 1/9*k**6 - 8/9*k**3 + 4/3*k**2 - 26. What is y in m(y) = 0?
-1, 0, 1, 2
Let o(k) = k + 10. Let s be o(-10). Suppose -4*z = -3*y + 14, 2*z = -4*y - s*z + 4. What is f in 48*f**5 - y*f - 4*f**4 + 0*f**4 + 4*f**2 - 52*f**3 + 6*f = 0?
-1, -1/4, 0, 1/3, 1
Let z(s) be the second derivative of -121*s**4/4 - 22*s**3 - 6*s**2 + 54*s. Solve z(i) = 0.
-2/11
Let l be 16/(-56) + 60/14. Let w(y) be the second derivative of y + 1/5*y**2 + 1/3*y**3 - 7/25*y**5 + 0 + 3/35*y**7 + 1/15*y**l - 1/25*y**6. Solve w(p) = 0.
-1, -1/3, 1
Let k(j) be the third derivative of 5*j**8/4032 - j**7/504 - 11*j**5/60 - 4*j**2. Let q(n) be the third derivative of k(n). Suppose q(o) = 0. What is o?
0, 2/5
Let k(v) = -v**2 + 50*v - 523. Let i be k(35). Factor -4/5*z**i - 16/5 - 16/5*z.
-4*(z + 2)**2/5
Suppose m - 127 = -262. Let w = m - -137. Suppose -1/2*p**2 - w - 5/2*p = 0. Calculate p.
-4, -1
Suppose 2*k + 4*u = -8, 2*u + 2 = 4*k + 4*u. Solve -128 + 21*o**3 + 41*o**k - 3*o**2 + o**3 + 2*o**4 + 32*o + 34*o**2 = 0.
-4, 1
Suppose 41*g = 42*g - 12. Suppose -6 - 9 - 1 + 8 - 4*b**3 + g*b = 0. Calculate b.
-2, 1
Suppose 2 + 2 = 2*u. Suppose -w**4 + w**4 + 3*w**3 - 2*w + w**4 - 2*w**4 - w**5 + w**u = 0. Calculate w.
-2, -1, 0, 1
Let s(i) be the first derivative of 2*i**5/15 + 17*i**4/6 + 14*i**3 - 27*i**2 - 64. Find u such that s(u) = 0.
-9, 0, 1
Solve 0 + 45/7*t**4 - 177/7*t**3 - 3/7*t**5 + 135/7*t**2 + 0*t = 0.
0, 1, 5, 9
Let g be 5550/6216 + 3/(-4). Factor 0*z**2 + 4/7*z - g*z**3 + 0.
-z*(z - 2)*(z + 2)/7
Let m(a) be the first derivative of 5*a**3/3 - 650*a**2 + 84500*a + 72. Factor m(l).
5*(l - 130)**2
Let z(d) be the first derivative of 3*d**4/4 + 14*d**3 + 36*d**2 + 341. Find m such that z(m) = 0.
-12, -2, 0
Let y = -5912 + 5916. Factor -2/7*q + 0*q**3 + 3/7*q**2 + 0 - 1/7*q**y.
-q*(q - 1)**2*(q + 2)/7
Let p be ((-1896)/315 + 6)/(3/(63/(-3))). Factor 8/15*d**2 - 8/15 - p*d + 2/15*d**3.
2*(d - 1)*(d + 1)*(d + 4)/15
Let d(t) be the second derivative of -t**7/168 + t**6/30 + 19*t**5/80 - 35*t**4/24 - 4*t**3 + 36*t**2 + 691*t. Let d(x) = 0. Calculate x.
-3, 2, 4
Let v = 27/1750 - 1/875. Let x(f) be the second derivative of 0 + 5*f - 1/21*f**3 - 1/42*f**4 + 0*f**2 + 1/105*f**6 + v*f**5. What is q in x(q) = 0?
-1, 0, 1
Let u be (-22 + -2)*(69/(-9) + 7). Let b be ((-6)/(-15))/(u/15). Let 0 - b*q**4 - 3/8*q + 3/8*q**3 + 3/8*q**2 = 0. Calculate q.
-1, 0, 1
Factor 52 - 2/13*h**3 - 18*h - 48/13*h**2.
-2*(h - 2)*(h + 13)**2/13
Let l(v) = 3 - 4*v**2 + 8 - 42*v + 1 - 12*v**2. Let h(j) = -11*j**2 - 28*j + 8. Let c(g) = 8*h(g) - 5*l(g). Factor c(a).
-2*(a + 2)*(4*a - 1)
Let k(j) be the third derivative of -j**7/42 + j**6/12 + j**5/12 - 5*j**4/12 + 13*j**2. Factor k(o).
-5*o*(o - 2)*(o - 1)*(o + 1)
Let b(t) be the second derivative of -t**7/140 - t**6/240 + t**5/40 + t**4/48 + t**2/2 - t. Let u(j) be the first derivative of b(j). Factor u(d).
-d*(d - 1)*(d + 1)*(3*d + 1)/2
Let h(j) be the third derivative of -j**7/735 + 37*j**6/105 - 35*j**5 + 4459*j**4/3 - 16807*j**3/3 - 90*j**2. Solve h(n) = 0.
1, 49
Suppose 5*a + 5*p - 50 = 0, -2*a + 5*p + 5 = -1. Let k = -5 + a. Factor -26 - 3*j + k*j**2 + 23 + 3*j.
3*(j - 1)*(j + 1)
Let z(g) be the first derivative of -5/3*g + 5/2*g**2 + 4 + 5/12*g**4 - 5/3*g**3. Solve z(l) = 0 for l.
1
Let c = 23 + -20. Factor -8*a**4 + 25*a + 2*a**5 + 3*a**4 - 30*a**c + 3*a**5 - 10*a**2 + 15.
5*(a - 3)*(a - 1)*(a + 1)**3
Let z = -6 + 8. Suppose -45 = -5*v + 5*s, 0 = -z*v + 6*v - 5*s - 41. Let -o**2 - v*o + 6*o + 4*o - 3 - 2*o**2 = 0. What is o?
1
Let v(k) be the third derivative of k**6/60 - k**5/6 + 7*k**4/12 - k**3 + 4*k**2 + 2*k. Let v(z) = 0. Calculate z.
1, 3
Let b(c) be the first derivative of -50*c**3/21 + 320*c**2/7 - 2048*c/7 - 72. Determine o, given that b(o) = 0.
32/5
Let f(u) be the second derivative of u**8/13440 - u**6/1440 - u**4/12 - 9*u. Let t(j) be the third derivative of f(j). Factor t(w).
w*(w - 1)*(w + 1)/2
Let a(c) = -c**3 - 6*c**2 - 15*c - 10. Let p(x) = -5*x**3 - 35*x**2 - 90*x - 60. Let v(d) = 35*a(d) - 6*p(d). Let v(u) = 0. What is u?
-1, 2
Let l = 22 - 17. Suppose -2 = d + l*t, -2*d - d = 5*t - 4. Determine w, given that -w**4 - 3*w**2 + w**4 + d*w**4 = 0.
-1, 0, 1
Factor -4/7*y**4 + 8/7*y + 4/7*y**2 - 8/7*y**3 + 0.
-4*y*(y - 1)*(y + 1)*(y + 2)/7
Let v be -6 - -19 - (1 + -1). Let j = -10 + v. Factor 0*h**2 - h**j - 2*h**3 - 2*h**2 + h**3.
-2*h**2*(h + 1)
Let -282*t + 173*t**2 + t**2 - 21*t**3 + 219*t**2 + 396*t = 0. What is t?
-2/7, 0, 19
Let q = -14987/51220 - 7/1970. Let n = 9/20 + q. Factor n*m**2 - 6/13 - 4/13*m.
2*(m - 3)*(m + 1)/13
Let p(x) be the first derivative of -x**9/2016 + x**7/280 - x**5/80 - x**3 + 3. Let o(b) be the third derivative of p(b). Factor o(c).
-3*c*(c - 1)**2*(c + 1)**2/2
Solve 2/13*k**3 - 8/13*k + 8/13 - 2/13*k**2 = 0.
-2, 1, 2
Let k(y) = -16*y - 60. Let x be k(-4). Let v(q) be the third derivative of -4*q**2 + 1/300*q**5 + 0 + 0*q - 1/30*q**x + 2/15*q**3. Factor v(o).
(o - 2)**2/5
Let h be 1*3*(-22)/(-33). Suppose 4 = h*a - 4. Factor 9*q**3 - 4*q**2 - q**3 - 26*q**a + 22*q**4.
-4*q**2*(q - 1)**2
Suppose -5*f = 10, 5*w + 8*f - 5*f + 6 = 0. Let m(a) be the third derivative of 0 + a**2 + 0*a + 2/27*a**3 + w*a**5 - 1/36*a**4 + 1/540*a**6. Factor m(h).
2*(h - 1)**2*(h + 2)/9
Let m(l) = 6*l**2 + 40*l**3 + 0*l**2 - 41*l**3 - 5*l. Let j be m(5). Factor 0*f**2 + j*f + 0 + 1/2*f**3 - 1/2*f**4.
-f**3*(f - 1)/2
Let d be 40/(-16 + 8) - -5*1. Let u(o) be the third derivative of 1/210*o**7 + 0*o**3 + 0*o + d*o**4 - 1/30*o**5 - 2*o**2 + 1/120*o**6 + 0. Factor u(i).
i**2*(i - 1)*(i + 2)
Let d(v) be the second derivative of -6/5*v**2 + 3/100*v**5 + 4/5*v**3 + 2*v - 1/4*v**4 + 0. Factor d(p).
3*(p - 2)**2*(p - 1)/5
Let y be ((-3645)/282)/(-5) - 3. Let u = 4/47 - y. Solve 5/6*m + 1/6*m**4 - 1/6*m**3 - u*m**2 - 1/3 = 0 for m.
-2, 1
What is i in 7*i**2 - 110 - 12*i**2 + 0*i + 65*i = 0?
2, 11
Let b(r) = -65*r**3 - 1695*r**2 + 3785*r + 225. Let p(z) = -3*z**3 - 77*z**2 + 172*z + 10. Let w(o) = 2*b(o) - 45*p(o). Let w(h) = 0. What is h?
-17, 0, 2
Let o = -2030742/206329 - -2292/229. Let z = 40/53 - o. Factor -8/17 - 32/17*j + 50/17*j**3 - z*j**2.
2*(j - 1)*(5*j + 2)**2/17
Factor 3*o**3 - 2*o - 16*o - 258*o**2 + 243*o**2.
3*o*(o - 6)*(o + 1)
Suppose 0 = 4*n - 6*n + 12. Let b be (-4)/(4 - n - 0). Let 26 - 5*j**2 - 23 - 5*j**b - 2*j**2 = 0. What is j?
-1/2, 1/2
Let v = 9 - 9. Let f be v - -1 - (-7 + 6). Let s(a) = a**3 - 3*a**2 - a + 1. Let g(u) = -u**2 - 1. Let w(m) = f*g(m) - 2*s(m). Factor w(z).
-2*(z - 2)*(z - 1)*(z + 1)
Let u(s) = -s**3 + 9*s**2 - 16*s + 6. Let a be u(7). Let l = a + 26. Factor -1/5*n**5 - 81*n - l*n**3 + 243/5 + 3*n**4 + 54*n**2.
-(n - 3)**5/5
Suppose 2/3*n**3 - 2*n**2 + 2 - 2/3*n = 0. What is n?
-1, 1, 3
Factor 5/3*o**3 - 2/3 - 4*o**2 + 3*o.
(o - 1)**2*(5*o - 2)/3
Let w(c) = -c + 8. Let p be w(9). Let h(s) = -2*s**3 - s - 1. Let r be h(p). Factor 5*m**3 - 3*m**2 - 4*m**3 + 3*m**5 - r*m**4 - 4*m**3 + 5*m**4.
3*m**2*(m - 1)*(m + 1)**2
Suppose -o + 1 = -k + 3, 4*k = 5*o + 4. Suppose 9*i - k = 6*i. Let 0 + 2/9*w + 2/9*w**i = 0. Calculate w.
-1, 0
Factor -4078*c + 8162*c - 4075*c + 3*c**2.
3*c*(c + 3)
Suppose 0 = 5*z - 3*s - 231, -186 = -4*z + 2*s + s. Suppose -17*q + 26*q = z. Factor -3/4*g**q + 15/4*g**3 - 6*g + 3/4*g**4 - 3 - 3/4*g**2.
-3*(g - 2)**2*(g + 1)**3/4
Suppose 17*l - 13*l + 30 = n, 0 = 2*n + 5*l + 31. Factor -4/7*g**n + 4*g + 0.
-4*g*(g - 7)/7
Let r(z)