.
s*(s + 1)**3/6
Suppose -16 - 50 = 4*d - 5*r, 0 = -2*d - r - 26. Let m be (-8)/(-8)*(-16)/d. Find o such that -m*o - 2/7 + 8/7*o**3 + 2/7*o**2 = 0.
-1, -1/4, 1
Let o(j) be the third derivative of j**6/1440 - j**5/240 - 8*j**3/3 - 28*j**2. Let a(d) be the first derivative of o(d). What is u in a(u) = 0?
0, 2
Let h(c) be the third derivative of c**8/2352 + c**7/294 + c**6/840 - 17*c**5/420 - 11*c**4/84 - 4*c**3/21 + 618*c**2. Let h(x) = 0. What is x?
-4, -1, 2
Let v(z) = -2*z - 8. Let l be v(-6). Suppose 0*w + 2*w = l. Let 4*a - 2*a - 4*a**2 - 1 + 3*a**w = 0. What is a?
1
Let c be (-1*3)/((9/(-2))/3). Find z such that -62 + 2*z - 4*z**2 - c*z**3 + 116 - 50 = 0.
-2, -1, 1
Let r = -3 + -30. Let v be (-8)/(-6) - (r/9 - -3). Find a such that 3*a**3 + 33/4*a + 39/4*a**v + 3/2 = 0.
-2, -1, -1/4
Factor -186 - 48*g - 58 + 52 - 3*g**2.
-3*(g + 8)**2
Let m = -7871/16 + 492. Let o(v) be the third derivative of 1/120*v**5 - m*v**4 + 0*v**3 + 0 + 0*v - 6*v**2. Solve o(k) = 0 for k.
0, 3
Let i(l) = l**3 + 11*l**2 + 7*l - 3. Let h be i(-8). Let w = h - 656/5. Solve 1/5*t**2 + w + 6/5*t = 0 for t.
-3
Suppose 5*a - 5*k - 25 = 35, k = -2*a + 12. Let q(n) = -n + 8. Let g be q(a). Let 1/4*v**2 + g + 1/2*v = 0. What is v?
-2, 0
Factor -77*j - 104*j**2 + 6*j - 9*j + 32 - 251*j**3 - 252*j**3 + 475*j**3.
-4*(j + 2)**2*(7*j - 2)
Let c(x) = 6 - 9*x**2 + 2*x**2 - 1 - 2*x**2 + x**3. Let z be c(9). Find r such that -r**3 + 3*r**5 - 11*r**4 + 13*r**4 - 4*r**5 + 0*r**z = 0.
0, 1
Let z = -2380 - -2380. Factor z + 0*k - 4/3*k**2.
-4*k**2/3
Let d(t) = -4*t**2 - 14*t - 8. Let v(y) = -51*y - 7*y**2 - 24 + 8*y - 5*y**2. Let o(g) = 7*d(g) - 2*v(g). Determine k, given that o(k) = 0.
-2, -1
Let k be (-5)/(-2)*(-44)/(-275)*10. Suppose 4*x = -5*c + 9, 2*c + 10 = -k*x - x. What is g in -2/7*g**c + 16/7*g + 10/7*g**4 + 0 - 12/7*g**3 - 8/7*g**2 = 0?
-1, 0, 2
Let x be -3 + (2 - -1) - -3. Suppose 5*r - 14 = -x*n, -2*n - 2*n = -3*r - 9. Factor 2*i**3 - i**n - 5*i**3.
-4*i**3
Let t(h) be the first derivative of -h**4/3 + 1135*h**3/9 - 40186*h**2/3 - 20164*h/3 + 265. Let t(n) = 0. Calculate n.
-1/4, 142
Determine o, given that 0 - 44/17*o**3 + 20/17*o**5 - 2/17*o**4 + 14/17*o**2 + 12/17*o = 0.
-3/2, -2/5, 0, 1
Let r be 9/((-54)/24)*15/(-2). Factor 120*q**3 + 8*q**4 + 2185*q**2 - 88*q**4 - r*q - 5 - 2190*q**2.
-5*(q - 1)**2*(4*q + 1)**2
Let i(q) = -37*q - 5*q**3 - 2 + 36*q + 1 + 4*q**2. Let l(v) = -26*v**3 + 20*v**2 - 6*v - 4. Let t(m) = 16*i(m) - 3*l(m). Factor t(u).
-2*(u - 2)*(u - 1)*(u + 1)
Suppose -2*q + 5 = -3. Let d be (-3)/(6/q) + 2. Solve -a + 6*a + d*a - 3 + a - 3*a**2 = 0.
1
Suppose -2*d + 40 = 4*h - 6*d, h + 2*d = -5. Let z(w) be the second derivative of 0 - 1/4*w**4 - w**3 - w + 0*w**2 + 3/20*w**h. Factor z(s).
3*s*(s - 2)*(s + 1)
Let a(f) = 4*f - 47. Let j be a(14). Let y be ((-18)/20)/(j/(-15)). What is g in 0*g + 3/2*g**4 + 3/2*g**3 - 3/2*g**5 - y*g**2 + 0 = 0?
-1, 0, 1
Let r = 194034 + -56270097/290. Let z = -1/58 - r. Factor -2/5*j**3 - 2/5*j + 0 - z*j**2.
-2*j*(j + 1)**2/5
Let k(x) be the third derivative of -x**5/120 + 3*x**4/8 + 19*x**3/12 - 251*x**2. Factor k(n).
-(n - 19)*(n + 1)/2
Let t(c) = -c**3 + 5*c**2 + 6*c + 14. Let z be t(7). Let h = z + 46. Solve 5/4*m**2 - 7/4*m**5 + 0 + 9/4*m**3 - 1/2*m - 5/4*m**h = 0.
-1, 0, 2/7, 1
Let s(d) be the third derivative of 1/28*d**5 - 1/280*d**6 - 3/28*d**4 + 0 + 0*d**3 - 27*d**2 + 0*d. Factor s(c).
-3*c*(c - 3)*(c - 2)/7
Let v be (-11)/((-275)/190) - 2/(-5). Factor -9*w**2 - v*w**2 + w**3 + 17*w**2.
w**3
Find p, given that -1/2*p**3 + 0 + 11/3*p**2 - 5/6*p**5 - 11/3*p**4 + 4/3*p = 0.
-4, -1, -2/5, 0, 1
Suppose -4*c - 2*r = -0 - 16, 0 = 2*c + 3*r - 12. Suppose h + 2*h + 9 = 3*i, -5*h = -4*i + 12. Determine w, given that -6/5 - 3/5*w**i - c*w - 12/5*w**2 = 0.
-2, -1
Let v(s) be the third derivative of 1/160*s**5 + 0*s + 0*s**3 + 0 - 17*s**2 + 1/16*s**4. Factor v(w).
3*w*(w + 4)/8
Suppose -2*c - c + 3*i = -3, -4*i = 4*c - 20. Let m = 6 - c. Factor 2*v + 16*v**3 - 6*v**2 - 5*v**2 + m*v**4 - 10*v**4.
-v*(v - 1)**2*(7*v - 2)
Let s(g) be the first derivative of 18 + 6/7*g + 5/14*g**2 + 1/21*g**3. Factor s(w).
(w + 2)*(w + 3)/7
Let r(x) be the second derivative of 0*x**2 - 4/25*x**5 + 0*x**3 + 0 - 1/15*x**4 - 36*x - 7/150*x**6. Suppose r(q) = 0. Calculate q.
-2, -2/7, 0
Let d(b) = 4*b**2 - 12*b + 13. Let p(x) be the second derivative of x**4/12 + x**2/2 + 9*x. Let v(a) = d(a) - p(a). Determine r so that v(r) = 0.
2
Let p(r) be the third derivative of -1/4*r**3 - 8*r**2 + 0*r**5 - 3/32*r**4 + 0*r + 1/160*r**6 + 0. Factor p(d).
3*(d - 2)*(d + 1)**2/4
Determine a, given that 3/5*a**2 + 33/5*a + 72/5 = 0.
-8, -3
Let g be ((-10)/(-6) - 2)*(-30)/2. Let b be g - (220/35)/4. Suppose 18/7*t**4 + 0*t + 0 - 36/7*t**3 - 3/7*t**5 + b*t**2 = 0. Calculate t.
0, 2
Let m(v) = -8*v**3 + 16*v**2 + 42*v + 41. Let l(f) = 3*f**3 - 8*f**2 - 21*f - 20. Let n(a) = 10*l(a) + 4*m(a). Factor n(s).
-2*(s + 2)*(s + 3)**2
Determine k, given that 45 + 52 + 20*k**3 - 141 - 80*k**2 + 6*k**3 + 52 - 98*k = 0.
-1, 1/13, 4
Let u(o) = -2*o + 19. Let v be u(8). Suppose 0 = -m + m + v*m. Suppose m + 2/3*b**3 - 1/3*b**2 - 2/3*b + 1/3*b**4 = 0. What is b?
-2, -1, 0, 1
Solve j**4 - 11*j**2 - 8*j**2 + 16*j + 7*j**2 = 0.
-4, 0, 2
Let l(g) = -g**2 - 2*g + 1. Let f(n) = 18*n + 12. Let r(s) = f(s) + 3*l(s). Factor r(x).
-3*(x - 5)*(x + 1)
Let f be (-5106)/(-9660) + 6/(-14). Solve 1/5*j**3 - 1/10*j**4 - f*j**5 + 1/5*j**2 - 1/10*j - 1/10 = 0.
-1, 1
Let a(q) be the first derivative of -2*q**3/9 + 56*q**2/3 - 1568*q/3 - 19. Suppose a(g) = 0. Calculate g.
28
Let v(c) = 10*c**3 + 5*c**2 - 16*c - 47. Let x(q) = -3*q**3 - 2*q**2 + 5*q + 16. Let f(r) = -2*v(r) - 7*x(r). Solve f(i) = 0.
-3, 2
Let u(f) be the second derivative of -f**7/70 + 3*f**6/10 - 9*f**5/10 - 19*f**4/2 - 45*f**3/2 - 243*f**2/10 + 72*f. Factor u(m).
-3*(m - 9)**2*(m + 1)**3/5
Suppose 2*l + 2*d - 19 = -l, -3*d = -5*l. Suppose 0 = -3*p + 9 - l. Find g, given that -6*g**2 + 10*g**3 - 6 - 4*g**4 - p*g + 4 + 4 = 0.
-1/2, 1
Factor 4/5*d**4 + 0*d + 32/5*d**2 + 0 - 24/5*d**3.
4*d**2*(d - 4)*(d - 2)/5
Let x = 33 + 14. Let c be 94*(-1)/(-4)*2. Suppose 2*v**2 + x - c - v**2 = 0. Calculate v.
0
Let f(p) be the first derivative of p**4 - 88*p**3/3 + 210*p**2 - 576*p + 517. Let f(s) = 0. What is s?
3, 16
Let a = -111 - -556/5. Let z(o) be the first derivative of -3/10*o**4 + a*o**3 + 3/25*o**5 + 0*o + 1 + 0*o**2. Factor z(h).
3*h**2*(h - 1)**2/5
Let f(p) be the first derivative of -4*p**3/69 + 107*p**2/23 + 108*p/23 - 242. Find v, given that f(v) = 0.
-1/2, 54
Let l be 1*5/(-15)*12/(-20). Let k(h) be the second derivative of 0 + l*h**5 - 2/3*h**3 - h**2 - 7*h + 0*h**4 + 1/15*h**6. Find x, given that k(x) = 0.
-1, 1
Let h = 4 + -2. What is d in -6*d**2 + 1 + 1 + h*d**3 + 6 + 0 = 0?
-1, 2
What is k in -248/5*k - 16/5*k**3 + 268/5*k**2 + 12 - 16/5*k**4 = 0?
-5, 1/2, 3
Suppose 56 = -10*t + 3*t. Let i be (-24)/(-9) - t/(-6) - 1. What is j in 0 + i*j - 1/3*j**2 = 0?
0, 1
Let h be 27/(-36)*934/(-132). Let w = h - 41/8. Find p such that 0 + 2/11*p + 2/11*p**2 - w*p**3 - 2/11*p**4 = 0.
-1, 0, 1
Find u, given that -2*u**2 + 27*u + 12*u - 3*u**3 - 27*u + 8 = 0.
-2, -2/3, 2
Let h(w) be the first derivative of w**5/5 - 13*w**4/3 + 70*w**3/3 + 98*w**2 - 17*w + 31. Let v(k) be the first derivative of h(k). Suppose v(u) = 0. What is u?
-1, 7
Let t = 34366 - 378024/11. Factor 0 - 30/11*h + t*h**2.
2*h*(h - 15)/11
Suppose i = 7*v - 9*v - 2, 0 = 5*v + 3*i + 6. Let g(b) be the third derivative of 0*b**3 + 2*b**2 - 1/6*b**4 + 0*b + 7/30*b**5 + v. Factor g(r).
2*r*(7*r - 2)
Let a(y) = 10*y**3 + 30*y**2 - 20*y - 15. Let u(r) = r**3 - r**2 - 1. Let l(c) = -a(c) - 5*u(c). Suppose l(k) = 0. Calculate k.
-2, -2/3, 1
Let a(k) be the second derivative of k**6/75 + 2*k**5/25 - 7*k**4/30 - 2*k**3/3 - 234*k. Factor a(r).
2*r*(r - 2)*(r + 1)*(r + 5)/5
Let d(a) = -3*a. Let n be d(-1). Suppose -36*y + 45*y = 2250. Factor 254 - y - 3*k - 3*k**2 - k**3 + n*k.
-(k - 1)*(k + 2)**2
Let r(t) = 4*t**2 + t**3 - 13*t**2 - 1 + t**5 - t**2 + 9*t**2. Let v(a) = -6*a**5 - 10*a**4 - 6*a**3 + a**2 + 1. Let m(p) = -r(p) - v(p). Factor m(w).
5*w**3*(w + 1)**2
Suppose 0*l - l = 2*f - 2, -29 = -2*l + f. Let b = l - 35/3. Determine d, given that -1/3*d**2 + b - 1/3*d**3 + 1/3*d = 0.
-1, 1
S