2)*(j - 1)**2
Suppose -2 = 2*d - 8. Let x = 112295/9 + -12477. Solve 2/9*o**5 + 0 + 2/9*o**2 - x*o**4 + 4/9*o - 2/3*o**d = 0.
-1, 0, 1, 2
Let g be (-20)/(-15)*8/(-112)*-3. Determine r, given that -8/7*r**2 - 22/7*r - 12/7 + g*r**3 = 0.
-1, 6
Let r(c) be the second derivative of -c**4/16 + 51*c**3/8 + 39*c**2/2 + 19*c + 3. Determine s, given that r(s) = 0.
-1, 52
Let o = -30 + 33. Let 4*b**2 - 4*b**2 + o*b**2 = 0. Calculate b.
0
Suppose -2*s + k = 84 + 52, 190 = -3*s - 2*k. Let t be (-15)/10*4*8/s. Factor t*l + 16/11 - 10/11*l**3 - 12/11*l**2 - 2/11*l**4.
-2*(l - 1)*(l + 2)**3/11
Let v(b) = 2*b**4 + 12*b**2 - 8*b. Let i(y) = y**3 + 7*y + 0*y**3 + 22*y**4 - 24*y**4 - 11*y**2. Let d(j) = -6*i(j) - 5*v(j). Find s, given that d(s) = 0.
0, 1
Suppose 3*w - 3*r + 72 = 0, -w = 3*w + 5*r + 78. Let p = w - -22. Factor 2*b**3 + 2*b**4 + 2/3*b**2 + p + 0*b + 2/3*b**5.
2*b**2*(b + 1)**3/3
Factor 300*h**2 + 3*h**5 + 2*h**5 + 185*h**3 + 157*h + 23*h + 50*h**4.
5*h*(h + 2)**2*(h + 3)**2
Let z(b) be the first derivative of -4*b**5/15 - 5*b**4/4 - 8*b**3/9 + b**2/2 + 17. Suppose z(m) = 0. What is m?
-3, -1, 0, 1/4
Let w be (-24)/56 - 6/(-14). Suppose j + 2*k + 6 = w, -2*j + 3*j + k + 1 = 0. Determine s so that j*s**3 - 12 - 76*s**2 + 60*s + 17*s**3 + 7*s**2 = 0.
2/7, 1, 2
Let r be (6 + -6)*(-2)/(-4) - 92. Let b = -458/5 - r. Let 0*n**2 - 3/5*n - b + 1/5*n**3 = 0. What is n?
-1, 2
Let d(t) be the third derivative of -t**8/20160 + t**7/1008 - t**6/120 + 11*t**5/30 + t**2 + 36. Let s(f) be the third derivative of d(f). Factor s(p).
-(p - 3)*(p - 2)
Find q, given that 11*q + 56*q**2 + 3*q**3 + 72 + 19*q - 95*q**2 = 0.
-1, 2, 12
Let s(r) = 2*r**2 + 2*r + 68. Let m be s(0). What is w in -11*w**5 + m*w**2 + 12*w**5 - 5*w**5 + 24*w + 12*w**4 + 60*w**3 = 0?
-1, 0, 6
Suppose 1/2*k**2 + 12 - 11/2*k = 0. What is k?
3, 8
Suppose 10 = 3*x + 4*z, -55*x = -58*x - z + 7. Factor 468/7*v - 108/7 - 390/7*v**3 - 75/7*v**4 - 327/7*v**x.
-3*(v + 3)**2*(5*v - 2)**2/7
Let k = -12 + 2. Let d be 8/(-10) - 38/k. Factor -8*u + 4*u**2 - 5*u**d + 2*u**4 + 4*u + 3*u.
u*(u - 1)**2*(2*u - 1)
Let k be (4 - 2)/(-2) - -103 - -4. Suppose 4*j + k = 118. Factor -2/3*d**2 - 1/3*d**5 + 2/3*d**j - 1/3*d + 1/3*d**4 + 1/3.
-(d - 1)**3*(d + 1)**2/3
Let i(w) be the third derivative of w**9/141120 + 11*w**8/47040 + w**7/336 + 5*w**6/336 + w**5/6 - w**2. Let u(t) be the third derivative of i(t). Factor u(d).
3*(d + 1)*(d + 5)**2/7
Let a(r) be the first derivative of -r**6/12 + 3*r**5/10 - r**4/4 - r**3/3 + 3*r**2/4 - r/2 - 19. Factor a(g).
-(g - 1)**4*(g + 1)/2
Find k such that 4*k + 45 + 6*k**2 - 33 + 17*k - 3*k**3 = 0.
-1, 4
Let k(l) be the second derivative of l**5/25 + 4*l**4/15 - 22*l**3/15 + 12*l**2/5 + 5*l + 5. Factor k(u).
4*(u - 1)**2*(u + 6)/5
Suppose z = -z - 5*v + 4, 0 = 4*v. Determine u so that -3 + 0 - 1 + 2*u + z*u**2 = 0.
-2, 1
Let t(z) be the first derivative of -z**5/10 - z**4/12 + 303. Find l, given that t(l) = 0.
-2/3, 0
Let t = -2252 - -2254. Factor 0 + 2/9*f**t + 4/9*f.
2*f*(f + 2)/9
Determine k so that -70*k - 3*k**2 + 61*k - 1452 - 57*k - 66*k = 0.
-22
Let m = 21679/5 - 21676/5. Solve -6/5*a + 0 - m*a**2 = 0.
-2, 0
Let y be (-80)/(-70)*(-7)/(-4). Find h, given that 12/5*h**y - 12/5 - 3/5*h + 3/5*h**3 = 0.
-4, -1, 1
Let q = 3372 - 10114/3. Factor 0*s + 1/3 - q*s**2 + 1/3*s**4 + 0*s**3.
(s - 1)**2*(s + 1)**2/3
Suppose 0 = 2*q + 4, 5*f - 5*q + 307 + 143 = 0. Let x = f + 95. Let -33/2*r - 9/2*r**4 - 1/2*r**5 - 15*r**x - 23*r**2 - 9/2 = 0. Calculate r.
-3, -1
Let x = -34825/3 + 11615. Factor 4*a**3 - x*a**2 + 16/3 - 4*a + 4/3*a**4.
4*(a - 1)**2*(a + 1)*(a + 4)/3
Factor -4/19 - 2/19*k**2 - 6/19*k.
-2*(k + 1)*(k + 2)/19
Let f = 6108/17 + -125007/136. Let u = -558 - f. Factor -9/8*i**5 + u*i - 15/4*i**3 - 15/4*i**4 + 3/4 + 0*i**2.
-3*(i + 1)**4*(3*i - 2)/8
Factor 20*l**2 + 15671*l - 31348*l + 15659*l.
2*l*(10*l - 9)
Let n(h) = h**3 + 2*h**2 - 7*h - 9. Let p be n(-3). Determine s, given that 3*s - 9*s**2 + p + 2 - 3*s**3 + 4 = 0.
-3, -1, 1
Let a = 2654 + -13268/5. Let v be 6/(-75)*5/(-1). Factor -4/5 + v*o**2 - a*o.
2*(o - 2)*(o + 1)/5
Let r(b) be the third derivative of b**8/420 - 2*b**6/45 + 2*b**3/3 - 38*b**2. Let g(k) be the first derivative of r(k). Determine h so that g(h) = 0.
-2, 0, 2
Let n be 4 - ((-162)/(-24) + -3). Let j(v) be the second derivative of 0 - v**3 + 3*v - 3/2*v**2 - n*v**4. Factor j(b).
-3*(b + 1)**2
Suppose 0 = 12*t - 8*t - 11*t. Let g(x) be the third derivative of 1/120*x**6 + t*x**3 + 0*x**4 - x**2 + 0*x + 0*x**5 + 0 + 0*x**7 - 1/336*x**8. Factor g(o).
-o**3*(o - 1)*(o + 1)
Suppose 6*p - 4*p - 4 = 0. Let m(q) = q**2 - q + 1. Let n(l) = -10*l**2 + 13*l - 14. Let k(j) = p*n(j) + 22*m(j). Factor k(v).
2*(v - 1)*(v + 3)
What is m in -5*m - 5*m**2 + 5*m - 190 + 235 = 0?
-3, 3
Let o(w) = w**3 + 16*w**2 + 3*w + 49. Let m be o(-16). Solve -m + 1/2*d**2 + 1/2*d = 0 for d.
-2, 1
Let k(h) = h**2 - h - 1. Let i(r) = 9*r**2 - 9*r - 24. Suppose -3*n + 2*c = -10 + 2, -4*n + c + 19 = 0. Let g(o) = n*k(o) - i(o). Let g(m) = 0. Calculate m.
-2, 3
Factor -13/5*k**2 - 4/5 - 16/5*k - 3/5*k**3.
-(k + 2)**2*(3*k + 1)/5
Let n(d) be the third derivative of -2*d**7/105 - d**6/10 + 13*d**5/15 + 5*d**4/2 + 52*d**2. Factor n(v).
-4*v*(v - 3)*(v + 1)*(v + 5)
Let q(r) be the second derivative of 3/100*r**5 + 1/20*r**4 - 6/5*r**2 + 2*r + 12 - 2/5*r**3. Factor q(i).
3*(i - 2)*(i + 1)*(i + 2)/5
Suppose -5*m = 25, 0 = 3*c + 5*m - 2*m + 6. Factor -23*n + 17*n**3 - 5*n + 24*n**2 - 36*n**3 + 23*n**c.
4*n*(n - 1)*(n + 7)
Let x(g) be the second derivative of g**5/90 - g**4/54 - 20*g**3/27 - 2*g + 12. Find h, given that x(h) = 0.
-4, 0, 5
Let r(m) be the first derivative of 4*m**2 - 4/3*m**3 + 19 - 4*m. Factor r(l).
-4*(l - 1)**2
Suppose 0 = -x - 3*x + 16. Let b(g) = g**3 - 5*g**2 + 4*g + 4. Let o be b(x). Solve 4*s + s**o + 6*s - 1 - 12*s + 2*s**3 = 0.
-1, 1
Let p(a) be the third derivative of a**7/315 + a**6/36 + 7*a**5/90 + a**4/12 - 193*a**2. Factor p(r).
2*r*(r + 1)**2*(r + 3)/3
Let k(t) be the first derivative of t**8/168 - t**7/35 + t**6/20 - t**5/30 - 6*t**2 - 2. Let n(i) be the second derivative of k(i). Factor n(m).
2*m**2*(m - 1)**3
Let w be 2/3 + (12 + -8 - (-120)/(-45)). Factor -m + 1/5*m**w - 6/5.
(m - 6)*(m + 1)/5
Let s(l) be the first derivative of l**9/1008 - 3*l**8/1400 + l**7/1400 + 13*l**3/3 + 9. Let z(a) be the third derivative of s(a). Solve z(o) = 0.
0, 1/5, 1
Let n be 152 - 167 - 137/(-9). Factor 0*j**2 - n*j**3 + 0*j + 0 + 2/9*j**4.
2*j**3*(j - 1)/9
Let a(w) = 8*w**2 - 8*w + 2. Let i be a(1). Let d = 14 - 10. Solve -4/3*r**d + 1/3*r - 5/3*r**i + 8/3*r**3 + 0 = 0 for r.
0, 1/2, 1
Let z(c) = -c**3 + 11*c**2 - 7*c - 5. Let s be z(10). Let q be (-2)/8*(5 - s). Solve 12*o**4 - q*o**2 + 8*o**3 + 5*o**5 + 7*o**4 + o**2 + 2*o**5 = 0.
-2, -1, 0, 2/7
Suppose -28/9*g**3 + 16/9*g - 64/9 + 56/9*g**2 + 2/9*g**5 - 2/9*g**4 = 0. Calculate g.
-4, -1, 2
Let p(x) be the first derivative of 5*x**3/3 - 25*x**2/2 - 30*x - 132. Factor p(g).
5*(g - 6)*(g + 1)
Let n(i) be the first derivative of i**3/12 - 19*i**2/8 + 9*i/2 - 5. Factor n(p).
(p - 18)*(p - 1)/4
Let t(p) be the third derivative of 0 + 1/6*p**6 + 55/24*p**4 + 0*p + 21*p**2 - 13/12*p**5 - 5/3*p**3. Suppose t(h) = 0. Calculate h.
1/4, 1, 2
Let x(h) = -4*h - 8. Let a be x(-4). Suppose 2*w - a*w = 0. Factor 0*l**4 + w*l**4 - 2 + l**2 - 2*l**4 + 3*l**2.
-2*(l - 1)**2*(l + 1)**2
Let f(j) be the first derivative of -2*j**7/21 - 3*j**6/10 - j**5/5 + j**4/6 - 9*j**2 + 16. Let m(w) be the second derivative of f(w). Factor m(x).
-4*x*(x + 1)**2*(5*x - 1)
Let v(u) be the first derivative of 7*u**3/6 - 113*u**2/2 + 32*u - 30. Find r such that v(r) = 0.
2/7, 32
Suppose 2*p + 3*p = -15. Let a(f) = f**5 - 4*f**3 + 3*f**2 - 3*f - 3. Let r(o) = o**3 - o**2 + o + 1. Let u(j) = p*r(j) - a(j). Factor u(y).
-y**3*(y - 1)*(y + 1)
Let o(p) be the third derivative of 1/21*p**3 + 0*p + 15*p**2 + 0 - 1/56*p**4 + 1/420*p**5. Factor o(v).
(v - 2)*(v - 1)/7
Let i(y) be the third derivative of 0*y**4 + 0*y**3 + 0 + 0*y - 19*y**2 + 1/60*y**5. Determine t, given that i(t) = 0.
0
Let o be -3*-3*(-6)/(-27). Factor 79 + 15*f**4 + 37*f**4 + 28*f + 132*f**o + 148*f**3 - 87.
4*(f + 1)**3*(13*f - 2)
Let u = -4 + 6. Let v be (16/4)/(-1*(0 - 2)). Factor w + u*w**v + w - 6*w.
2*w*(w 