tive of -o**6/660 - o**5/330 + o**4/132 - 2*o**3/3 - 9*o**2/2 - 3*o + 1. Let d(j) be the second derivative of r(j). Factor d(k).
-2*(k + 1)*(3*k - 1)/11
Let b be (-2)/(-8) - (-1625)/1300. Solve -3/2 + b*l**2 - 3/4*l**3 + 3/4*l = 0.
-1, 1, 2
Let t(v) be the second derivative of -v**4/36 - v**3/3 + 2*v - 34. Factor t(d).
-d*(d + 6)/3
Suppose 2*o - 1 = 5*u + 6*o, 4*u = 2*o + 20. Determine l so that 20*l + 3 + 1 + 2 - 8*l**u - 18*l**2 = 0.
-3, -1/4, 1
Let j = 41 - 9. Let n be j - (2/1 - 2). Factor 4*l - 2*l**2 - 11*l**2 - 8 - n*l + l**2.
-4*(l + 2)*(3*l + 1)
Let d(f) be the second derivative of -f**5/4 + 41*f**4/6 + 53*f**3/6 - 17*f**2 + 46*f + 1. Factor d(y).
-(y - 17)*(y + 1)*(5*y - 2)
Factor 18/11*r**2 + 10/11*r + 0.
2*r*(9*r + 5)/11
Suppose -9 = -7*y + 26. Suppose -a + y*a - 8 = 0. Let 15/4*r**a + r - 1 = 0. What is r?
-2/3, 2/5
Let -17*v + 129*v**4 + 30*v + 4*v**3 - 133*v**4 - 13*v + 48*v**2 = 0. Calculate v.
-3, 0, 4
Suppose 5 = 2*g + w, 4*g + 2 + 8 = 2*w. Suppose -5*x + 4*a - 1 = g, 3*a + 2*a - 32 = -4*x. Factor 2*v**2 - 9 - 2*v**2 - 3*v**2 - 3*v + x*v**3 - 12*v.
3*(v - 3)*(v + 1)**2
Let q(v) be the third derivative of 4*v**2 + 10/3*v**3 + 0*v + 5/8*v**4 + 0 - 1/12*v**5. Factor q(a).
-5*(a - 4)*(a + 1)
Suppose 74*o + 81/2*o**3 - 180*o**2 - 8 = 0. What is o?
2/9, 4
Let p(q) = -3*q**3 + q**2 + q - 1. Let m be p(-1). Find w such that -25*w**3 - 10*w + 5*w**m + 28*w**2 + 2*w**2 = 0.
0, 2/5, 1
Let j = -2861/18 + 159. Let z(a) be the second derivative of -3*a + 1/45*a**6 + j*a**4 + 0 + 0*a**3 + 0*a**2 - 1/15*a**5. Factor z(l).
2*l**2*(l - 1)**2/3
Let m(b) be the first derivative of -30*b - 155/2*b**2 - 145/3*b**3 - 5*b**4 - 13. Factor m(n).
-5*(n + 1)*(n + 6)*(4*n + 1)
Suppose 4*l + m + 7 = 149, -8 = -4*m. Factor 18*y + 17*y - 28*y**3 + 15 + 25*y**2 + 68*y**3 - l*y**3.
5*(y + 1)**2*(y + 3)
Suppose 2*b = -b + 12. Let k be (-32)/(-20)*(b - -1). Solve 2*u + 14*u**3 - 7*u**3 - u**2 - k*u**3 = 0.
-2, 0, 1
Let k(h) be the third derivative of -h**6/1200 + 13*h**5/600 - h**4/6 + 3*h**3/5 - 2*h**2 - 26. Factor k(l).
-(l - 9)*(l - 2)**2/10
Let i = 14 - 43. Let z = 29 + i. Suppose -2/5*f**2 + 0 + z*f = 0. What is f?
0
Let h(v) be the third derivative of v**8/112 - 8*v**7/35 + 51*v**6/40 - 8*v**5/5 - 13*v**4/2 + 24*v**3 - 67*v**2. What is u in h(u) = 0?
-1, 1, 2, 12
Find n, given that 42*n**2 + 5 - 84*n**2 + 47*n**2 - 10*n = 0.
1
Let b(r) be the first derivative of -4*r**5/15 + r**4 + 4*r**3/3 - 14*r**2/3 - 8*r - 43. Solve b(f) = 0 for f.
-1, 2, 3
Solve -20/7*v - 1/7*v**2 + 0 = 0.
-20, 0
Let h(o) = o**3 - 6*o**2 + 3*o - 267. Let b be h(9). Find v such that -12/5 + 42/5*v**b + 18/5*v + 72/5*v**2 = 0.
-1, 2/7
Let j(b) be the first derivative of -4*b**3/3 + 32*b**2 - 256*b - 145. Determine n so that j(n) = 0.
8
Factor -16*k**2 + 41*k**2 + 32*k**3 - 37*k**3 + 19 - 40*k + 1.
-5*(k - 2)**2*(k - 1)
Let j(y) be the third derivative of y**5/140 - 61*y**4/56 + 59*y**3/7 - 976*y**2. Suppose j(v) = 0. Calculate v.
2, 59
Suppose -2*f = -4*j - 24, -f + 5*j = j - 20. Let x be (-30)/f*4/(-6). Solve 3*q**2 - 3*q + 8 - x - 3*q = 0 for q.
1
Let p(o) be the second derivative of o**5/70 + 5*o**4/42 - 2*o**3/7 - 5*o. Factor p(x).
2*x*(x - 1)*(x + 6)/7
Let c(q) be the third derivative of 0*q + 1/12*q**4 + 0 - 6*q**2 - 1/90*q**5 - 2/9*q**3. Solve c(i) = 0.
1, 2
Let j(k) be the third derivative of k**8/1512 - 4*k**7/315 + k**6/15 + 67*k**2. Factor j(g).
2*g**3*(g - 6)**2/9
Let f(b) be the second derivative of b**6/90 - b**5/45 - b**4/9 - 7*b**2/2 - 14*b. Let j(s) be the first derivative of f(s). Factor j(z).
4*z*(z - 2)*(z + 1)/3
Factor 0 + 2/3*z**3 + 56/3*z + 32/3*z**2.
2*z*(z + 2)*(z + 14)/3
Let p(j) be the first derivative of j**4/4 + j**3/3 + j - 8. Let d(c) = -21*c**3 - 12*c**2 + 3*c - 24. Let v(f) = d(f) + 18*p(f). Factor v(b).
-3*(b - 2)*(b - 1)*(b + 1)
Let c = 9323 - 9321. Factor 0 + 4*w**3 + 0*w**2 - 16/3*w**4 - 2/3*w + c*w**5.
2*w*(w - 1)**3*(3*w + 1)/3
Determine h so that 4*h - 6/7*h**2 + 2/7*h**4 - 16/7 - 8/7*h**3 = 0.
-2, 1, 4
Suppose 2*c = 7*c + 3*s - 48, s = -4*c + 37. Let g be 3/((c/(-10))/(5/(-25))). Determine h so that 4/3*h**4 - g*h**2 - 4/3*h**3 - 1/3*h**5 - 2/3 + 5/3*h = 0.
-1, 1, 2
Let t = -2639 + 2641. Solve -5/2*o**t + 0*o + 0 - 5*o**3 - 5/2*o**4 = 0.
-1, 0
Let t(d) be the third derivative of -d**10/1134000 + d**5/15 - 8*d**2. Let n(p) be the third derivative of t(p). Suppose n(r) = 0. Calculate r.
0
Let b = -7 - -5. Let q(y) = -y + 1. Let c(k) be the first derivative of -2*k**3/3 + 4*k**2 - 2*k - 12. Let h(s) = b*q(s) - c(s). Suppose h(g) = 0. Calculate g.
0, 3
Suppose 5*o - 7*o + 40 = 0. Let 47*f**3 - 97*f**4 + 37*f**4 + 105*f**2 - 100*f - 75*f**4 + 43*f**3 + o = 0. What is f?
-1, 1/3, 2/3
Let d(u) be the second derivative of -2*u**7/21 - 4*u**6/15 + 2*u**4/3 + 2*u**3/3 + 2*u + 24. Solve d(g) = 0.
-1, 0, 1
Suppose 3*o - h = 14, -13*o + 23 = -9*o + 3*h. Find p, given that -o - 35/2*p**2 - 45/2*p = 0.
-1, -2/7
Find c, given that -1448*c**2 + 300*c - 776*c**2 - 1208*c**2 - 9 + 385*c**2 + 547*c**2 = 0.
3/50
Let o(z) = -z**2 + 17*z + 4. Let a be o(17). Suppose -5*i**a - 597*i**2 + 15*i**3 + 627*i**2 + 13*i - 53*i = 0. What is i?
-2, 0, 1, 4
Let x(y) be the first derivative of -37 + 7/8*y**5 + 11/48*y**6 + 0*y + 1/8*y**2 + 39/32*y**4 + 17/24*y**3. Let x(u) = 0. What is u?
-1, -2/11, 0
Let l(b) = b**3 + b**2 + 5*b + 21. Let i be l(0). Suppose 3*a + 9 - i = 0. Determine g so that 3/5*g**3 + 0 - 1/5*g**5 + 0*g**a + 0*g - 2/5*g**2 = 0.
-2, 0, 1
Let z(m) = -m**2 - 5*m - 6. Let n(o) = -o**3 + 4*o + 5. Let d(v) = v**2 - v - 6. Let x be d(0). Let p(c) = x*n(c) - 5*z(c). Let p(y) = 0. What is y?
-1/2, -1/3, 0
Suppose -2/3*s**2 - 1058/3 + 92/3*s = 0. What is s?
23
Let s be -36*(-3)/9*2 - 4. Factor -s*j**2 + 0*j**2 + 18*j**4 - 12*j**2 - 22*j**3 - 7*j + 15*j.
2*j*(j - 2)*(j + 1)*(9*j - 2)
Let r(j) be the second derivative of -1/10*j**5 + 0*j**2 + 0*j**4 + 0*j**3 + 31*j + 0. What is b in r(b) = 0?
0
Let t(p) be the third derivative of p**5/30 - 37*p**4/12 - 38*p**3/3 + 31*p**2. What is h in t(h) = 0?
-1, 38
Let w(h) be the second derivative of -h**8/1680 - h**7/315 + h**4/3 + 14*h. Let n(j) be the third derivative of w(j). Factor n(b).
-4*b**2*(b + 2)
Let r(z) be the third derivative of -5*z**2 - 1/9*z**4 + 0*z + 0 + 1/45*z**5 + 0*z**3 - 1/720*z**6. Factor r(s).
-s*(s - 4)**2/6
Let p be -1 + (-36)/(7 - 16). Let y(b) be the first derivative of 14 + 0*b - 5/3*b**p + 5*b**2. Let y(v) = 0. Calculate v.
0, 2
Factor 3/5*x**5 + 0 + 0*x + 3*x**4 + 9/5*x**2 + 21/5*x**3.
3*x**2*(x + 1)**2*(x + 3)/5
Let u be 82/(-12)*3*4. Let n = 82 + u. Solve 2/3*o + n - 16/3*o**4 - 4*o**3 + 2*o**2 = 0 for o.
-1, -1/4, 0, 1/2
Let l(x) = x**4 - x**3 - x**2 + 2. Let m(i) = -6*i**4 - 14*i**3 - 14*i**2 - 5*i - 2. Let b(c) = l(c) + m(c). Suppose b(k) = 0. Calculate k.
-1, 0
Let m = 15 - -3. Let -18*u**3 + 7*u**2 - m*u**5 - 33*u**4 + 8*u**2 - 18*u**2 = 0. Calculate u.
-1, -1/2, -1/3, 0
Let x(r) be the first derivative of r**3 + 15*r**2/2 + 12*r + 15. Let h(j) = j + 1. Let a(g) = 6*h(g) - x(g). Suppose a(z) = 0. Calculate z.
-2, -1
Suppose -1207*m + 1233*m = 40 + 64. Determine b, given that 0 + 8*b**2 - 9*b**m + 9/2*b**5 - 2*b - 7/2*b**3 = 0.
-1, 0, 1/3, 2/3, 2
Let o = -1427 - -1428. Factor 3*r**3 - o - 35/4*r**2 + 6*r.
(r - 2)*(3*r - 2)*(4*r - 1)/4
Let p(x) be the first derivative of -5*x**8/2016 + x**7/252 + x**6/144 - x**5/72 + 3*x**2/2 + 13. Let q(j) be the second derivative of p(j). Factor q(m).
-5*m**2*(m - 1)**2*(m + 1)/6
Suppose 233*i = -35*i - 53*i + 963. Determine n, given that 5/4*n**i + 75/4*n + 125/4 - 45/4*n**2 = 0.
-1, 5
Determine w, given that -78/5*w**2 + 144*w + 160 + 2/5*w**3 = 0.
-1, 20
Let t(k) be the first derivative of -2*k**3/7 + 51*k**2/7 - 44. Factor t(g).
-6*g*(g - 17)/7
Let h(z) = -2*z**3 - z**2 - 2. Let g be h(-2). Suppose 2*x = 4*x - g. Find a, given that 3*a**3 + 6 - 4*a**5 + 0*a**x - 2 - 8*a**2 + 5*a**3 + 4*a**4 - 4*a = 0.
-1, 1
Find v, given that -2/11*v**3 + 24/11*v**2 + 26/11*v + 0 = 0.
-1, 0, 13
Let z = 1569/4 + -392. Let c(t) be the third derivative of -2*t**2 + z*t**4 + 0*t**3 - 1/20*t**5 + 0 + 0*t. Factor c(p).
-3*p*(p - 2)
Suppose 3*y = -4*h + y + 9238, 0 = 2*h + 2*y - 4618. Suppose -2310 - 2*s**3 + 0*s**3 + h = 0. What is s?
0
Let f(l) be the third derivative of l