u(z) be the third derivative of -z**5/210 - 5*z**4/84 - 4*z**3/21 + 25*z**2. Factor u(v).
-2*(v + 1)*(v + 4)/7
Let h(q) = q**3 + 9*q**2 + 5*q + 3. Let x(r) = -2*r**3 - 10*r**2 - 4*r - 4. Let b(d) = -4*h(d) - 3*x(d). Determine t so that b(t) = 0.
-1, 0, 4
Let l(d) be the second derivative of d**4/54 + d**3/27 - 2*d**2/9 - 7*d. Determine s, given that l(s) = 0.
-2, 1
Let p(o) be the second derivative of -o**7/105 - o**6/30 - o**5/30 + o**2/2 + 3*o. Let d(w) be the first derivative of p(w). Suppose d(c) = 0. What is c?
-1, 0
Suppose 15 = -i - 5*o, 5*i + 0*i + 2*o = -6. Factor i*a - 2/9*a**3 + 0 + 2/9*a**2.
-2*a**2*(a - 1)/9
Let d(v) be the first derivative of 2/15*v**5 + 8/3*v**3 - 3 + 0*v - v**4 - 8/3*v**2. Factor d(z).
2*z*(z - 2)**3/3
Let b be ((-16)/(-60))/((-4)/(-54)). Suppose 0 + 2/5*d**3 + b*d + 12/5*d**2 = 0. Calculate d.
-3, 0
Let g(c) be the first derivative of -2*c**5/5 - 2*c**4 - 4*c**3 - 4*c**2 - 2*c - 3. Factor g(q).
-2*(q + 1)**4
Factor 145*w + 9 + 2 - 1 + 137*w**2 - 2*w**2.
5*(w + 1)*(27*w + 2)
Let g(v) = -v**3 + 8*v**2 - v + 10. Let p be g(8). What is o in -4*o**3 - 2*o**2 + 3*o**3 + 0*o**p = 0?
-2, 0
Let r be (-2)/(-9) - 64/(-1008). Suppose 2/7 + 4/7*n + r*n**2 = 0. What is n?
-1
Suppose 2*g = 6*g + 4*m, -5*m = 0. Let v(n) be the third derivative of -1/210*n**7 + 0*n - 1/360*n**6 + g*n**4 + 1/90*n**5 + 0 + 0*n**3 + n**2. Factor v(h).
-h**2*(h + 1)*(3*h - 2)/3
Determine h, given that -31*h**4 + 52*h + 36 - 11*h**4 - 243*h**3 + 81*h**2 + 116*h = 0.
-6, -1/2, -2/7, 1
Factor 128/9*n + 2/9*n**3 + 0 + 32/9*n**2.
2*n*(n + 8)**2/9
Suppose 0*u + 32 = -4*u. Let s = 10 + u. Let -2/11*t**4 - 2/11*t**3 + 2/11*t**s + 2/11*t**5 + 0 + 0*t = 0. What is t?
-1, 0, 1
Let r(o) be the first derivative of -16/5*o + 2/25*o**5 + 4/5*o**2 + 4/5*o**3 + 1 - 1/2*o**4. Factor r(j).
2*(j - 2)**3*(j + 1)/5
Suppose s - 17 = 3*v, -s - 4 - 14 = 4*v. Suppose 1/4*x**s + 0 - 1/4*x = 0. What is x?
0, 1
Let w(s) = -2*s**2 + 3*s - 3. Let p(u) = -5*u**2 + 9*u - 8. Let z(t) = -3*p(t) + 8*w(t). Factor z(i).
-i*(i + 3)
Let g(c) be the first derivative of 0*c**2 + 2/3*c**3 + 3/2*c**4 + 6/5*c**5 + 4 + 1/3*c**6 + 0*c. Determine a, given that g(a) = 0.
-1, 0
Suppose 5*w = 5*n + 50, w - 33 = 3*n + 1. Let a be (-9)/n + (-2)/4. Factor 0 + a*y**3 + y - y**2.
y*(y - 2)**2/4
Let h(c) be the first derivative of -c**7/35 - c**6/60 + c**5/10 + c**4/12 - c**2/2 - 2. Let a(y) be the second derivative of h(y). Factor a(x).
-2*x*(x - 1)*(x + 1)*(3*x + 1)
Let l(y) be the second derivative of 1/2*y**2 + y + 0*y**3 + 0 + 1/84*y**4 + 1/210*y**5. Let z(q) be the first derivative of l(q). Factor z(m).
2*m*(m + 1)/7
Suppose -5 = -3*w + 2*w. Suppose w*m - 2 = 8. Factor 1 - 5*l**3 + 2*l**4 - 5*l + 0 + 9*l**m - 2*l**3.
(l - 1)**3*(2*l - 1)
Suppose -z = 5*v - 37, -5*v - 3*z + 51 = 20. Suppose d - v = -d. Factor 0*y + 0*y**3 + 4/7*y**2 - 2/7*y**d - 2/7.
-2*(y - 1)**2*(y + 1)**2/7
Let q be (-4)/(-1) + (-6 - -2). Factor 4*l + 5 + q*l - 8 - l**2.
-(l - 3)*(l - 1)
Let r be 90/27*2/10. Let z be ((-4)/30)/((-3)/15). Let 0*n + 0 - r*n**2 - z*n**3 = 0. What is n?
-1, 0
Let m(o) = o**2 - 6*o + 5. Let u be m(5). Suppose i - 4*i = u. Let 0 + 1/4*f**5 + 0*f**2 + 0*f**4 + i*f - 1/4*f**3 = 0. Calculate f.
-1, 0, 1
Let l(f) be the first derivative of -5*f**4/16 + 5*f**3/6 + 15*f**2/8 + 7. Factor l(h).
-5*h*(h - 3)*(h + 1)/4
Let w be (2871/77)/9 - (4 + 0). Determine l so that 0*l**2 + 0*l + 0 + 2/7*l**3 - w*l**4 = 0.
0, 2
Suppose 2*j - 22 = -2*a, -2*j = -2*a - 35 + 9. Suppose -6*f**2 - 7*f**4 - 7*f**4 + 10*f**4 - 12*f + 9 + f**4 + j*f**3 = 0. What is f?
-1, 1, 3
Let x be -4 + (-2 - 0) + 40/6. Suppose x*y + 0 - 2/3*y**3 + 2*y**2 - 2*y**4 = 0. Calculate y.
-1, -1/3, 0, 1
Let p(m) be the first derivative of -2*m**6/15 + m + 8. Let g(j) be the first derivative of p(j). Factor g(l).
-4*l**4
Let a(w) be the third derivative of 0*w**4 + 1/120*w**5 + 0 - 1/12*w**3 + 4*w**2 + 0*w. Factor a(t).
(t - 1)*(t + 1)/2
Determine w, given that 0 - 8*w - 1/2*w**5 - 3*w**4 - 1/2*w**3 + 12*w**2 = 0.
-4, 0, 1
Determine w, given that 2*w + 44*w**4 + 9*w**2 + w - 3*w**3 - 6 - 47*w**4 = 0.
-2, -1, 1
Let v(k) be the first derivative of 0*k - 3 + 0*k**2 - 1/6*k**3 + 9/16*k**4. Factor v(o).
o**2*(9*o - 2)/4
Let x be 2/((-3 - -1)/(-2)). Determine v, given that -4*v + v - 3*v**3 - 2 + 4*v**2 + 4*v**x = 0.
-1/3, 1, 2
Let w(h) be the third derivative of h**7/105 - h**5/15 + h**3/3 - 4*h**2. Let w(k) = 0. Calculate k.
-1, 1
Let k = -550 + 552. Let n = -1 - -1. Factor n + 0*f - 2/3*f**3 - 2/3*f**k.
-2*f**2*(f + 1)/3
Let l(r) be the first derivative of r**6/105 + r**5/14 + 4*r**4/21 + 4*r**3/21 - 4*r - 1. Let i(k) be the first derivative of l(k). Solve i(t) = 0.
-2, -1, 0
Suppose 57 = -8*p + 89. Factor 67/4*b**2 + 37/4*b**p + 7/4*b**5 + 7*b + 73/4*b**3 + 1.
(b + 1)**3*(b + 2)*(7*b + 2)/4
Solve 7*u**2 + 4*u + 0*u - 5*u**2 = 0 for u.
-2, 0
Let s be 3 - (-1)/3*0. Factor 16 + 0*o**2 - o**2 - 16 + s*o.
-o*(o - 3)
Let z be (-56)/(-6) + (5 - 2). Let v = z + -11. Let 1/3*j**2 + v*j + 4/3 = 0. What is j?
-2
Suppose 8/7 - 8/7*q**2 - 2/7*q**3 + 2/7*q = 0. What is q?
-4, -1, 1
Let g = 96 - 92. Factor 5/2*v**4 + 1/2*v**2 + 0 + g*v**3 - v.
v*(v + 1)**2*(5*v - 2)/2
Let t(b) be the second derivative of -1/24*b**4 + 4*b + 1/40*b**5 + 0*b**2 + 0 - 1/6*b**3. Find c such that t(c) = 0.
-1, 0, 2
Factor 3/4*i**2 + 3/4*i**3 + 0 + 0*i.
3*i**2*(i + 1)/4
Let g(x) = x**2 + 15*x - 14. Let r be g(-16). Factor 0 - 2/11*b**r - 2/11*b.
-2*b*(b + 1)/11
Let i(v) = -v**2 + 2*v + 8. Let n(f) = 3*f**2 - 6*f - 24. Let d(h) = -21*i(h) - 6*n(h). Find o such that d(o) = 0.
-2, 4
Let s = 292/5 + -58. Suppose 3*f = 4*q - 16, 4*q - 4 = 3*q. Factor 0 + f*c + s*c**3 + 0*c**2 - 2/5*c**4.
-2*c**3*(c - 1)/5
Factor 12/5*s**3 + 3/5*s**4 - 36/5*s + 27/5 - 6/5*s**2.
3*(s - 1)**2*(s + 3)**2/5
Let p(x) be the third derivative of 1/32*x**4 - 5*x**2 + 0*x - 1/24*x**3 + 0 - 1/80*x**5 + 1/480*x**6. Suppose p(m) = 0. What is m?
1
Let t be (6/8*4)/1. Let b(w) be the third derivative of 0*w - 1/3*w**t + 0 + 1/15*w**5 - 1/105*w**7 + 0*w**6 + w**2 + 0*w**4. Determine y, given that b(y) = 0.
-1, 1
Let n(r) be the first derivative of 0*r**2 + 0*r - 1/12*r**3 + 2. Factor n(c).
-c**2/4
Factor 0 + 6/7*z - 2/7*z**2.
-2*z*(z - 3)/7
Let w(a) be the second derivative of a**4/12 + a**3/6 + 7*a. Determine b, given that w(b) = 0.
-1, 0
Let s be 32 + 9/(3 - 6). Let x = s - 85/3. Factor -2/3*f**2 + 4/3 + x*f.
-2*(f - 2)*(f + 1)/3
Let l = 12 + -8. Factor 9*t**2 + 2*t - 5*t + 5*t**4 - 2*t**l - 9*t**3.
3*t*(t - 1)**3
Let k(i) = -13*i - 13. Let z be k(-1). Solve -1/5*a + 1/5*a**3 - 4/5*a**4 + 4/5*a**2 + z = 0 for a.
-1, 0, 1/4, 1
Let z(m) be the second derivative of 2*m**7/15 - 2*m**6/15 - 2*m**5/25 - 2*m. Factor z(i).
4*i**3*(i - 1)*(7*i + 2)/5
Let x(z) = -2*z - 5. Let u(l) = -l - 1. Let q(h) = u(h) - x(h). Let t be q(0). Suppose w - w**t + w**2 + 13 - 13 - w**3 = 0. What is w?
-1, 0, 1
Let g(y) = y**4 - 4*y**3 + 9*y**2 + 10*y. Let t(m) = 9*m**4 - 33*m**3 + 72*m**2 + 81*m. Let p(h) = -33*g(h) + 4*t(h). Suppose p(x) = 0. Calculate x.
-1, 0, 2
Let -1/5 + 1/10*g**4 - 3/10*g + 3/10*g**3 + 1/10*g**2 = 0. What is g?
-2, -1, 1
Let h = 58 - 55. Factor 0 + 1/4*b**h + 1/2*b**2 + 0*b.
b**2*(b + 2)/4
Let h(f) be the second derivative of -f**5/20 + f**4/4 - 2*f**2 - 14*f. Factor h(l).
-(l - 2)**2*(l + 1)
Let n(y) be the second derivative of 3*y**5/80 - 3*y**4/16 + 3*y**3/8 - 3*y**2/8 - 21*y. Factor n(b).
3*(b - 1)**3/4
Suppose -2*v + 2*h + 2 = 6*h, -3*v = -5*h - 3. Let t be 2*v/3*3. Suppose 0 + 1/4*c - 1/4*c**t = 0. What is c?
0, 1
Let q(n) = n**3 - 3*n**2 + n - 3. Let l be q(3). Suppose -4*k + l = -12. Factor 3 - k*i**2 + 3*i - 4*i**3 + 2*i**3 - 3*i**3 + 2*i**3.
-3*(i - 1)*(i + 1)**2
Let h(i) be the third derivative of -i**6/780 - i**5/195 - i**4/156 - 11*i**2. Let h(t) = 0. What is t?
-1, 0
Let h(i) be the second derivative of 1/6*i**3 + 1/12*i**4 - 3*i + 0*i**2 - 1/30*i**6 + 0 - 1/20*i**5. What is m in h(m) = 0?
-1, 0, 1
Let n(b) = b**3 + b**2 + b - 28. Let f be n(0). Let h be 6/(-3) + f/(-12). Factor h*q**3 + 0*q - 1/3*q**4 + 2/3*q**2 + 0.
-q**2*(q - 2)*(q + 1)/3
Let c be 4 + 13/(2 + -3). Let u be (2 - 0)/(1 - c). Factor -u*f**2 - 1/5*f**3 + 0 + 2/5*f.
-f*(f - 1)*(f + 2)/5
Factor 0 + 3/8*r**2 + 3/8*r**3 - 3/4*r.
3*r*(r - 1)*(r + 2)/8
