/3 + i**2/2 + 5*i - 3. Let b(q) = -13*q**3 - 9*q**2 + 2*q + 9. Let v(f) = 6*b(f) - 11*t(f). Factor v(d).
-(d - 1)**2*(d + 1)
Let k(l) be the second derivative of l**6/120 - l**5/60 + 3*l**2/2 + 2*l. Let h(g) be the first derivative of k(g). Factor h(q).
q**2*(q - 1)
Suppose j + 8 = -3. Let g = 11 + j. Factor 6/5*c**2 - 6/5*c**3 - 2/5*c + g + 2/5*c**4.
2*c*(c - 1)**3/5
Let r(t) be the first derivative of 0*t - 4/9*t**3 + 1/12*t**4 + 2/3*t**2 + 3. Factor r(s).
s*(s - 2)**2/3
Let d(c) = -c**3 - 4*c**2 - c + 6. Let n be d(-3). Let r(x) be the second derivative of 3/20*x**5 + n + 2*x**2 + 0*x**3 + 3*x - 7/12*x**4. Factor r(j).
(j - 2)*(j - 1)*(3*j + 2)
Let o = 2705/14 + -2311/12. Let h = o + 1/28. Factor 0*j**2 - h*j**3 + 0 + 0*j.
-2*j**3/3
Let h(p) = -p**3 + 17*p**2 + 18*p. Let r be h(18). Suppose 0*j**2 + r + 0*j - 2/9*j**4 + 0*j**3 = 0. What is j?
0
Let d(f) be the first derivative of -2*f**3/39 + 4*f**2/13 - 6*f/13 - 32. Factor d(j).
-2*(j - 3)*(j - 1)/13
Let x(m) be the second derivative of -1/60*m**5 - 1/2*m**2 + 0 + 2*m + 1/3*m**3 - 1/24*m**4. Let p(k) be the first derivative of x(k). Factor p(o).
-(o - 1)*(o + 2)
Suppose -52 = -3*w + 2*c - 7, 4*w + c - 71 = 0. Solve -d + 4*d**2 + 0*d**5 + 11*d**3 - w*d**3 + 4*d**4 - d**5 = 0.
0, 1
Let c(w) be the second derivative of 0 + 0*w**2 + 0*w**3 - 1/84*w**4 - 3*w - 1/140*w**5. Factor c(n).
-n**2*(n + 1)/7
Let y(a) = 9*a**4 - 24*a**3 + 29*a**2 - 6*a + 4. Let h(q) = -10*q**4 + 25*q**3 - 30*q**2 + 5*q - 5. Let i(p) = -4*h(p) - 5*y(p). Find w such that i(w) = 0.
0, 1, 2
Let c(r) be the third derivative of 1/18*r**4 + 4*r**2 + 0*r + 0*r**3 + 0 - 1/90*r**5. Factor c(v).
-2*v*(v - 2)/3
Let u be 55/280 - 6/(-16). Let v(h) be the first derivative of -u*h + 1/14*h**4 + 0*h**3 + 3 - 3/7*h**2. Let v(s) = 0. What is s?
-1, 2
Let h(d) be the first derivative of 1 - 2/9*d**3 - 1/90*d**5 + 1/12*d**4 - 1/2*d**2 + 0*d. Let o(i) be the second derivative of h(i). Factor o(t).
-2*(t - 2)*(t - 1)/3
Let f = 4/369 + 2932/1845. Suppose 5*y = 3*h + 25, -5*h + 0*h = -2*y + 29. What is o in -8/5*o - 2/5*o**y - f = 0?
-2
Let r(v) = -3*v**3 + 3*v**2 - 10*v - 1. Let k(l) = 2 + 2*l**3 - 3*l + 13*l - 9*l**2 + 7*l**2. Let t(o) = 5*k(o) + 4*r(o). Factor t(p).
-2*(p - 3)*(p + 1)**2
Let x(d) be the first derivative of -d**4/16 - 3*d**3/4 - 27*d**2/8 + 5*d + 1. Let y(m) be the first derivative of x(m). Factor y(s).
-3*(s + 3)**2/4
Solve 0 - 2/7*b**2 + 2/7*b = 0 for b.
0, 1
Let j be ((-1)/6)/(-4*8/48). Factor -1/2*w**3 + 0 - j*w**2 + 0*w - 1/4*w**4.
-w**2*(w + 1)**2/4
Let y(f) = 16*f**5 + 16*f**4 + f**3 - 21*f**2 - 6*f + 5. Let m(u) = -3*u**5 - 3*u**4 + 4*u**2 + u - 1. Let h(t) = 22*m(t) + 4*y(t). Factor h(x).
-2*(x - 1)**2*(x + 1)**3
Let l be 4/2 + 2/(-2). Let x(u) = u**2 + 1. Let s(b) = -5*b**2 - 4*b - 3. Let i(w) = l*s(w) + 3*x(w). Factor i(v).
-2*v*(v + 2)
Suppose 6 = 5*c - 2*c. Determine i so that 6*i**3 + 57*i**2 - 47*i**2 + 2*i + c*i = 0.
-1, -2/3, 0
Let q(k) = -k**2 - 10*k - 1. Let v be q(-9). Let i be (1/5)/(v/30). What is x in -3*x + i*x**2 + 3 = 0?
2
Let -14*y**4 + 2*y**2 - 11*y**4 - 4 + 6*y - 6*y**3 + 27*y**4 = 0. Calculate y.
-1, 1, 2
Let q(h) be the first derivative of h**7/189 - h**5/45 + h**3/27 - 3*h - 7. Let r(d) be the first derivative of q(d). What is o in r(o) = 0?
-1, 0, 1
Solve -28*w**4 - 48*w**2 - 10 - 6*w**5 - 7 - 52*w**3 - 22*w + 13 = 0 for w.
-1, -2/3
Let r(s) be the first derivative of -3*s**4/8 - s**3/2 + 8. Factor r(b).
-3*b**2*(b + 1)/2
Suppose v - 11 = -3*p, 2*v = 3*p + 2*p - 22. Factor 2*o**4 - 5*o + 4*o**4 - 2 + p*o**3 - 3*o**4 - 2*o**2 + o**5 + o**4.
(o - 1)*(o + 1)**3*(o + 2)
Let a(v) be the second derivative of v**5/20 - v**4/3 + 3*v. Factor a(d).
d**2*(d - 4)
Suppose 12 = 2*w + w. Suppose 2*m - 14 = -3*l, m + 5 = 4*l - 10. Factor l*x - x**2 - 3 - x + w - 3.
-(x - 2)*(x - 1)
Let l be (-138)/(-27) + 12/54. What is n in 196/3*n**5 - l*n**2 - 28*n**4 - 32*n**3 + 0 + 0*n = 0?
-2/7, 0, 1
Suppose -n + 4*d = 4*n - 32, 0 = n - 3*d - 13. Let z(b) be the second derivative of -1/2*b**2 + b + 2/3*b**3 - 1/4*b**n + 0. Suppose z(g) = 0. Calculate g.
1/3, 1
Suppose -7*f = -3*f - 60. Let s = f + -10. Factor 0 + 0*l - 1/2*l**s - 1/2*l**4 + 1/2*l**3 + 1/2*l**2.
-l**2*(l - 1)*(l + 1)**2/2
Factor -320*k + 328*k**2 - 288 - 572*k + 105*k - 28*k**3 - 125*k.
-4*(k - 6)**2*(7*k + 2)
Determine a, given that 30*a**3 - 6*a**5 - 24*a + 16/3 - 20/3*a**2 + 4/3*a**4 = 0.
-2, -1, 2/9, 1, 2
Let y(j) = -3*j**2 + j + 7. Let b(t) = t**2 - 2. Suppose -f + 2*x = -3*x + 27, 2*f + 3*x + 2 = 0. Let v(d) = f*b(d) - 2*y(d). Determine k, given that v(k) = 0.
-2, 0
Suppose -2*v = 2 - 8. Suppose v*y - 2 = 7. Factor 4*p**5 - 2*p**3 - p + 2*p + p**4 + 1 - 2*p**2 - y*p**5.
(p - 1)**2*(p + 1)**3
Let -17*l**2 + 1 - 7*l**2 - 69*l**3 + 73*l**3 - 4*l + 23 = 0. What is l?
-1, 1, 6
Let j(w) = 3*w**5 - 15*w**4 + 45*w**3 - 39*w**2 + 18*w. Let f(s) = -s**4 - s. Let t(b) = 6*f(b) + j(b). Suppose t(r) = 0. Calculate r.
0, 1, 4
Let v = 149 + -5363/36. Let d(t) be the second derivative of -1/18*t**3 + 0 - v*t**4 + 0*t**2 - 2*t. Factor d(q).
-q*(q + 1)/3
Let k(d) = 2*d - 38. Let v be k(21). Let n(y) be the third derivative of -1/2*y**3 + 0*y + 1/4*y**v + 3*y**2 + 3/20*y**5 + 0. Factor n(b).
3*(b + 1)*(3*b - 1)
Let s(z) = z - 3. Let r be s(8). Find u such that 10*u**3 - 12*u**3 + r*u + 2*u**2 - 2*u**4 - 3*u = 0.
-1, 0, 1
Let h(z) be the third derivative of -1/90*z**6 + 0 + 0*z**3 + 1/36*z**4 - 1/90*z**5 + 0*z - 4*z**2. Factor h(d).
-2*d*(d + 1)*(2*d - 1)/3
Let f(b) be the first derivative of b**5/15 - 5*b**4/6 + 4*b**3 - 9*b**2 + 9*b + 3. Factor f(p).
(p - 3)**3*(p - 1)/3
Let n be ((-12)/(-5))/((-6)/(-20)). Let x be (6/n)/((-3)/(-2)). Factor -x*u + 1/2*u**3 - 1/2*u**4 + 1/2*u**2 + 0.
-u*(u - 1)**2*(u + 1)/2
Let n be 75/(-50)*(-1 + -1). Let f(z) be the first derivative of -1/9*z**2 + 2/27*z**n + 0*z + 3. Factor f(b).
2*b*(b - 1)/9
Suppose -4 = 2*w - 6*w. Solve -4*n**2 + w - 28*n - 65 + 3*n - 7*n = 0 for n.
-4
Let d(q) = -q**3 - 27*q**2 + 58*q + 3. Let l be d(-29). Suppose -l - 75/4*p**2 + 15*p = 0. Calculate p.
2/5
Let n be (6/90)/((-1)/(-3)). Let q(w) be the second derivative of 0 + 1/30*w**3 - 2/15*w**4 + n*w**2 - w + 1/20*w**5. Factor q(k).
(k - 1)**2*(5*k + 2)/5
Factor 0*t + 0*t**2 + 0*t**4 - 1/3*t**3 + 1/3*t**5 + 0.
t**3*(t - 1)*(t + 1)/3
Let z(h) = h**3 - 5*h**2 + 8. Let y(v) = v. Let a(l) = 4*y(l) + 2*z(l). Factor a(s).
2*(s - 4)*(s - 2)*(s + 1)
Suppose 0*a - 4*a = -3*s + 12, 0 = 3*a + 9. Factor 2*h**2 - 45*h**4 + s*h**3 + 2*h**3 + 43*h**4 - 3*h**5 + h**5.
-2*h**2*(h - 1)*(h + 1)**2
Let f(x) = -x**2 + 3*x + 2. Let y be (-2)/(-3) + 14/6. Let s be f(y). Suppose -2*n**s + 2 + n - 1 - 2*n**3 - 2*n**4 + n**5 + 3*n**4 = 0. What is n?
-1, 1
Factor 12 + 23*o - 94*o**3 + 17*o + 0*o**2 + 70*o**3 + 4*o**2.
-4*(o + 1)*(2*o - 3)*(3*o + 1)
Let r(u) = 4*u**2 + 2*u - 2. Let i(f) = 3*f**2 + f - 2. Let o(c) = 6*i(c) - 5*r(c). Factor o(t).
-2*(t + 1)**2
Let o be ((-1)/(30/(-9)))/((-24)/(-20)). Factor -1/4*p**2 + 0 - o*p.
-p*(p + 1)/4
Factor 4*y + y**3 - 3*y**2 + 4*y**2 - 5*y**4 - 5*y + 4*y**4.
-y*(y - 1)**2*(y + 1)
Let j(z) = -3 - z + 1 - z**2 + 4 - 3. Let f(w) = -9*w**2 - 3*w - 6. Let n(t) = f(t) - 6*j(t). Factor n(r).
-3*r*(r - 1)
Solve 4*d - d**3 + 6*d**4 + 6*d**2 - 20*d**2 + 5*d**3 = 0.
-2, 0, 1/3, 1
Let u(p) be the second derivative of -p**4/15 + 8*p**3/15 + 2*p**2 - 13*p. Determine v, given that u(v) = 0.
-1, 5
Let b(f) be the third derivative of -f**6/60 - f**5/10 - 3*f**2. Find o, given that b(o) = 0.
-3, 0
Let n be 1/(-9) + (-6)/(-52 - 2). Factor n*m + 2/5*m**2 - 2/5.
2*(m - 1)*(m + 1)/5
Let k = -49/60 + 29/12. Factor 12/5*c**2 + 2/5 - 8/5*c + 2/5*c**4 - k*c**3.
2*(c - 1)**4/5
Suppose -3*o = -5*c + 25, 4*c - 20 = -o - o. Suppose 0 = j + 4*b - 36 + 13, o = -2*j + 2*b - 4. Factor 2/9*x**4 + 2/9*x**2 + 0*x - 4/9*x**j + 0.
2*x**2*(x - 1)**2/9
Let r = 91 + -89. Determine o, given that 42*o**3 + 23/2*o**r - 32*o**5 + o + 40*o**4 + 0 = 0.
-1/4, 0, 2
Let s(w) = 2*w**2 - 2*w - 2. Let v(y) = -y**4 + y**3 - 10*y**2 + 10*y + 11. Let p(b) = -22*s(b) - 4*v(b). Factor p(o).
4*o*(o - 1)**2*(o + 1)
Let m(s) be the second derivative of -s**8/840 + 3*s**2/2 + 7*s. Let z(x) be the first derivative of m(x). Factor z(t).
-2*t**5/5
Let u(v) = 11*v**4 + 4*v**3 + 15*v**2 - 2*v. Let y(q) = 