*u**4 - 3*u**3 - 4*u**2. Let j(h) = h**5 + h**3 + h**2. Let c(r) = -12*j(r) - 3*y(r). Factor c(i).
-3*i**3*(i + 1)**2
Let o(x) be the third derivative of x**6/24 - x**5/6 - 25*x**4/24 + 5*x**3 - 22*x**2. Suppose o(q) = 0. Calculate q.
-2, 1, 3
Factor 1/2*v - 1/6*v**2 + 0.
-v*(v - 3)/6
Find p such that 28/3*p**2 - 23/3*p**4 - 8/3*p + 7/3*p**5 + 0 + 2*p**3 = 0.
-1, 0, 2/7, 2
Let j(c) be the third derivative of -c**5/300 - c**4/60 + 31*c**2. Suppose j(f) = 0. Calculate f.
-2, 0
Let x(p) = p**3 - p**2 + 3*p - 8. Let j be x(2). Find m, given that 2*m - 2/3 - 4/3*m**j = 0.
1/2, 1
Let j(p) be the first derivative of p**5/30 + 3*p**2 + 7. Let o(c) be the second derivative of j(c). Let o(t) = 0. What is t?
0
Let u(j) be the first derivative of 4*j**3/39 + j**2/13 - 6*j/13 + 35. Solve u(s) = 0.
-3/2, 1
Let f be 144/66 - 2/11. Suppose -19 + f = -3*z + 2*h, 3*z - 13 = h. Solve 4/3*i**z + 0*i + 0 + 2/3*i**4 + 2/3*i**2 = 0.
-1, 0
Factor -36*n**2 + 80*n - 50 - 2/5*n**4 + 32/5*n**3.
-2*(n - 5)**3*(n - 1)/5
Suppose 0*c = -c - 17. Let i(g) = 3*g**3 + 3*g**2 - 3*g + 3. Let p(n) = 8*n**3 + 9*n**2 - 8*n + 8. Let b(k) = c*i(k) + 6*p(k). What is w in b(w) = 0?
-1, 1
Let z = -403/4 - -100. Let s = z - -5/4. Let -s*g**4 + 10*g - 9*g**2 + 7/2*g**3 - 4 = 0. What is g?
1, 2
Let i(c) = -15*c**3 - 25*c**2 + 95*c - 45. Let f(a) = 7*a**3 + 13*a**2 - 47*a + 23. Let m(h) = -5*f(h) - 2*i(h). Find g, given that m(g) = 0.
-5, 1
Let n(y) be the third derivative of -y**7/30 + y**6/24 + 3*y**5/20 - 5*y**4/24 - y**3/3 + 3*y**2. Find o such that n(o) = 0.
-1, -2/7, 1
Let s(v) be the third derivative of 0*v**3 + 2/15*v**5 + 0*v**4 - 43/105*v**7 + 0*v + v**2 + 5/12*v**8 + 0 - 1/15*v**6. Suppose s(j) = 0. Calculate j.
-2/7, 0, 2/5, 1/2
Factor k**3 + 28*k**2 - k + 2 + 3*k**4 - 31*k**2 + 0*k**4 - 2*k**4.
(k - 1)**2*(k + 1)*(k + 2)
Let y(u) = -8*u + 2. Let h(c) = 9*c - 3. Let s(j) = 3*h(j) + 4*y(j). Let k be s(-1). Factor 0 + 3*o**3 + k - 4 - 3*o**2.
3*o**2*(o - 1)
Let l be (-9)/(-27) + (-83)/231. Let x = 71/231 - l. Factor f**3 - 1/3*f**2 + x*f**5 + 0 - f**4 + 0*f.
f**2*(f - 1)**3/3
Let i = 473 - 1891/4. Factor 1/4*y**3 + i*y**5 - 1/2*y**4 + 0*y + 0*y**2 + 0.
y**3*(y - 1)**2/4
Let p(u) be the third derivative of -u**5/180 - u**4/6 - 2*u**3 + 17*u**2. What is s in p(s) = 0?
-6
Let c = -16 + 19. Let m(b) be the third derivative of -1/3*b**c + 0*b - 3*b**2 - 1/24*b**4 + 0 + 1/60*b**5. Find w, given that m(w) = 0.
-1, 2
Let j(q) be the second derivative of 1/30*q**3 - 2*q - 1/5*q**2 + 1/60*q**4 + 0. Find i such that j(i) = 0.
-2, 1
Let r(s) = s**4 - 4*s**3 + s**2 + 6*s. Let c(u) = u**2 + 2*u + u**3 - 4*u**3 + 3*u + u**4. Suppose -3*j - 3*j = -36. Let f(a) = j*c(a) - 5*r(a). Factor f(y).
y**2*(y + 1)**2
Let u be 2/(-4)*-4*1. Find w, given that 2*w - 4*w**3 - 6*w**3 + 3 - 8*w**u + 1 + 4*w**3 = 0.
-1, 2/3
Suppose 5*h - 3*a - 15 = -0*h, -12 = -4*h + 3*a. Factor 1/4*y**2 + 1/4*y - 1/4 - 1/4*y**h.
-(y - 1)**2*(y + 1)/4
Factor -11*f**3 + 3*f**3 - 8*f**3 + 248*f**4 - 252*f**4.
-4*f**3*(f + 4)
Let u be 0 - (-1 - (-3)/4). Let c(v) be the first derivative of -u*v**2 - 1 - 2/5*v**5 + 1/2*v - 11/8*v**4 - 3/2*v**3. Find r, given that c(r) = 0.
-1, 1/4
Let k(i) be the first derivative of i**7/350 - i**6/600 - i**3/3 + 1. Let l(m) be the third derivative of k(m). Solve l(v) = 0 for v.
0, 1/4
Let i(p) = -p - 6. Let q be i(-8). Factor o + 0 + 1/2*o**q.
o*(o + 2)/2
Let v(p) = -p**3 + 16*p**2 - 25*p + 14. Let j(h) = h**3 - h**2 + 1. Let l(z) = 4*j(z) - v(z). Factor l(r).
5*(r - 2)*(r - 1)**2
Let o(n) = -n**4 - 6*n**3 + 6*n**2 - 2*n. Let w(a) = a**4. Let l = -4 - 2. Let f(d) = l*w(d) - 2*o(d). Factor f(i).
-4*i*(i - 1)**3
Let r(u) = -2*u + 7. Let w be r(5). Let n = -1 - w. Factor z**2 - 2*z - 2*z**n + 3*z.
-z*(z - 1)
Let l(r) = r**2 + r - 4. Let y be l(-4). Let m = y - 6. Suppose 2*q**2 - 2*q**3 - m*q**3 + 0*q + 2*q = 0. What is q?
-1/2, 0, 1
Let m(h) be the third derivative of -h**7/420 - h**6/270 + h**5/60 + h**4/18 + h**3/3 + h**2. Let g(y) be the first derivative of m(y). Factor g(n).
-2*(n - 1)*(n + 1)*(3*n + 2)/3
Let f = -124 + 1605/13. Let d = f + 145/52. What is m in -1/2 + d*m + 5/4*m**3 - 3*m**2 = 0?
2/5, 1
Suppose 2*o + o = 6. Let j(n) = n**2 - n - 1. Let t(k) be the second derivative of -k**4/12 + 3*k**2/2 - 4*k. Let r(p) = o*t(p) + 4*j(p). Factor r(u).
2*(u - 1)**2
Let i(l) = -157*l**3 + 90*l**2 + 64*l + 8. Let j(w) = 78*w**3 - 45*w**2 - 32*w - 4. Let n(f) = -3*i(f) - 5*j(f). Factor n(m).
(m - 1)*(9*m + 2)**2
Suppose 3*o + 2*a = -14, 3*o - a - 17 = 7*o. Let w(u) = -2*u - 6. Let y be w(o). Factor 0*f**y + 4/5*f - 2/5 - 4/5*f**3 + 2/5*f**4.
2*(f - 1)**3*(f + 1)/5
Let y(g) be the third derivative of -g**6/288 + g**5/160 + g**4/48 - 7*g**3/6 + 5*g**2. Let q(z) be the first derivative of y(z). Factor q(c).
-(c - 1)*(5*c + 2)/4
Let a(h) be the first derivative of -1/60*h**5 - 1/8*h**4 - 1 - 3/2*h**2 - 1/3*h**3 + 0*h. Let i(j) be the second derivative of a(j). Find z such that i(z) = 0.
-2, -1
Let c(o) = -o**2 - 5*o - 3. Let y be c(-3). Find r, given that y*r**2 - 4 + 0*r**2 - r**3 + 0*r**2 = 0.
-1, 2
Factor 2/3*z**4 + 32/3 - 8*z**2 + 2/3*z**3 + 8/3*z.
2*(z - 2)**2*(z + 1)*(z + 4)/3
Let s(o) = 13*o + 146. Let b be s(-11). Solve -3/2*l**2 - 9/2*l**b - 9/2*l**4 + 0 - 3/2*l**5 + 0*l = 0.
-1, 0
Let a(d) be the first derivative of 2*d**5/15 - 4*d**3/9 + 2*d/3 + 4. Factor a(r).
2*(r - 1)**2*(r + 1)**2/3
Let u = -49756 + 4677201/94. Let g = u - -2/47. Factor 1/2*z + 3/2*z**2 + 1/2*z**4 + 0 + g*z**3.
z*(z + 1)**3/2
Solve 1/3*y**3 + 49*y + 343/3 + 7*y**2 = 0.
-7
Let o(n) be the third derivative of n**7/280 - n**6/120 - n**5/20 - 2*n**3/3 - 2*n**2. Let u(v) be the first derivative of o(v). What is q in u(q) = 0?
-1, 0, 2
Let x(d) be the first derivative of 0*d**4 + 0*d**3 + 1/120*d**6 - 1/2*d**2 + 0*d + 1 + 0*d**5. Let w(f) be the second derivative of x(f). Factor w(u).
u**3
Suppose -p + 3 = 0, v - 9*p + 5*p + 7 = 0. Let 0*k**2 + 0*k**4 - 2/13*k - 2/13*k**v + 4/13*k**3 + 0 = 0. What is k?
-1, 0, 1
Determine n so that -3/2*n + 3/2*n**5 + 0*n**3 + 0 - 3*n**4 + 3*n**2 = 0.
-1, 0, 1
Let h = 3 - -1. Let -c**4 - c - 2*c**3 + 3*c**5 - 2*c**4 + 0*c**3 - c**4 + h*c**2 = 0. Calculate c.
-1, 0, 1/3, 1
Factor -1/2*r + 1/6*r**4 - 1/3 + 1/2*r**3 + 1/6*r**2.
(r - 1)*(r + 1)**2*(r + 2)/6
Let w be 2 - ((-12)/4 + 1). Let s be ((-5)/(-20))/(2/w). Solve -s*q - 1/2*q**2 + 0 = 0 for q.
-1, 0
Suppose -11 - 19 = -5*b. Suppose -q = -0*q - 3*z + b, 3*z = 5*q - 6. Factor 1/3*r**5 - 2/3*r**q + 1/3*r + 1/3 - 2/3*r**2 + 1/3*r**4.
(r - 1)**2*(r + 1)**3/3
Let c = 11 - 8. Let o(v) be the second derivative of 1/6*v**4 + 0 + c*v + 4/3*v**3 + 4*v**2. Find h, given that o(h) = 0.
-2
Let g(q) = 19*q**2 + 4*q + 9. Let w be g(5). Find n such that -14*n + 158*n - 468*n**2 - 16 - 289*n**4 + 136*n**3 - 11*n**4 + w*n**3 = 0.
1/3, 2/5, 1
Factor -8/5*h - 2/5*h**3 + 0 - 3/5*h**4 + 1/5*h**5 + 12/5*h**2.
h*(h - 2)**2*(h - 1)*(h + 2)/5
Let v be (4/5)/((-2)/(-10)). Suppose -o = -3*o + v. Find p, given that 3*p**3 - 3/2*p - p**4 - 3/2*p**5 - 1 + o*p**2 = 0.
-1, -2/3, 1
Let d = 63 + -61. Determine p, given that 0 - 1/2*p**d + 1/2*p = 0.
0, 1
Let y = -12 - -9. Let j be 3 - (y + 5)/(-2). Find o, given that 2/7*o**2 + 2/7*o**j + 4/7*o**3 + 0*o + 0 = 0.
-1, 0
Let o be -4*(-4)/65 - 20/(-130). Let r be (-6)/(-3)*(3 - 2). Find b such that 0 - 4/5*b**4 + o*b - 2/5*b**5 + 0*b**3 + 4/5*b**r = 0.
-1, 0, 1
Suppose -40 = -0*n + 5*n + 4*z, n - 1 = z. Let p be ((-1)/(-6))/(n/(-12)). Solve -p + 0*d + 1/2*d**2 = 0.
-1, 1
Let y(n) = 111*n**3 + 72*n**2 - 30*n + 3. Let z(t) = -223*t**3 - 144*t**2 + 59*t - 6. Let f(l) = 7*y(l) + 3*z(l). Factor f(k).
3*(k + 1)*(6*k - 1)**2
Solve 52/15*r**3 - 4/5*r**4 + 2*r + 24/5*r**2 + 4/15 - 6/5*r**5 = 0.
-1, -1/3, 2
Let z be 1 + (0 + 16)/4. Factor w**2 + 12*w - z*w**2 + 0*w**2.
-4*w*(w - 3)
Let n = 31/76 + -3/19. Suppose 5/4*g**2 - n - 1/4*g - 3/4*g**3 = 0. Calculate g.
-1/3, 1
Suppose 0 = 3*i + q - 13, -4*q - 8 = -0*q. Let p = 8 - i. Factor -3*n + 2*n**3 + 1 - p*n**3 + n**2 + 2*n**2.
-(n - 1)**3
Let d(l) be the third derivative of -l**6/420 + l**4/12 - 2*l**3/7 + 23*l**2. Factor d(n).
-2*(n - 2)*(n - 1)*(n + 3)/7
Let p(t) be the second derivative of 3/5*t**5 + 1/2*t**4 - 5/2*t**3 - 2/5*t**6 + 3*t + 1/14*t**7 + 3*t**2 + 0. Factor p(q).
3*(q - 2)*(q -