 first derivative of 1/25*f**5 + 0*f - 1/10*f**2 - 3/20*f**4 - 1 + 1/5*f**3. Factor x(s).
s*(s - 1)**3/5
Factor 15*a**5 + 18*a**4 - 43*a**4 + 3*a**3 + 7*a**3.
5*a**3*(a - 1)*(3*a - 2)
Let a(r) be the second derivative of 0*r**3 + 0*r**2 + 0*r**5 + 0 - r + 0*r**4 + 1/60*r**6 - 1/168*r**7. Determine t so that a(t) = 0.
0, 2
Let n(k) = k**3 + k**2 + k + 1. Suppose -6*m = -3*m + 6. Let w(q) = -10*q**3 - 10*q**2 - 8*q - 8. Let i(s) = m*w(s) - 18*n(s). Find y such that i(y) = 0.
-1, 1
Let q(t) be the third derivative of 2*t**7/735 + 2*t**6/105 + 2*t**5/35 + 2*t**4/21 + 2*t**3/21 - 5*t**2. Factor q(a).
4*(a + 1)**4/7
Find s, given that 56*s**2 + 111*s**3 + 21*s**4 + 25*s**2 + 24*s + 33*s**2 = 0.
-4, -1, -2/7, 0
Factor -1/7 - 24/7*y**3 + 9/7*y - 2*y**2.
-(y + 1)*(4*y - 1)*(6*y - 1)/7
Let g(k) = 37*k**2 - 138*k + 31. Let w(p) = 56*p**2 - 207*p + 47. Let d(z) = -7*g(z) + 5*w(z). Find u such that d(u) = 0.
2/7, 3
Let o(u) be the third derivative of -1/840*u**7 - 1/48*u**5 + 0*u**3 + 0 + 0*u + 1/48*u**4 + 1/120*u**6 - 6*u**2. Factor o(f).
-f*(f - 2)*(f - 1)**2/4
Let h(a) be the third derivative of a**8/168 + a**7/35 - 2*a**5/15 + 11*a**2. Determine g so that h(g) = 0.
-2, 0, 1
Let b(x) be the first derivative of -2*x**3/15 + x**2/5 + 4*x/5 - 2. Factor b(m).
-2*(m - 2)*(m + 1)/5
Let d(w) be the first derivative of 2*w**3/27 - 8*w/9 - 11. Solve d(c) = 0 for c.
-2, 2
Let s(n) be the third derivative of -n**6/270 - n**5/360 + 2*n**3/3 + 3*n**2. Let i(c) be the first derivative of s(c). Solve i(x) = 0.
-1/4, 0
Let g(n) be the third derivative of -n**7/1680 - n**6/120 - n**5/80 + n**4/24 + 7*n**3/48 - 41*n**2. Factor g(b).
-(b - 1)*(b + 1)**2*(b + 7)/8
Let y(f) be the third derivative of 0*f**3 + 0 + 0*f**4 - 1/840*f**7 - 1/480*f**6 + 0*f**5 - f**2 + 0*f. Suppose y(o) = 0. What is o?
-1, 0
Let f(b) be the second derivative of 3*b**5/80 - b**4/16 + b**3/24 - b**2/2 - 3*b. Let t(x) be the first derivative of f(x). Factor t(k).
(3*k - 1)**2/4
Let r(z) be the second derivative of 1/36*z**4 + 0*z**3 - 1/6*z**2 + 0 + z. Determine y so that r(y) = 0.
-1, 1
Let q(v) = -v**3 - v**2. Let d(m) = 64*m**4 - 76*m**3 + 16*m**2 + 5*m - 1. Let g(c) = d(c) + 4*q(c). Factor g(a).
(a - 1)*(4*a - 1)**2*(4*a + 1)
Let o be (-10)/12 + (-3)/18. Let z = 6 + o. Factor -2 + 4*f**2 - 6*f**4 + z + 2*f**5 - 1 + 4*f**3 - 6*f.
2*(f - 1)**4*(f + 1)
Suppose -5 = -j - 2*n, 0 = n - 4 + 3. What is y in 3*y**4 - y**4 + y**4 + 3*y**3 + 0*y**4 - j*y**5 - 3*y**2 = 0?
-1, 0, 1
Let g(d) be the first derivative of d**9/1008 - d**8/280 - d**7/280 + d**6/60 + 2*d**3 + 6. Let v(x) be the third derivative of g(x). Factor v(o).
3*o**2*(o - 2)*(o - 1)*(o + 1)
Let n(s) = 16*s**2 - 5*s + 11. Let g(h) = 3*h**2 - h + 2. Let u(q) = -11*g(q) + 2*n(q). Solve u(j) = 0 for j.
0, 1
Let x(q) = -q**2 + 14*q - 13. Let c be x(13). Suppose 5*p - 10 + c = 0. Factor 81/2*f**2 + p - 18*f.
(9*f - 2)**2/2
Factor 0*p - 6*p**2 - p - 5*p + 5*p.
-p*(6*p + 1)
Let i be (-25)/(-2)*(170/(-50) - -4). Factor i*o**2 + 1/2 + 25/2*o**3 - 9/2*o.
(o + 1)*(5*o - 1)**2/2
Let n(g) be the second derivative of -1/15*g**6 - 2*g + 0*g**2 + 0*g**3 + 0 - 1/10*g**5 + 0*g**4. Factor n(h).
-2*h**3*(h + 1)
Let w be (-34)/(-8) + (-5 - (2 - 3)). Factor -3/4*r**4 + w*r**2 + 1/2*r**3 + 0*r + 0.
-r**2*(r - 1)*(3*r + 1)/4
Let x(y) be the first derivative of -y**8/3360 - y**7/1680 + 5*y**3/3 + 4. Let c(v) be the third derivative of x(v). Determine k, given that c(k) = 0.
-1, 0
Let k(b) = -24*b**3 + 54*b**2 - 63*b + 27. Let w(f) = f**4 + 49*f**3 - 108*f**2 + 127*f - 55. Let o(s) = -7*k(s) - 3*w(s). Factor o(g).
-3*(g - 2)**3*(g - 1)
Let a(u) be the first derivative of -2*u + 0*u**4 + 0*u**3 + 1/20*u**5 + 0*u**2 + 2. Let g(v) be the first derivative of a(v). Factor g(p).
p**3
Let a(m) = 6*m**2 - 5*m - 3. Let z(w) = -30*w**2 + 26*w + 16. Let s(i) = 16*a(i) + 3*z(i). Factor s(v).
2*v*(3*v - 1)
Let n(d) = d**3 + 6*d**2 + 2. Let v be n(-6). Factor v + 2*o**3 - 3*o - o**3 + 0*o.
(o - 1)**2*(o + 2)
Solve 2*d**3 + 12*d**2 + 4*d**5 - 8*d - 12*d**4 + 0*d**5 + 2*d**3 = 0.
-1, 0, 1, 2
What is l in -10/3*l + 14/3*l**2 - 4/3 = 0?
-2/7, 1
Suppose 0 = -4*j - 3*f + 15, -j + 19 = 4*j + 4*f. Solve -7*c**3 + 2*c**4 - 9*c**2 - 2*c**3 + j*c**2 - 5*c**4 = 0 for c.
-2, -1, 0
Let a(z) = -z**2 + 6*z - 1. Suppose 2*v - 3 = 7. Let c be a(v). Factor 0*l**3 - 3*l**2 + 3*l**3 - 3*l**c - 4*l**3 - 5*l**3.
-3*l**2*(l + 1)**2
Let o = 14 + -11. Let y(x) be the second derivative of -12*x**3 - o*x + 0 + 109/6*x**4 + 49/15*x**6 + 4*x**2 - 63/5*x**5. Find j, given that y(j) = 0.
2/7, 1
Factor -3 + 15*f**2 + 8*f - 32*f + 129*f**2.
3*(4*f - 1)*(12*f + 1)
Let -3*y + 18*y**2 + 8*y**3 - 3*y**5 + 12*y**4 - 6*y**2 - 26*y**3 = 0. What is y?
0, 1
Let k(v) be the first derivative of 0*v + 0*v**2 + 2*v**3 - 1/2*v**6 + 3/4*v**4 + 1 - 6/5*v**5. Suppose k(r) = 0. What is r?
-2, -1, 0, 1
Let t be 4/6 - 75/(-9). Let b be (t/(-6) + 2)/1. Suppose b + l - 3/2*l**2 = 0. What is l?
-1/3, 1
Let n(m) be the second derivative of 0 - 1/2*m**2 + 1/3*m**3 + m - 1/12*m**4. Let h(d) = 2*d**2 - 4*d + 2. Let g(p) = -4*h(p) - 7*n(p). Factor g(c).
-(c - 1)**2
Factor -7*r + 6 + 4*r + 0*r**2 - 2*r**2 - r.
-2*(r - 1)*(r + 3)
Suppose 0*k = 10*k - 12*k. Let o(x) be the second derivative of 1/70*x**5 + 4/21*x**3 + k*x**2 + 2/21*x**4 + x + 0. Solve o(u) = 0 for u.
-2, 0
Let t = 287 + -285. Factor -2/7*q**4 + 4/7*q**3 - 2/7*q**t + 0*q + 0.
-2*q**2*(q - 1)**2/7
Determine u so that 0 - 1/2*u**3 + 2*u + 0*u**2 = 0.
-2, 0, 2
Let s be (3/(-6))/(4 + -3 - 2). Factor -z - s*z**2 - 1/2.
-(z + 1)**2/2
Let x(j) be the third derivative of 6/35*j**7 + 46/15*j**5 + 11/2*j**4 + 3*j**2 + 0*j + 6*j**3 + 1/84*j**8 + 0 + j**6. Let x(y) = 0. Calculate y.
-3, -1
Let p(w) be the third derivative of 1/315*w**7 - 1/90*w**5 + 1/36*w**4 + 0 + 0*w**3 - 1/180*w**6 + 0*w + 3*w**2. Factor p(d).
2*d*(d - 1)**2*(d + 1)/3
Let j be (12/(-9) + 3)*3. Let a be (-1)/j + 34/70. Factor a*d**2 + 0*d - 2/7.
2*(d - 1)*(d + 1)/7
Let t(w) = -44*w**2 + 118*w - 288. Let k(j) = 5*j**2 - 13*j + 32. Suppose -12 = -3*l - 168. Let h(r) = l*k(r) - 6*t(r). Suppose h(g) = 0. What is g?
4
Let y(k) be the third derivative of -k**5/80 - k**4/32 + 3*k**3/2 + 51*k**2. Factor y(p).
-3*(p - 3)*(p + 4)/4
Let y(h) = h**2 + h - 1. Let m be y(2). Let j be m*(141/135 - 1). Factor -4/3*t**3 + 0 + 0*t - 2*t**4 - j*t**2 - 8/9*t**5.
-2*t**2*(t + 1)**2*(4*t + 1)/9
Factor 3*h**3 + 6*h + 360*h**2 - 369*h**2 + 0*h**3.
3*h*(h - 2)*(h - 1)
Factor -7*r**3 + r**4 - r**3 + r**4 + 8*r**2.
2*r**2*(r - 2)**2
Let u(j) be the third derivative of -j**6/120 + j**5/30 + j**4/6 - 4*j**3/3 + j**2. Factor u(s).
-(s - 2)**2*(s + 2)
Suppose -2*o - a = 4 - 3, 0 = 3*o + a - 1. Let z(b) be the second derivative of -1/3*b**o + 0*b**3 + 2*b + 1/18*b**4 + 0. Let z(p) = 0. Calculate p.
-1, 1
What is m in 5/2*m**4 + 0*m**3 + 0 - 10*m**2 + 0*m = 0?
-2, 0, 2
Factor -3*b**2 - 894 + 16*b - 4*b + 930.
-3*(b - 6)*(b + 2)
Let f(h) be the first derivative of -h**4/66 - 2*h + 1. Let x(i) be the first derivative of f(i). Factor x(b).
-2*b**2/11
Let t = 19/240 - 1/16. Let u(n) be the second derivative of 0 + 1/18*n**4 - 3*n + 0*n**2 + 0*n**3 - t*n**5. Suppose u(v) = 0. What is v?
0, 2
Suppose 3*u = -u + 96. Factor 3*n**5 + 3*n**3 - 6*n**5 - u + 24.
-3*n**3*(n - 1)*(n + 1)
Let -174 - 178 + 2*n + 6*n**2 + 346 - 2*n**3 = 0. Calculate n.
-1, 1, 3
Let g be -2*(-3)/6*-3. Let z be g/((-36)/44) - 3. Factor 2/3*h**3 - z*h + 0*h**2 + 0.
2*h*(h - 1)*(h + 1)/3
Let c = -2/83 - -93/415. Let f(p) be the first derivative of c*p**4 - 11/10*p**2 - 2 + 7/30*p**6 + 2/5*p - 16/25*p**5 + 14/15*p**3. Factor f(l).
(l - 1)**3*(l + 1)*(7*l - 2)/5
Factor 50*o - 125*o**2 + 366*o**3 + 113*o**5 + 400*o**4 + 207*o**5 - 5 - 466*o**3.
5*(o + 1)**2*(4*o - 1)**3
Suppose 15*p + 40 = 19*p. Find b such that 2*b**3 - p - 2*b**2 + 4 + 6 = 0.
0, 1
Let p(d) = -2*d**3 - 28*d**2 + 54*d - 36. Let m(t) = -5*t**3 - 84*t**2 + 163*t - 108. Let c(b) = -6*m(b) + 17*p(b). Determine x, given that c(x) = 0.
1, 3
Factor 0*v**3 - 6/7*v + 0 + 9/7*v**2 - 3/7*v**4.
-3*v*(v - 1)**2*(v + 2)/7
Factor -6*y + 4*y**2 + 20 - 39 + 19 + 2*y**3.
2*y*(y - 1)*(y + 3)
Let p(k) be the third derivative of 0 + 0*k**3 + 0*k + 0*k**6 - 1/24*k**4 - k**2 + 1/336*k**8 - 1/105*k**7 + 1/30*k**5. Factor p(l).
l*(l - 1)**3*(l + 1)
L