6 - 10. Suppose -5*a + 33 = v. Factor -5*r + r**2 - 3*r**3 - a + 4*r**3 + 3 + 5.
(r - 1)**2*(r + 3)
Let t(i) be the first derivative of -i**6/12 + i**5/5 + i**4/8 - i**3/3 + 1. Determine o, given that t(o) = 0.
-1, 0, 1, 2
Let n = -107 + 118. Suppose 0 = -n*u - 2*u + 26. Suppose 0*w - 9/5*w**3 + 2/5*w**u + 0 + 7/5*w**4 = 0. What is w?
0, 2/7, 1
Let g = 20 - 16. Solve 7*w**4 - 8*w**2 - 31*w**g - 15*w**5 + 32*w**2 - 12*w + 23*w**3 + 4*w**3 = 0.
-2, -1, 0, 2/5, 1
Let x(n) be the second derivative of -n**4/54 - 8*n**3/27 - 5*n**2/3 + 11*n + 4. Factor x(m).
-2*(m + 3)*(m + 5)/9
Let i be (108/(-7) + 16)*5/2. Determine o, given that i - 3/7*o**2 + 13/7*o = 0.
-2/3, 5
Let l = 1327 - 3980/3. Factor -l*v**2 + 1/3*v + 0 - 1/3*v**3 + 1/3*v**4.
v*(v - 1)**2*(v + 1)/3
Find u, given that 7*u**3 - 239/3*u**2 + 44/3 + 28*u = 0.
-2/7, 2/3, 11
Let z(a) be the second derivative of 1/165*a**6 + 1/11*a**3 + 0*a**2 - 3*a - 5/66*a**4 + 0 + 1/110*a**5. Factor z(m).
2*m*(m - 1)**2*(m + 3)/11
Let a be (-10)/2*27/(-45). Let s(n) be the first derivative of -3*n - 2*n**a + 0*n**4 - 3 + 1/5*n**5 + 4*n**2. Determine b so that s(b) = 0.
-3, 1
Suppose 2*u = 2*r - 86, -2*r - 8 = 2*r. Let t be (-46)/(-18) - (-10)/u. Determine q, given that -q**4 + t*q**2 + 0*q - 1/3*q**5 - 4/3 + 1/3*q**3 = 0.
-2, -1, 1
Factor 16*f**4 - 8*f**4 + 70*f**2 - 2*f**5 - 8*f**3 - 70*f**2.
-2*f**3*(f - 2)**2
Factor -12*c**3 + 53*c - 100*c**2 - 236*c - 48 + 7*c.
-4*(c + 2)*(c + 6)*(3*c + 1)
Let o(y) = -2*y - 1. Let j be o(-2). Factor -4*h**j + 4*h**2 - 119*h - 2 + 2 + 127*h.
-4*h*(h - 2)*(h + 1)
Let w(j) be the third derivative of 0 + 0*j**3 + 0*j - 1/90*j**5 + 11*j**2 - 1/180*j**6 + 0*j**4. Factor w(k).
-2*k**2*(k + 1)/3
Let l be (-1)/(2/20*-2). Determine k, given that 3*k**3 - 4*k**4 + 0*k**3 - 3*k**2 - k**3 + l*k**2 = 0.
-1/2, 0, 1
Let -6*z**2 + 7*z**3 - 1405*z**4 - 12*z**2 + 1408*z**4 + 8*z = 0. What is z?
-4, 0, 2/3, 1
Let l(v) be the second derivative of v**6/1020 + v**5/510 - v**4/204 - v**3/51 + 13*v**2 - 8*v + 3. Let j(z) be the first derivative of l(z). Factor j(c).
2*(c - 1)*(c + 1)**2/17
Let s(t) be the second derivative of -32*t + 0*t**3 + 5/6*t**4 + 1/4*t**5 + 0 + 0*t**2. Factor s(n).
5*n**2*(n + 2)
Let p(u) be the first derivative of -3*u**4/14 + 2*u**3 - 12*u**2/7 - 72*u/7 - 86. Factor p(t).
-6*(t - 6)*(t - 2)*(t + 1)/7
Let m(d) be the first derivative of -d**6/72 + d**5/8 + 5*d**4/6 + 9*d**3 + 34. Let k(t) be the third derivative of m(t). Factor k(r).
-5*(r - 4)*(r + 1)
Factor 14/5*y**3 - 4*y**2 + 0 - 3/5*y**4 + 8/5*y.
-y*(y - 2)**2*(3*y - 2)/5
Let z(g) be the third derivative of g**5/20 + 3*g**4/8 - 5*g**3 + 83*g**2 + 2*g. Factor z(w).
3*(w - 2)*(w + 5)
Suppose 2*w - 13 = -5*n, n = 3*w + w - 15. Let r(u) be the first derivative of -2/3*u**3 + 0*u + 0*u**2 - 1/4*u**w + 1. Factor r(b).
-b**2*(b + 2)
Solve a**2 + 69*a + 361 + 104*a - 211*a = 0.
19
Let c(n) = n + 1 + 5 - 4. Let i be c(0). Factor -2 + 3*w - w**2 + 0*w**2 + i*w**2 - 2*w.
(w - 1)*(w + 2)
Let t(a) = -9*a**2 - 21*a + 6. Let m(b) = b**2 - 4*b - 4. Let g be m(4). Let o(z) = -5*z**2 - 10*z + 3. Let i(f) = g*t(f) + 9*o(f). Solve i(c) = 0.
-1, 1/3
Let v = 106 + -1164/11. Let k(f) be the first derivative of v*f**2 - 2/11*f**3 + 1/22*f**4 + 0*f + 3. Factor k(x).
2*x*(x - 2)*(x - 1)/11
Let p = 127 - 63. Let -11*l**3 + p + 48*l + 32*l**3 - 20*l**3 + 0*l**2 + 12*l**2 = 0. Calculate l.
-4
Let s = 21 - 18. Let c(f) be the first derivative of 2*f**2 + 0*f + 3 - 2/3*f**s. Let c(l) = 0. Calculate l.
0, 2
Let i = -378 + 761/2. Factor -2/3*u**5 + 0*u + i*u**4 + 5/3*u**2 - 10/3*u**3 - 1/6.
-(u - 1)**4*(4*u + 1)/6
Let n(q) be the first derivative of -3*q**5/80 - q**4/8 - q**3/8 - 3*q - 2. Let p(v) be the first derivative of n(v). Factor p(f).
-3*f*(f + 1)**2/4
Let s(f) = 12*f + 180. Let r be s(-15). Factor r + 0*i - 2/15*i**2.
-2*i**2/15
Factor -25*v + 5/2*v**4 + 0 + 15/2*v**2 + 15*v**3.
5*v*(v - 1)*(v + 2)*(v + 5)/2
Let z(j) = j**4 + j**3 - j**2. Let m be -4 + 0 + (12 - 9). Let o(p) = 2*p**4 - 2*p**3 + 2*p**2 - p. Let k(a) = m*o(a) + z(a). Factor k(i).
-i*(i - 1)**3
Determine i so that 6 - 22*i**2 - 18*i**3 - 2 + 32*i + 1 + 3 = 0.
-2, -2/9, 1
Let h = 19 + -12. Suppose -3*v + h*v = 96. Factor 8*j**2 - 14*j**4 - 2*j**4 + v*j**3 + 4*j**3.
-4*j**2*(j - 2)*(4*j + 1)
Let r be (-172)/1677*(-39)/6. Factor 2*w + r*w**2 + 4/3.
2*(w + 1)*(w + 2)/3
Let i = 2236 - 2234. Let x(n) be the first derivative of -3*n**3 - 3*n - 9 + 3/4*n**4 + 9/2*n**i. Find g, given that x(g) = 0.
1
Let u(t) be the third derivative of t**7/126 - 4*t**6/9 + 64*t**5/9 - 6*t**2 - 1. Factor u(f).
5*f**2*(f - 16)**2/3
Let i be 450/(-180)*(-8)/35. Determine m, given that 0*m**2 + i - 2/7*m**3 + 6/7*m = 0.
-1, 2
Let i(y) be the first derivative of y**5/5 - y**3/3 + y**2/2 - y + 51. Let s(c) = 14*c**4 + 3*c**3 - 14*c**2 + 2*c - 5. Let a(d) = 5*i(d) - s(d). Factor a(g).
-3*g*(g - 1)*(g + 1)*(3*g + 1)
Let l be (-2)/8 - 99/(-12). Suppose 4*i = 4*v - 8, l = -2*v + 3*v + i. Let j**v + j**5 + 119*j**4 + 4*j**3 - 125*j**4 = 0. What is j?
0, 1, 2
Let i(m) = -4*m**2 + 20*m - 4. Let q be (-33)/6 + (-5)/(-10). Let w(r) = -5*r**2 + 19*r - 4. Let h(k) = q*i(k) + 6*w(k). Factor h(s).
-2*(s - 1)*(5*s - 2)
Let o(c) be the second derivative of 1/2*c**3 + 0 + 0*c**2 - 1/4*c**4 + 25*c. Factor o(z).
-3*z*(z - 1)
Let m be (-15)/(-10) + 3/6. Let -52 - 5*p**4 + 0*p**2 + 4*p**m - 3*p**3 + 3*p + 50 + 3*p**2 = 0. What is p?
-1, 2/5, 1
Let x(g) be the third derivative of -g**8/672 + g**7/28 - g**6/8 - 19*g**5/12 - 75*g**4/16 - 27*g**3/4 + 4*g**2 + 32*g. Factor x(r).
-(r - 9)**2*(r + 1)**3/2
Suppose -10*w**2 + 11*w**2 + 14*w - 74*w - 5*w**2 - 56 = 0. What is w?
-14, -1
Suppose 5 = -r + 2. Let v be -2*r/(-12)*(-1 - -1). Factor 1/3*c**2 - 1/3*c**5 + 1/3*c**3 + 0*c + v - 1/3*c**4.
-c**2*(c - 1)*(c + 1)**2/3
Suppose 7 = 2*j - i, 4*j - 2*i + i - 17 = 0. Suppose 2*a - j*a = 0. Find g, given that g - g**4 + a*g - g - g**2 - 2*g**3 = 0.
-1, 0
Let o = 3698 - 55456/15. Suppose -4/15 - o*s**4 - 26/15*s - 46/15*s**3 - 18/5*s**2 = 0. What is s?
-1, -2/7
Let r(l) = -2*l**2 + 64*l - 60. Let x be r(31). Let m(w) be the second derivative of 9*w + w**x - 1/6*w**3 + 0 - 1/4*w**4. Factor m(q).
-(q + 1)*(3*q - 2)
Suppose -28 = -w - 18. Suppose m = 6*m - w. Factor 0*f - 1/2*f**5 - f**3 + 5/4*f**4 + 1/4*f**m + 0.
-f**2*(f - 1)**2*(2*f - 1)/4
Let h(p) = -p**3 - p**2 - p - 1. Let a = -4 + 3. Let m(q) = 4*q + 3 + 3*q**3 - 4*q**2 + 1 + 9*q**2. Let l(o) = a*m(o) - 4*h(o). Factor l(z).
z**2*(z - 1)
Determine x, given that 40/3*x**2 - 25/3*x - 5/3*x**3 - 250/3 = 0.
-2, 5
Let d(p) = -2*p**3 - 16*p**2 + 24*p - 6. Let z(b) = -2*b**2 - b - 1. Let g(s) = d(s) - 6*z(s). Factor g(y).
-2*y*(y - 3)*(y + 5)
Let c be 3 - (-1)/((-12)/6)*-2. Let a(l) be the second derivative of c*l + 0 + 3/20*l**5 + 0*l**2 + 1/2*l**3 + 1/2*l**4. Solve a(d) = 0.
-1, 0
Let u = 42 + -40. Let r be ((-6)/(-5))/(12/30). Solve 32*a + u*a**r - 16 + 3*a**3 - a**3 - 20*a**2 = 0 for a.
1, 2
Factor -200/13 - 98/13*d**4 + 84/13*d**3 - 120/13*d + 262/13*d**2.
-2*(d + 1)**2*(7*d - 10)**2/13
Let m = 171/7 - 92333/3780. Let i(k) be the third derivative of 1/72*k**4 + 9*k**2 + 1/27*k**3 + 0 - 1/360*k**6 + 0*k - m*k**5 - 1/1890*k**7. Solve i(y) = 0.
-2, -1, 1
Suppose o = -4*d + 3*d + 1, -4*o + 10 = 2*d. Let p = 1 - d. Solve -6*x**3 + 10*x**3 - x**p + 2*x**5 - 5*x**4 = 0 for x.
0, 1, 2
Let r(n) be the first derivative of -10 + 0*n + 0*n**2 - 2/15*n**3 - 1/10*n**4. Factor r(f).
-2*f**2*(f + 1)/5
Let t(r) be the second derivative of r**5/110 + 31*r**4/66 + 59*r**3/33 + 29*r**2/11 - 683*r. Factor t(p).
2*(p + 1)**2*(p + 29)/11
Let d(y) be the third derivative of -y**8/63 - 74*y**7/315 - y**6/10 + 48*y**5/5 + 6*y**4 + 2*y**2 - 179*y. Find h such that d(h) = 0.
-6, -1/4, 0, 3
Let o(b) = -10*b**5 - 85*b**4 - 110*b**3 - 10*b**2 + 25*b - 5. Let z(i) = i**5 - i**3 + i**2 + i - 1. Let y(t) = -o(t) + 5*z(t). Find u, given that y(u) = 0.
-4, -1, 0, 1/3
Suppose -2*i - 16*i + 54 = 0. Let g(m) be the third derivative of 0*m + 1/21*m**i + 0 - 1/42*m**4 + 3*m**2 + 1/210*m**5. Factor g(q).
2*(q - 1)**2/7
Suppose 0 = -5*x - 3 - 2. Let w(r) = -r**2 + r + 1. Let f(d) = -10*d**2 + 12*d + 1. Let s(u) = x*f(u) + 3*w(u). Factor s(v).
(v - 1)*(7*v - 2)
Let a = -36918 + 36920. Factor -16/9*h**3 - 2/9*h**4 - 64/9*h + 22