- 6 + 10/27*m**3 - 1/3*m**2. Factor z(b).
-2*(b - 3)**2*(b + 1)/9
Let p(k) be the third derivative of 1/84*k**8 + 0*k - 8/105*k**7 + 2/15*k**6 + 0*k**5 + 0*k**4 + 0 + 0*k**3 + 29*k**2. Factor p(t).
4*t**3*(t - 2)**2
Let u(i) be the first derivative of -2*i**5/35 + 12*i**4/7 - 96*i**3/7 + 72. Factor u(l).
-2*l**2*(l - 12)**2/7
Let m(s) = -s**3 - 2*s**2 - 2*s + 1. Let o be m(-2). Suppose o*a - 17 = -k + 3, 0 = 3*a - k - 12. Factor 8*c + 10*c**2 + 0 + a*c**3 - 1 - 2 + 5.
2*(c + 1)**2*(2*c + 1)
Let x(y) be the second derivative of y**4/30 + 644*y**3/15 + 103684*y**2/5 + 154*y. Find c such that x(c) = 0.
-322
Let h(a) be the first derivative of a**4/16 + 55*a**3/6 + 27*a**2 + 976. Factor h(m).
m*(m + 2)*(m + 108)/4
Determine c, given that 4*c**2 - 6*c + c**2 - 2*c**2 - 2*c**2 - 2*c = 0.
0, 8
Determine y so that 34/13*y + 56/13 - 20/13*y**2 + 2/13*y**3 = 0.
-1, 4, 7
Let q(v) be the first derivative of -13 + 0*v - 4/7*v**2 - 4/21*v**3. Factor q(n).
-4*n*(n + 2)/7
Let t(v) be the third derivative of -11/90*v**6 + 4/5*v**7 + 0 - 118/45*v**5 + 10/3*v**4 - 16/9*v**3 - 7/36*v**8 + 11*v**2 + 0*v. What is s in t(s) = 0?
-1, 2/7, 1, 2
Factor 4*a**2 - 29*a - a**5 - 6*a**3 - 20*a - 27*a - 5*a**4 + 84*a.
-a*(a - 1)*(a + 2)**3
Let 3/5*d**2 + 24/5*d + 48/5 = 0. Calculate d.
-4
Let z(m) be the first derivative of m**4/24 + m**3/2 + 9*m**2/4 + 9*m - 21. Let s(h) be the first derivative of z(h). Suppose s(y) = 0. What is y?
-3
Suppose 194672/5 + 12696/5*i + 276/5*i**2 + 2/5*i**3 = 0. Calculate i.
-46
Suppose u - 11 = 3*d + 5*u, d + 3*u = -12. Determine a so that 1/5*a**d + 1/5*a**2 - 1/5*a**4 - 1/5*a + 0 = 0.
-1, 0, 1
Let s be 6*1/4*10/3. Let f(o) be the second derivative of 0 - 3/20*o**s - 3/2*o**3 - 3/2*o**2 + o - 3/4*o**4. Factor f(q).
-3*(q + 1)**3
Let z be -2 + (3 - 3188/20). Let c = z + 159. Factor -6/5*k**3 + c*k**4 + 0*k**2 - 3/5 + 6/5*k.
3*(k - 1)**3*(k + 1)/5
Suppose 28/3*o**4 - 980/3*o + 200/3 + 356*o**2 - 316/3*o**3 = 0. What is o?
2/7, 1, 5
Factor -41287 + 4*x - 2*x**3 + 41283 + 2*x.
-2*(x - 1)**2*(x + 2)
Let w(k) be the first derivative of k**8/672 - k**6/240 + 17*k**2/2 + 10. Let o(l) be the second derivative of w(l). Factor o(y).
y**3*(y - 1)*(y + 1)/2
Let z(w) = -w**2 - w - 1. Let g(s) = 4*s**2 - 2*s - 2. Let q(y) = -g(y) - 5*z(y). Let k(f) = -2*f**2 - 13*f - 13. Let l(t) = -3*k(t) - 5*q(t). Factor l(b).
(b + 2)**2
Let n = -2301 + 16125/7. Factor -24/7 - 80/7*q - n*q**3 - 78/7*q**2.
-2*(q + 3)*(3*q + 2)**2/7
Let j be (24/(-36))/((-2)/(-15))*48. Let t be (-228)/j + 3/(-4). Factor 1/5*f**4 + 0*f**2 - t + 2/5*f**3 - 2/5*f.
(f - 1)*(f + 1)**3/5
Factor 64 - 177*b + 82*b - 221*b - 136 + 36*b**2.
4*(b - 9)*(9*b + 2)
Find y such that 1014/19*y - 4394/19 - 78/19*y**2 + 2/19*y**3 = 0.
13
Let f = 64766/151137 + 1/21591. Find o such that f*o**4 + 0*o + 0 + 0*o**3 - 12/7*o**2 = 0.
-2, 0, 2
Let u be 4*1 + -5 + 2. Let s be (-56)/14 + u*4. Factor 0 - 2/9*n**2 + 2/9*n**3 + s*n.
2*n**2*(n - 1)/9
Let p(z) be the first derivative of 2*z**5/25 + 77*z**4/30 + 220*z**3/9 + 224*z**2/5 - 192*z/5 - 114. What is j in p(j) = 0?
-12, -2, 1/3
Let x(b) = 3*b - 9. Let c(t) = -4*t**3 + 2*t + 1. Let g be c(-1). Let i be x(g). What is s in 2/3*s**3 - 2/3*s + 2/3*s**2 + i - 2/3*s**4 = 0?
-1, 0, 1
Let a(r) be the second derivative of -2*r**7/105 - 8*r**6/75 + 8*r**5/25 + 2*r**4/3 - 46*r**3/15 + 4*r**2 - 329*r. Suppose a(t) = 0. Calculate t.
-5, -2, 1
Let n(a) be the third derivative of 1/10*a**5 + 0 + 1/60*a**6 + 0*a + 0*a**3 + 0*a**4 - 9*a**2. Solve n(w) = 0.
-3, 0
Let o(x) be the third derivative of x**7/1575 - 31*x**6/900 + 17*x**5/30 - 5*x**4/4 + 47*x**2 + 3*x. Solve o(s) = 0.
0, 1, 15
Suppose 88*f - 67*f = 0. Let z(p) be the second derivative of -8*p + f - 9*p**2 + 2*p**3 - 1/6*p**4. Factor z(q).
-2*(q - 3)**2
Suppose -s + 16 = -8. Suppose -2*j - 4*i + 16 = -0*j, 0 = 5*j + 2*i - s. Find l, given that -4*l**4 - 2*l**2 - 5*l**5 + 2*l**4 - 6*l**j - 9*l**3 - 4*l**4 = 0.
-1, -2/5, 0
Let v = 171/4 - 85/2. Let d(k) be the first derivative of -v*k**4 + 0*k**2 + 2 - 1/3*k**3 + 0*k. Factor d(s).
-s**2*(s + 1)
Let f(r) be the third derivative of -r**7/945 - 7*r**6/1080 + r**5/90 + 17*r**4/24 + 2*r**2. Let k(o) be the second derivative of f(o). Factor k(a).
-2*(a + 2)*(4*a - 1)/3
Let a(v) be the third derivative of -v**9/20160 + v**8/3360 - v**7/1680 - v**5/6 + 17*v**2. Let y(j) be the third derivative of a(j). Factor y(q).
-3*q*(q - 1)**2
Suppose 2*p - 94 = -3*g + 34, 2*p = 2*g - 102. Suppose -v**5 + 3*v**3 - 47*v**4 - v**2 + 94*v**4 - g*v**4 - 2*v = 0. Calculate v.
-1, 0, 1, 2
Let g(l) be the first derivative of 1/8*l**3 + 0*l + 13 + 1/32*l**4 - 1/4*l**2. Find o such that g(o) = 0.
-4, 0, 1
Let l(c) be the second derivative of c**7/14 + 11*c**6/5 + 129*c**5/5 + 265*c**4/2 + 275*c**3/2 - 1500*c**2 + 209*c. Find g such that l(g) = 0.
-8, -5, 1
Let f(t) = 72*t + 8. Let r be f(3). Let d = r + -222. Factor -x + 0 + 1/2*x**d.
x*(x - 2)/2
Factor 6 + 33/5*k + 3/5*k**2.
3*(k + 1)*(k + 10)/5
Suppose 3*i - 4*y - 13 = 2*i, 9 = 3*i + 3*y. Suppose -5*g + i + 10 = 0. Factor -4/7 + 8/7*d + 0*d**2 + 4/7*d**4 - 8/7*d**g.
4*(d - 1)**3*(d + 1)/7
Let c(w) = 4*w**2 - 457*w + 456. Let s be c(1). Factor 3/2*j**s + 0*j - 15/2*j**2 + 0.
3*j**2*(j - 5)/2
Let i = 4 - 1. Let j = 13419/8 + -1677. Let 1/8*g - 1/4*g**5 + j*g**2 + 0 + 1/8*g**i - 3/8*g**4 = 0. What is g?
-1, -1/2, 0, 1
Factor 21/4 - 1/8*m**2 - 19/8*m.
-(m - 2)*(m + 21)/8
Let z = -1/56 - -71/840. Let o(q) be the second derivative of 2/3*q**3 + z*q**6 - 1/5*q**5 - 1/6*q**4 + 0 - 7*q + 0*q**2. Factor o(w).
2*w*(w - 2)*(w - 1)*(w + 1)
Let r(l) = -l**3 + 11*l**2 - 18*l - 16. Let k be r(6). Let y be 4 - 0 - 140/k. Determine f so that -3/2*f**4 + 3/4*f**5 + y*f**2 + 0 - 3/4*f**3 + 0*f = 0.
-1, 0, 1, 2
Let d(f) be the third derivative of -7*f**5/4 + f**4/4 + 728*f**2. Factor d(v).
-3*v*(35*v - 2)
Let s(n) be the third derivative of 0*n**3 + 1/3*n**4 - 1/15*n**5 + 0*n - 12*n**2 + 0. Factor s(q).
-4*q*(q - 2)
Let r = -79 - -87. Let s be 90/560 - (-1)/r. Let s*p - 6/7*p**4 + 2*p**3 + 0 - 10/7*p**2 = 0. What is p?
0, 1/3, 1
Let u(y) be the first derivative of 0*y**4 + 2/15*y**3 + 0*y - 13 + 2/15*y**2 - 2/75*y**5. Determine r so that u(r) = 0.
-1, 0, 2
Let s(k) be the first derivative of 0*k**2 + 0*k**5 + 1/120*k**6 + 3/280*k**7 + 4 - k**3 + 0*k + 0*k**4. Let p(d) be the third derivative of s(d). Factor p(z).
3*z**2*(3*z + 1)
Let g(y) be the third derivative of -y**5/180 + y**4/24 + 2*y**3/9 - 123*y**2. Solve g(s) = 0.
-1, 4
Let c(o) = -8*o**5 - 11*o**4 - 4*o**3 + 2*o**2 - 3*o. Let f(v) = -v**5 - v**4 - v**3 - v. Let l(i) = -4*c(i) + 12*f(i). Find g such that l(g) = 0.
-1, 0, 2/5
Suppose -7*p - 9 = -3*d - 4*p, 2*d + p + 3 = 0. Let i = 11 + -8. Factor -4/7*r**2 + 2/7*r**i + 2/7*r + d.
2*r*(r - 1)**2/7
Suppose 0 = -14*c + 13*c - 9. Let j be 4 - 6/(c/(-3)). Factor -m**2 - m - j*m**2 - 2*m.
-3*m*(m + 1)
Determine f so that -144/7*f**2 - 2/7*f**3 - 2592/7*f + 0 = 0.
-36, 0
Let n(r) = -25*r**2 + 120*r + 145. Let p(d) = -d**2 - d + 10. Let m(b) = -n(b) + 30*p(b). Let m(l) = 0. Calculate l.
-31, 1
Factor 0*m**2 + 338 - 4*m**2 + 14*m**2 + 52*m - 8*m**2.
2*(m + 13)**2
Let c(m) = 100*m**5 + 116*m**4 + 16*m**3 - 28*m**2 - 28. Let x(o) = -18*o**5 - 21*o**4 - 3*o**3 + 5*o**2 + 5. Let y(t) = -5*c(t) - 28*x(t). Factor y(j).
4*j**3*(j + 1)**2
Let a(q) be the third derivative of -q**5/140 - q**4/28 + 4*q**3/7 + 132*q**2. Factor a(r).
-3*(r - 2)*(r + 4)/7
Let y = 51 + -47. Factor -4*k**3 + 16*k**3 - 4*k**2 + 0*k**3 + y*k**5 - 12*k**4.
4*k**2*(k - 1)**3
Let h(r) = -r**3 + 5*r**2 - 5*r + 4. Let y be h(4). Let c(t) = t**2 - 171*t + 5673. Let g be c(45). Let y*f**2 + 2/3 + 1/3*f**g - f = 0. What is f?
-2, 1
Find t, given that 1/2*t**4 - 3*t**3 + 0 + 12*t - 19/2*t**2 = 0.
-3, 0, 1, 8
Let c(n) be the first derivative of n**7/210 + n**6/120 - n**5/60 - n**4/24 - 18*n**2 - 16. Let h(o) be the second derivative of c(o). Factor h(j).
j*(j - 1)*(j + 1)**2
Let i(d) = 2*d**2 + 16*d + 2. Let w be i(-8). Solve -4*p**4 + 29*p**3 + 12*p**w - 14*p**3 - 15*p**3 + 8*p = 0.
-1, 0, 2
Solve 27*t**2 - 25*t**3 + 19*t + 5*t**4 + 6*t + 0*t**4 - 32*t**2 = 0 for t.
-1, 0, 1, 5
Let b be 6/(-14) + (-517)/(-847). Suppose b*a**2 + 2/11*a + 0 = 0. What is a?
-1, 0
Let q be 1*(-4 + (-1 - 8)). Let o = q + 16. Factor 16