-6*o - 3*o**5 + 3*o**3 + 3*o**2 - 3*o**2. Let r(y) = 6*q(y) - 7*w(y). Factor r(g).
3*g**2*(g - 1)*(g + 1)*(g + 2)
Let a(s) be the first derivative of -1/30*s**6 + 17 - 2/15*s**3 - 3/10*s**4 + 1/5*s**5 - 3/5*s + 7/10*s**2. Factor a(z).
-(z - 3)*(z - 1)**3*(z + 1)/5
Let s(k) = 3*k**3 + 39*k**2 + 30*k - 72. Let x(b) = b**2 + b - 2. Let n(j) = s(j) - 9*x(j). What is d in n(d) = 0?
-9, -2, 1
Let l(r) be the second derivative of -2*r**6/15 + 2*r**5/5 + r**4/3 - 4*r**3/3 - r + 6. Factor l(n).
-4*n*(n - 2)*(n - 1)*(n + 1)
Let m be 4/(-22) - (-408)/66. Suppose -m = -t + 4. Let -3*p**4 + 0*p**5 - t*p**5 + p**4 + 4*p**5 = 0. What is p?
-1/3, 0
Let y(c) be the second derivative of c - 9/2*c**2 + 0 + 1/4*c**4 - c**3. Let y(w) = 0. What is w?
-1, 3
Let i be 6/4*14*(-8)/(-840). Let g(s) be the second derivative of 1/105*s**7 + 1/15*s**4 - 11*s - 1/25*s**5 + 1/15*s**3 - 1/75*s**6 + 0 - i*s**2. Factor g(c).
2*(c - 1)**3*(c + 1)**2/5
Let j = -606 + 253. Let c = j - -523. Let 408*k**4 + c*k**3 - 400*k - 96*k**5 - 264*k**2 - 84*k**5 - 96 + 362*k**3 = 0. Calculate k.
-2/3, -2/5, 1, 3
Let c = 5 - 0. Suppose c*m + 0*m - 5 = 0. Factor -6*u**2 + m + 3 - u**4 - u - 2*u**3 + 3*u + 3*u**4.
2*(u - 2)*(u - 1)*(u + 1)**2
Let z = -6/7 - -68/63. Let n(t) be the first derivative of -z*t**2 - 2/9*t - 4 - 2/27*t**3. Factor n(v).
-2*(v + 1)**2/9
Suppose -4*q + 0 = -20. Let m be (2/(-10))/(q + 32/(-6)). Factor 1/5*y**3 + 1/5 + m*y**2 + 3/5*y.
(y + 1)**3/5
Let y be (-108)/(-72) - (-4)/8. Let 17/3*q**3 + 0 + 20/3*q**4 - 2/3*q - 5/3*q**y = 0. What is q?
-1, -1/4, 0, 2/5
Let h be 2/(-1)*12/(-6). Suppose h*g + 4 = 48. Factor -2*t - 4*t**2 + t**5 - 15*t**4 + 3*t + g*t**4 + 6*t**3.
t*(t - 1)**4
Let t(p) be the third derivative of 0*p + 5*p**2 + 3/40*p**4 + 0*p**3 + 0 + 1/200*p**6 - 1/25*p**5. Factor t(q).
3*q*(q - 3)*(q - 1)/5
Factor 152*w - 70*w**2 + 15 - 41 - 50*w - 6*w**3.
-2*(w - 1)*(w + 13)*(3*w - 1)
Let q = 271/633 + -20/211. Factor -1/3 - q*b**2 - 2/3*b.
-(b + 1)**2/3
Find q such that -17*q + 55/2*q**2 + 2 + 361/4*q**3 - 250*q**4 + 100*q**5 = 0.
-2/5, 1/4, 2/5, 2
Let f(c) = c**2 - 7*c - 6. Let q be f(8). Suppose -2*a = -3*y + 10, 4*y - a - 6 = -q*a. Let 3/2*u**3 - 3/2*u + 3/2 - 3/2*u**y = 0. What is u?
-1, 1
Let w = 34058/7 + -4865. What is z in 0 + 0*z**2 - 4/7*z + w*z**3 + 1/7*z**4 = 0?
-2, 0, 1
Let b = 40 - 36. Factor b*x**3 + 18*x**2 - 35*x**2 + x**2 - 8 + 20*x.
4*(x - 2)*(x - 1)**2
Factor 117600/17*m + 2/17*m**3 + 5488000/17 + 840/17*m**2.
2*(m + 140)**3/17
Suppose -56 = -z - 54. Suppose 5/6*j**z + 0 + 1/3*j + 2/3*j**3 + 1/6*j**4 = 0. What is j?
-2, -1, 0
Let g(o) be the third derivative of 0 - 16*o**2 + 1/30*o**4 - 1/150*o**5 + 0*o + 0*o**3. What is v in g(v) = 0?
0, 2
Let y(z) be the third derivative of -z**6/420 + z**5/30 - 5*z**4/28 + 3*z**3/7 - 5*z**2 - 14*z. Factor y(m).
-2*(m - 3)**2*(m - 1)/7
Let c(t) be the first derivative of 2*t**2 + 0*t - 1/3*t**3 + 31. What is u in c(u) = 0?
0, 4
Let 17/8*t - 5/8*t**4 + 3/4 - 1/8*t**2 - 17/8*t**3 = 0. What is t?
-3, -1, -2/5, 1
Suppose -15 = 5*k, 2*k + 8 + 85 = 3*f. Let -3*x**5 - 8*x**4 - 4*x**3 - 9*x**3 + f*x**3 + 4*x**5 = 0. Calculate x.
0, 4
Let x(k) = -5*k**3 + k**2 - 2*k. Let s be x(2). Let q be 10/s - (-26)/8. What is y in -8/5*y**2 - 8/5*y + 78/5*y**q + 0 + 14*y**5 + 148/5*y**4 = 0?
-1, -2/5, 0, 2/7
Let n(a) be the first derivative of a**5/15 - a**4/6 - 4*a**3/9 + 4*a**2/3 - 59. Factor n(v).
v*(v - 2)**2*(v + 2)/3
Let q(u) be the third derivative of -u**8/23520 - u**7/4410 + u**6/2520 + u**5/210 + u**4/3 - 9*u**2. Let c(f) be the second derivative of q(f). Factor c(r).
-2*(r - 1)*(r + 1)*(r + 2)/7
Let a = 4420/7 + -13232/21. Factor -1/3*i**2 + a - 1/6*i**3 + 2/3*i.
-(i - 2)*(i + 2)**2/6
Suppose 2/7*j**3 + 18/7*j - 20/7*j**2 + 0 = 0. Calculate j.
0, 1, 9
Let j(g) = -8*g**2 - 779*g - 15. Let k(v) = -12*v**2 - 1168*v - 24. Let s(u) = 8*j(u) - 5*k(u). Let s(c) = 0. Calculate c.
-98, 0
Suppose -4*u + 2*d + 2 = 0, -4*u = 6*d - 4*d - 14. Suppose -22*a**2 + 18*a**2 + 10*a + 9*a**u = 0. What is a?
-2, 0
Let s(d) be the third derivative of d**8/5040 - d**7/420 + 7*d**5/15 - 24*d**2. Let w(u) be the third derivative of s(u). Suppose w(l) = 0. What is l?
0, 3
Suppose 0 = 55*k + 47*k. Factor 0 + 2/5*j**4 + k*j**3 - 6/5*j**2 - 4/5*j.
2*j*(j - 2)*(j + 1)**2/5
Factor 15/2*t + 171/8 + 1/8*t**2.
(t + 3)*(t + 57)/8
Let -20*c**5 + 75*c - 230*c**2 - 189*c**4 + 78*c**3 + 489*c**4 + 93*c**3 - 156*c**3 = 0. What is c?
-1, 0, 1/2, 15
Let o(u) be the first derivative of u**5/270 - 5*u**4/108 - 7*u**2 + 19. Let b(g) be the second derivative of o(g). Factor b(q).
2*q*(q - 5)/9
Let z = 214 - 207. Let k be z*4/10*(-55)/(-539). Factor 4/7*h**3 + 0*h - 2*h**4 + k*h**2 + 0 + 8/7*h**5.
2*h**2*(h - 1)**2*(4*h + 1)/7
Let v(z) be the first derivative of -2*z**5/5 - 7*z**4 - 104*z**3/3 - 66*z**2 - 54*z + 229. Find f, given that v(f) = 0.
-9, -3, -1
Let q(c) be the first derivative of -1/2*c**2 + 1/6*c**3 + 0*c + 12 + 1/8*c**4. Find v, given that q(v) = 0.
-2, 0, 1
Let a be (-3)/(-2)*((-22)/33 + 4). Let i(z) be the second derivative of -z - 7/10*z**a - 20/3*z**3 + 3*z**4 + 1/15*z**6 + 8*z**2 + 0. Factor i(f).
2*(f - 2)**3*(f - 1)
Let c = -177 - -167. Let j be (c/8 + 1)/(9/(-54)). Suppose -12 - j*q**3 - 18*q - 9*q**2 = 0. What is q?
-2
Let x(f) be the first derivative of -1/2*f**3 - 9/10*f**5 - 5/4*f**6 + 6*f + 13 + 51/8*f**4 - 9*f**2. Let x(p) = 0. What is p?
-2, -1, 2/5, 1
Let v(b) be the second derivative of 3*b**5/20 + b**4/6 - b**3/6 + 7*b. Let h be v(1). Factor -16*d + 10 - 4 + 6 + h*d**2.
4*(d - 3)*(d - 1)
Suppose -19 = -7*o - 5. Factor -19*z**2 + 20*z**o + z - 7*z + 8.
(z - 4)*(z - 2)
Let k(j) be the second derivative of j**6/90 - 7*j**5/10 + 517*j**4/36 - 266*j**3/3 + 722*j**2/3 - 76*j - 1. Determine c so that k(c) = 0.
2, 19
Let o = 31648/21 - 10547/7. Suppose -1/3*m**2 + m**3 + 0 + 0*m + o*m**5 - m**4 = 0. What is m?
0, 1
Let c(t) = -t**3 + 16*t**2 + 5*t - 12. Let h(y) = -2*y**2 - y + 1. Let i(w) = c(w) + 4*h(w). Solve i(x) = 0 for x.
-1, 1, 8
Let f(x) = x**2 - 5*x + 5. Let d be f(5). Suppose -d*n = 2*q - 59, -2*n + 0 + 12 = -5*q. Factor -10*w - 3*w**3 - 13*w - n*w + 7*w - 18*w**2.
-3*w*(w + 3)**2
Let p(b) = b**3 + 9*b**2 + 10*b - 4. Let v be p(-8). Let x = -17 - v. Factor 7 + 17*i - 20*i**3 - 2 + 36*i**2 + x + 4*i**4 - 45*i.
4*(i - 2)*(i - 1)**3
Let h be 2/((-50)/(-19 + 9)). Let -12/5 + h*i + 2/5*i**2 = 0. What is i?
-3, 2
Suppose -360*p + 81*p**2 + 11*p**3 - 11*p**3 + 229 + 143 + 3*p**3 = 0. What is p?
-31, 2
Suppose -2*s = s - 36. Let a = s + -8. Factor -12*q**2 - 1 + 11*q**3 - 12*q + 18*q - q**3 - 3*q**a.
-(q - 1)**3*(3*q - 1)
Let w(y) = -17*y - 25. Let k be w(12). Let j = k + 1615/7. Factor 64/7 + j*g**2 + 48/7*g + 1/7*g**3.
(g + 4)**3/7
Suppose 7/8*c + 1/4*c**2 + 1/2 - 1/8*c**3 = 0. What is c?
-1, 4
Let a(x) be the first derivative of x**6/24 - x**5/6 + 5*x**4/24 - x**2 - 9. Let j(d) be the second derivative of a(d). Factor j(w).
5*w*(w - 1)**2
Let s(x) be the first derivative of -7*x**4/12 + 79*x**3/9 - 11*x**2/3 - 58. Factor s(u).
-u*(u - 11)*(7*u - 2)/3
Let c(u) be the third derivative of -u**5/20 + 91*u**4/2 - 16562*u**3 + 184*u**2. Factor c(j).
-3*(j - 182)**2
Let b(l) be the first derivative of 2*l**6/3 - 8*l**5/5 - l**4 + 8*l**3/3 + 915. Factor b(s).
4*s**2*(s - 2)*(s - 1)*(s + 1)
Factor 23/2*w + 5/2*w**3 + 21/2*w**2 + 4 - 1/2*w**4.
-(w - 8)*(w + 1)**3/2
Factor 24*k**4 + 198*k + 45*k**4 + 132*k**2 + 12*k**3 - 73*k**4 + 96 + 14*k.
-4*(k - 8)*(k + 1)**2*(k + 3)
Let z(s) be the first derivative of -s**4/4 - 11*s**3 - 363*s**2/2 - 1331*s + 90. Suppose z(b) = 0. Calculate b.
-11
Let b(p) = -7*p**2 - 121*p - 118. Let a(z) = 155*z**2 + 2660*z + 2595. Let i(r) = 2*a(r) + 45*b(r). Find f, given that i(f) = 0.
-24, -1
Let o be (5 + 1)/(-2) + (-38458)/(-12194). Factor 0 - o*y**2 + 4/13*y.
-2*y*(y - 2)/13
Let a(p) = p**2 - 2. Let l(v) = 3*v**2 + 10*v - 36. Let g(o) = 2*a(o) + l(o). Factor g(w).
5*(w - 2)*(w + 4)
Suppose m - 2*m - 17 = -2*w, -3*m - 4*w = 11. Let y be 12/m*(-18)/8. Solve 8 + 6*j**2 + j**3 + 3*j**y - 6 - 2*j**3 + 6*j = 0 for j.
-1
Let s(a) be the second derivative of a**8/1176 - 4*a**7/735 + a**6/84 - a**5/105 + 3*a**2 + 15*a. Let x(z) be the first derivative of s(z). Factor x(u).
2*u**2*(u - 2)*(u - 1)**2/7
Let l = 1532/9 - 1169/3