*j + 288. Determine w so that 1/3*w**3 - 2/3*w**l + 0*w + j = 0.
0, 2
Let x be (-44)/(-154) + (66/14 - 1). Let k(u) be the third derivative of 0*u**3 + 0*u - 1/160*u**6 + 1/48*u**5 + 5*u**2 + 0 + 1/48*u**x. Factor k(h).
-h*(h - 2)*(3*h + 1)/4
Suppose -3*t - 3*m = -27, 4*t - 2*m + 26 = 8*t. Let z(o) be the second derivative of -2/9*o**3 + 1/3*o**5 + 3*o - 7/9*o**t + 0 + 2*o**2. Factor z(v).
4*(v - 1)**2*(5*v + 3)/3
Let z = 1834 + -3665/2. Let y(l) be the first derivative of z*l**2 - 13 + 0*l + 3/4*l**4 + 2*l**3. Factor y(q).
3*q*(q + 1)**2
Suppose -12*i + 233 = 197. Let k(x) be the first derivative of 6/5*x**5 + 1/2*x**6 + 0*x + 0*x**4 - 2*x**i - 5 - 3/2*x**2. What is t in k(t) = 0?
-1, 0, 1
Suppose 1/4*n**2 + 9/2 - 11/4*n = 0. Calculate n.
2, 9
Let q(a) = -a**2 - 5*a + 1802. Let x be q(-45). Let 4/7*c**x + 100/7 - 40/7*c = 0. Calculate c.
5
Let g = 16/31 + 1285/93. Let l = g - 77/6. Factor -2*o + l*o**2 - 2.
(o - 2)*(3*o + 2)/2
Let c be (-83)/(-3) + (-12)/(-36). Suppose 5*a - 19 = 3*g, -g - 5*a - 1 = -c. Factor 32/5*d - 8/5 - 14/5*d**3 - g*d**2.
-2*(d - 1)*(d + 2)*(7*d - 2)/5
Let l(j) = -j**3 - 3*j**2 + 12*j + 8. Let u(z) = -2*z**3 - 2*z**2 + 12*z + 8. Let r(v) = 2*l(v) - 3*u(v). Suppose r(y) = 0. Calculate y.
-1, 2
Let x(f) = f**2 - f + 2. Let r be x(1). Suppose 9 = r*m + 3*v, -2*v = 2*m - 3 - 3. Factor m + 0*g**2 + 0*g + 1/3*g**3.
g**3/3
Determine d, given that -91*d + 224*d - 3*d**2 - 14283 + 52*d + 229*d = 0.
69
Suppose 189 + 27 = -2*j. Let p be ((-243)/j)/(6*(-1)/(-4)). Find q, given that -3/4*q**4 - 3/4*q**2 + p*q**3 + 0 + 0*q = 0.
0, 1
Factor -74*b**5 - 18*b - 74*b**5 + 24*b**2 + 146*b**5 - 8*b**4 + 4*b**3.
-2*b*(b - 1)**2*(b + 3)**2
Let j(c) = c**2 - 37*c + 273. Let x be j(10). Let r(y) be the first derivative of 2/15*y**5 - 2/3*y - 2/3*y**2 + 0*y**x + 7 + 1/3*y**4. Solve r(l) = 0 for l.
-1, 1
Let d = 29 - 27. Let b = 7 + -7. Let -4/9*n**d + 2/9 + 2/9*n**4 + b*n**3 + 0*n = 0. Calculate n.
-1, 1
Suppose 411/7*k**2 + 129/7*k**4 - 381/7*k**3 - 108/7 - 15/7*k**5 - 36/7*k = 0. Calculate k.
-2/5, 1, 2, 3
Let j(d) = d**2 + 13*d + 24. Let r be j(-11). Let n be ((-100)/225)/(r/(-9)). Suppose 0 - 8/3*s - 4/3*s**3 + 6*s**n = 0. Calculate s.
0, 1/2, 4
Let g(n) be the third derivative of 5*n**8/336 - 2*n**7/21 - n**6/24 + n**5/3 - n**2 - 39. Factor g(x).
5*x**2*(x - 4)*(x - 1)*(x + 1)
Suppose 6*s = 13*s - 287. Factor s*t - 19*t - 35*t**2 + 18*t - 5*t**3.
-5*t*(t - 1)*(t + 8)
Let o = -3196/5 - -54392/85. Find s such that o*s - 10/17*s**2 - 2/17*s**3 + 0 = 0.
-6, 0, 1
Let r(a) = a - 1. Let j(d) = -8 - 3*d - 3*d**2 + 5*d**2 + 9*d. Let m(v) = j(v) - 2*r(v). Factor m(u).
2*(u - 1)*(u + 3)
Suppose 0 = -z + 3*z - 5*h - 19, -5*z - 5 = 5*h. Suppose -3 - 23 = -z*o. Solve -27*q - q**3 + 3*q - o*q**2 + 5 - 14 - q**3 = 0 for q.
-3, -1/2
Let b(i) be the third derivative of -1/15*i**5 - 18*i**2 + 1/3*i**3 + 0*i - 7/24*i**4 + 0. Factor b(w).
-(w + 2)*(4*w - 1)
Let n be (7/(-12))/((-6)/48). Let t = -13/3 + n. Let 1/3*y**2 - 1/3 - 1/3*y + t*y**3 = 0. Calculate y.
-1, 1
Let a = 12 + -6. Let j be (a - 4)/(2/2). Factor 0*f**2 - 4 + 3*f**j + 0 + 1.
3*(f - 1)*(f + 1)
Let u(l) = 2 - l**2 - 4*l**3 + 46*l**4 - 47*l**4 + 4*l**2. Let x(y) = -y**5 - y**4 + y**3 + y**2 - y + 1. Let g(v) = u(v) - 2*x(v). Factor g(a).
a*(a - 1)**2*(a + 2)*(2*a + 1)
Let y be (3/2)/(-6 + (-351)/(-52)). Let x(d) be the first derivative of 1/4*d**y - 1/4*d + 1 - 1/12*d**3. Factor x(h).
-(h - 1)**2/4
Suppose -21*w - 7 = -70. Suppose 4/7 + 2/7*z - 4/7*z**2 - 2/7*z**w = 0. Calculate z.
-2, -1, 1
Let o(h) be the third derivative of 0*h**3 + 0*h**5 + 15*h**2 + 1/70*h**7 + 0*h**4 + 1/224*h**8 + 1/80*h**6 + 0 + 0*h. Let o(n) = 0. Calculate n.
-1, 0
Let y(z) be the first derivative of 2*z**3/45 - 38*z**2/15 + 722*z/15 - 73. Factor y(v).
2*(v - 19)**2/15
Let r = 2422 - 9685/4. Let -3/4*o**2 + 3/2*o**3 + r*o**4 - 3/2*o + 0 = 0. Calculate o.
-2, -1, 0, 1
Let h(t) = -t**2 - 1. Let r be h(2). Let s be r/(125/(-65)) - 2. Suppose s*x + 3/5*x**2 + 0 = 0. Calculate x.
-1, 0
Let n(s) be the first derivative of -2*s**7/105 + s**6/5 - 3*s**5/5 + 4*s**2 - 6. Let a(b) be the second derivative of n(b). Factor a(y).
-4*y**2*(y - 3)**2
Let i(a) be the second derivative of -5*a**4/24 - 7*a**3/2 - 4*a**2 + 327*a. Find k, given that i(k) = 0.
-8, -2/5
Let m be ((-12)/(-9) + -1)/(2/(-6)) + 3. Solve -6/11*c + 0 - 1/11*c**m = 0.
-6, 0
Let g(p) = -3*p**2 + 399*p + 396. Let j(u) = -11*u**2 + 1597*u + 1585. Let m(k) = 23*g(k) - 6*j(k). Factor m(h).
-3*(h + 1)*(h + 134)
Suppose -j - 4*d = 4*j - 7, -4*j - 5*d + 2 = 0. Factor -28*c**j + 1 + 15*c**3 + 15 - 16*c**2 + 9*c**3 + 4*c.
-4*(c - 1)*(c + 1)*(c + 4)
Factor 2*n**3 + 32/3 - 92/3*n**2 - 22*n.
2*(n - 16)*(n + 1)*(3*n - 1)/3
Suppose -2*s + 3*i = -0*i - 51, -5*i = 5. Let -6*w - 3*w**5 - 126*w**4 + 15*w**5 + 94*w**4 + s*w**3 + 2*w = 0. What is w?
-1/3, 0, 1
Let n(d) = -18*d**2 - 80*d - 168. Let r(l) = -116*l**2 - 520*l - 1092. Let s(x) = -32*n(x) + 5*r(x). Find t, given that s(t) = 0.
-7, -3
Let h be (-129)/(-4644) + 2/(-36)*(-44)/11. Factor -h*p**2 + 9/4*p + 0.
-p*(p - 9)/4
Let h(j) = -j + 4. Suppose o = x - 4*o - 10, x + 5*o + 10 = 0. Let q be h(x). Let 2 - 4 - 3*y**q + 0*y**3 - 3*y**3 - 2*y**4 + 7*y**2 + 3*y = 0. Calculate y.
-1, 2/5, 1
Let y(b) be the third derivative of b**6/20 + 3*b**5/8 + 3*b**4/4 - b**3 - 60*b**2. Let y(d) = 0. Calculate d.
-2, 1/4
Let a = -10 - -12. Suppose -a = 2*k - 4. Determine l, given that 6 - 6*l**2 + 10 - 4*l**2 + 25*l - k = 0.
-1/2, 3
Suppose 5*a + 5*h - 30 = 0, -2*a + 5 = -3*h + 18. Let j be (-13)/((-65)/25) + a + -4. Factor -18/5 - 2/5*m**j - 12/5*m.
-2*(m + 3)**2/5
Suppose -2*h = 7*h - 27. Suppose -h*w + 21 - 9 = 0. Solve 0*s**2 + 0*s**w + 0 + 1/5*s**5 - 2/5*s**3 + 1/5*s = 0 for s.
-1, 0, 1
Factor -6*m**3 + 0*m**3 + 2*m**3 - 2*m**4.
-2*m**3*(m + 2)
Let s be (-2)/(9/30 - (-105)/(-150)). What is u in 0*u + 0 + 26/3*u**4 - 10/3*u**s + 32/15*u**2 - 112/15*u**3 = 0?
0, 4/5, 1
Let y(j) be the first derivative of 2*j**3/5 - 7*j**2/5 + 4*j/5 + 114. Find g, given that y(g) = 0.
1/3, 2
Let v(r) be the third derivative of r**7/15120 - r**6/2160 - r**4/12 - 2*r**2. Let h(k) be the second derivative of v(k). Factor h(m).
m*(m - 2)/6
Let p(l) = -7*l + 10. Let j be p(-8). Let u be ((-3)/2)/(j/23 - 3). Factor 7/2*g**2 + 3 + u*g.
(g + 3)*(7*g + 2)/2
Let q(k) be the first derivative of 16*k**5/5 + 85*k**4 + 812*k**3 + 3038*k**2 + 1372*k + 254. Factor q(h).
4*(h + 7)**3*(4*h + 1)
Let q(o) be the first derivative of 14*o**6/9 - 10*o**5/3 - 43*o**4/6 + 196*o**3/9 - 52*o**2/3 + 16*o/3 - 32. Solve q(v) = 0.
-2, 2/7, 1/2, 1, 2
Let w(x) be the second derivative of x**6/420 - x**5/140 - x**4/84 - 6*x**2 + 9*x. Let h(i) be the first derivative of w(i). Factor h(m).
m*(m - 2)*(2*m + 1)/7
Let i(b) be the second derivative of 16/7*b**2 + 20/21*b**3 + 28*b + 0 + 1/70*b**5 + 4/21*b**4. Factor i(r).
2*(r + 2)**2*(r + 4)/7
Let h = -2 - -20. Let v = -14 + h. Factor 0 + 1/6*k**2 + 1/2*k**3 + 1/2*k**v + 0*k + 1/6*k**5.
k**2*(k + 1)**3/6
Let q(o) be the second derivative of o**6/90 - o**5/15 - o**4/2 + 2*o**3 - 7*o. Let d(p) be the second derivative of q(p). Factor d(x).
4*(x - 3)*(x + 1)
Let t be (-2)/(-24)*-2 - 296/(-48). Let d be (4 - 4)/(t/3). Factor d*h - h**3 - 1/2 + 3/2*h**2.
-(h - 1)**2*(2*h + 1)/2
Let u(x) be the first derivative of 1/10*x**4 - 5 - 1/15*x**6 + 2/15*x**3 - 2/25*x**5 + 0*x + 0*x**2. Suppose u(o) = 0. What is o?
-1, 0, 1
Let f(x) be the first derivative of 5/9*x**3 - 6 + 0*x**2 + 0*x**4 - 1/3*x**5 + 0*x. Factor f(s).
-5*s**2*(s - 1)*(s + 1)/3
Suppose 33*n - 28 = 31*n. Let t(i) = 2*i**4 + 9*i**3 + i**2 - 10*i - 4. Let r(u) = -u**3 - u**2. Let m(c) = n*r(c) + 2*t(c). Solve m(q) = 0 for q.
-1, 2
Let y(m) be the second derivative of 0 + 1/14*m**7 + 2/5*m**6 - 5*m + 3/5*m**5 - 3*m**2 - 1/2*m**4 - 5/2*m**3. Factor y(n).
3*(n - 1)*(n + 1)**3*(n + 2)
Let m be (-1)/(-1) - -2 - (4 + -5). Factor 16*c**2 + 4*c - 4*c**m + 0*c - 36*c + 0*c**4 + 8*c**3.
-4*c*(c - 2)**2*(c + 2)
Let o be -3*(-2 - 6/(-9)). Let c(p) = p**3 - 3*p**2 - 3*p + 4. Let u be c(o). Solve 2*r**2 - 5*r**2 - 4*r - u*r + 0*r**2 = 0 for r.
-4, 0
Let w = -7501/2 + 37511/10. Factor 6/5*k**2 + w - 6/5*k**3 - 3/5*k**5 - 9/5*k**4 + 9/5*k.
-3*(k - 1)*(k + 1)**4/5
Let v(i) = -20*i**3 - 2416*i**2 + 2439*i - 614. Let 