) = 2*i**2 - 59*i - 27. Let m be h(30). Let u(c) be the first derivative of 8/3*c**m + c**4 + 2*c**2 - 3 + 0*c. Find f such that u(f) = 0.
-1, 0
What is t in 3/2 + 1/10*t**2 - 4/5*t = 0?
3, 5
Factor 3/5*d**3 + d + 9/5*d**2 + 0 - 1/5*d**4.
-d*(d - 5)*(d + 1)**2/5
Suppose 3/5*p**3 + p**5 - 8/5*p + 22/5*p**4 - 22/5*p**2 + 0 = 0. What is p?
-4, -1, -2/5, 0, 1
Let j(t) be the first derivative of 4*t**3/3 - 6*t**2 + 8*t - 17. Factor j(c).
4*(c - 2)*(c - 1)
Suppose -2/3*a**4 + 182/3*a**3 - 18000 + 19800*a - 1860*a**2 = 0. What is a?
1, 30
Let f(v) be the third derivative of 0*v + 1/8*v**4 - v**3 + 4*v**2 + 1/20*v**5 + 0. Let i(k) = k. Let q(t) = f(t) - 6*i(t). Find p, given that q(p) = 0.
-1, 2
Let c be (-6)/(-8) - 1/(-4) - -18. Suppose c - 7 = 2*v + 3*k, -2*v - 2*k + 8 = 0. Find g such that 1/4*g + 1/4*g**2 + v = 0.
-1, 0
Let i(d) be the first derivative of d**9/2016 - 3*d**7/560 + d**6/120 + d**3/3 - 8. Let c(l) be the third derivative of i(l). Suppose c(x) = 0. What is x?
-2, 0, 1
Suppose 19*v = 8*v - 35*v. Let a(q) be the first derivative of 8 - 2/55*q**5 - 2/11*q**4 + v*q + 0*q**2 + 0*q**3. What is k in a(k) = 0?
-4, 0
Let x(p) be the first derivative of -p**4/22 - 16*p**3/33 - 19*p**2/11 - 24*p/11 - 67. Let x(u) = 0. What is u?
-4, -3, -1
Factor 5*o**5 - 44*o**2 - 33*o**4 + 410*o**3 - 82*o**4 - 546*o**2 + 197*o - 2 + 188*o - 93.
5*(o - 19)*(o - 1)**4
Let b(y) be the first derivative of 0*y**2 + 9 + 0*y + 0*y**3 + y**5 + 5/4*y**4. Find t, given that b(t) = 0.
-1, 0
Suppose -3*p = 4*l + 14, 8*l - 31 = -3*p + 13*l. Factor 1/5*t**2 + 5 + p*t.
(t + 5)**2/5
Let z(k) be the first derivative of -4*k**5/5 + 17*k**4 + 148*k**3/3 + 38*k**2 + 282. Solve z(t) = 0.
-1, 0, 19
Let h(m) = -m**4 + m**2 - 1. Let g = 25 - 41. Let i = g + 28. Let n(k) = 15*k**4 - 3*k**3 - 21*k**2 + 3*k + 18. Let j(f) = i*h(f) + n(f). Factor j(q).
3*(q - 2)*(q - 1)*(q + 1)**2
Let l be (1 + 2)*(-20 - -23). Suppose 0 = 3*z - 4*k - 2, -z - l = -6*z + k. Solve 7*r**2 + 5*r**3 - 8*r + 11*r - r**z - 2*r**3 = 0.
-1, 0
Let a = -8159/5 - -1632. Find r, given that 4/5*r - a*r**3 + 2/5*r**2 - 8/5 = 0.
-2, 2
Suppose -19*k + 23*k = 76. Suppose -34 = -k*z + 2*z. Factor 6/7 + 2/7*b**4 - 8/7*b**z - 4/7*b + 4/7*b**3.
2*(b - 1)**2*(b + 1)*(b + 3)/7
Let n = -43 + 64. Suppose -9*g = -6*g - n. Let 49/4*r**2 + g*r + 1 = 0. What is r?
-2/7
Let w(t) be the first derivative of 9*t**3/5 - 33*t**2/10 + 6*t/5 + 73. Factor w(d).
3*(d - 1)*(9*d - 2)/5
Suppose -20 = -f + 5*p, -3*f + 3*p + 18 = -6. Suppose 4*s**3 - 16*s**2 + 4*s**4 + 10*s**2 - s**f - 5*s + 2*s**5 + 2*s**4 = 0. What is s?
-5, -1, 0, 1
Let m(a) be the second derivative of 0 + 1/6*a**6 + 5/6*a**3 + 3/4*a**5 + 5/4*a**4 - a + 0*a**2. Factor m(j).
5*j*(j + 1)**3
Let y be (-36)/(-14)*287/123. Factor 3/2*w**2 + y + 6*w.
3*(w + 2)**2/2
Let s be (16/(-20))/((-2)/5). Let a be 5/5 + s + (-21)/15. Factor 8/5*b**4 + 2/5*b**5 + a*b**2 + 2/5*b + 12/5*b**3 + 0.
2*b*(b + 1)**4/5
Suppose 176 = -14*a + 22*a. Let b be 4/a + (-2294)/(-330) + -7. Factor 0*o**2 + 2/15 - 4/15*o + 4/15*o**3 - b*o**4.
-2*(o - 1)**3*(o + 1)/15
Suppose 0 = 7*n + 2*n - 4*n. Let x(a) be the first derivative of 3/4*a**4 + n*a + 0*a**2 + 0*a**3 + 1. Determine s so that x(s) = 0.
0
Let t(m) = m**3 + 35*m**2 + 65*m - 33. Let w be t(-33). Factor 1/3*r**4 + 0 + 0*r + 1/3*r**5 + w*r**3 + 0*r**2.
r**4*(r + 1)/3
Let r(k) = -k**3 + 9*k**2 - 13*k - 3. Let s be r(7). Factor 10/7*u**s + 22/7*u + 6*u**2 + 34/7*u**3 + 4/7.
2*(u + 1)**3*(5*u + 2)/7
Let c(s) = -s**2 + 9*s + 142. Let w be c(17). Suppose -h - 3 = -a - 7, h = -a. Factor -3/2*l**h - 6*l - w.
-3*(l + 2)**2/2
Let f be 4/14*(-23 - -2)/(-3). Let a be f/(-6)*(-57)/38. Factor a*b + 0*b**2 - 1/3 - 1/6*b**3.
-(b - 1)**2*(b + 2)/6
Let x(f) = f + 0 - 2 + 3. Let y(a) = -5*a**3 + 10*a**2 + 20*a + 5. Let d(b) = 15*x(b) - y(b). What is n in d(n) = 0?
-1, 1, 2
Let l(s) be the third derivative of s**5/36 - 125*s**4/36 + 245*s**3/18 - 144*s**2. Factor l(i).
5*(i - 49)*(i - 1)/3
Suppose 5*p + 4*m - m - 30 = 0, 4*m = p - 6. Let -13 + 15 + 24*j - 36*j**2 + 16*j**3 - p = 0. What is j?
1/4, 1
Suppose -622*o = -618*o - 8. Find q such that 1/2*q**o - 1 + 1/2*q = 0.
-2, 1
Let -10/7*o**4 + 0*o - 2/7*o**5 - 6/7*o**2 + 0 - 2*o**3 = 0. Calculate o.
-3, -1, 0
Let a(k) be the first derivative of -2*k**5/25 + 11*k**4/10 - 18*k**3/5 + 5*k**2 - 16*k/5 + 53. Factor a(o).
-2*(o - 8)*(o - 1)**3/5
Let t be 6*(-4 + (-20)/(-6)). Let u(k) = -k - 1. Let l(i) = i**2 - 12*i - 13. Let q(a) = t*l(a) + 36*u(a). Suppose q(f) = 0. Calculate f.
-1, 4
Factor 2*p**2 + 2*p**2 + p - 12 - 6*p - 3*p.
4*(p - 3)*(p + 1)
Suppose 489*a + 32 = 492*a - 4*i, 3*a = -2*i - 16. Factor 0*j**4 + 0*j + 0 + a*j**2 + 3/4*j**3 - 3/4*j**5.
-3*j**3*(j - 1)*(j + 1)/4
Let z(p) be the first derivative of -p**8/1120 - p**7/560 + p**6/240 + p**5/80 - 9*p**3 + 25. Let a(g) be the third derivative of z(g). Factor a(w).
-3*w*(w - 1)*(w + 1)**2/2
Let y(m) be the first derivative of -4*m**3/3 - 14*m**2 - 40*m - 103. Let y(s) = 0. Calculate s.
-5, -2
Suppose m - 14 = -2*g + 5*m, 0 = -m - 1. Let f be 10/4 - (-2)/(-5)*g. Determine i so that f + 1/4*i**2 + 3/4*i = 0.
-2, -1
Let b(s) = 6*s**2 - 45*s + 195. Let x(a) = -13*a**2 - 3 - a + 2 + 12*a**2. Let m(n) = -b(n) - 3*x(n). Factor m(h).
-3*(h - 8)**2
Let f(r) be the first derivative of -2*r - 4 + 9/2*r**2 + 11/3*r**3. Let f(q) = 0. Calculate q.
-1, 2/11
Let x be ((42/(-49))/(-1 - -6))/((-9)/28). Solve -2/15*b**2 + x*b - 8/15 = 0.
2
Let b = -18 - -24. Let d = -2 + b. Determine c so that -d*c**2 + c + 3*c**2 + 0*c**2 = 0.
0, 1
Let f be 3/6 - (-1)/2. Let u be f/(4/16) - 0. Suppose 2 - u*m - m**4 + 4*m**3 + 0*m**3 - m**4 = 0. Calculate m.
-1, 1
Let n(o) be the second derivative of o**4/36 + 128*o**3/9 + 8192*o**2/3 - o - 91. Factor n(z).
(z + 128)**2/3
Let w(h) be the first derivative of 4*h**3/3 + 50*h**2 + 437. Factor w(b).
4*b*(b + 25)
Factor 1/3*z**2 + 31/3 - 32/3*z.
(z - 31)*(z - 1)/3
Suppose -k = -3*j + 6, -7*j + 4*k = -4*j - 6. Let d(y) be the second derivative of 0 - 8*y - 1/6*y**4 + 0*y**j + 2/3*y**3 - 1/10*y**5. Let d(n) = 0. What is n?
-2, 0, 1
Suppose m - 2 = 6*r, -5*m - 50*r + 10 = -55*r. Determine g so that 1/2*g**3 - 1/2*g + 0 + 1/2*g**4 - 1/2*g**m = 0.
-1, 0, 1
Let g(j) be the third derivative of j**6/180 - 19*j**5/90 + 35*j**4/36 - 17*j**3/9 - 198*j**2. Solve g(b) = 0.
1, 17
Determine y so that 192/7*y + 4/7*y**2 - 28 = 0.
-49, 1
Let 19*k - k**4 - 82*k**3 - 8*k**4 + 94*k**3 - 51*k**3 - 4 - 7*k**2 = 0. Calculate k.
-4, -1, 1/3
Suppose -5*a + 13 = -3*q, 2*a - q - 31 = -26. Factor -2/5*i - 8/5 + 1/5*i**a.
(i - 4)*(i + 2)/5
Let u be ((-11)/44*-2)/(1/6). Determine z so that z**2 + 0 + 2/3*z + 1/3*z**u = 0.
-2, -1, 0
Let p(i) = 6*i + 5*i - 1 - 75*i**2 - 4 + 81*i**2. Let m(d) = 7*d**2 + 11*d - 6. Let h(a) = -5*m(a) + 6*p(a). Determine b, given that h(b) = 0.
-11, 0
Factor -54*y**3 + 16*y + 2*y**4 + 226*y + 12*y**3 + 198*y**2.
2*y*(y - 11)**2*(y + 1)
Let y(u) = 23*u**3 - 11*u**2 - 117*u + 64. Let n(l) = -24*l**3 + 12*l**2 + 116*l - 64. Let r(x) = 5*n(x) + 4*y(x). Factor r(d).
-4*(d - 2)*(d + 2)*(7*d - 4)
Let r(c) be the third derivative of 1/672*c**8 + 0*c**4 + 0*c**5 + 1/60*c**6 + 0*c**3 - 1/105*c**7 - 7*c**2 + 0*c + 0. Factor r(n).
n**3*(n - 2)**2/2
Let h(u) be the third derivative of -u**8/3024 + u**7/630 + u**6/360 - 7*u**5/540 - u**4/36 - 15*u**2. What is j in h(j) = 0?
-1, 0, 2, 3
Solve -156 + 130*r - 2*r**2 + 47*r + 146*r - 165*r = 0.
1, 78
Determine w, given that 48/5 + 12/5*w**2 + 39*w = 0.
-16, -1/4
Let r = -76/5 + 329/20. Let p = -67 - -70. Factor o**p + 0 + r*o**2 + 1/4*o.
o*(o + 1)*(4*o + 1)/4
Let g be (-90)/14 - 9/(-21). Let l(i) = i**2 + 1. Let z(w) = 3*w**2 + 3*w + 12. Let o(x) = g*l(x) + z(x). Solve o(b) = 0 for b.
-1, 2
Let k(y) = y**3 - 13*y**2 + 10*y + 21. Let h be k(12). Let m be 4/(-48)*h*1. Find q, given that -1/4*q + 0 + 0*q**2 + m*q**3 = 0.
-1, 0, 1
Let w(d) = 2*d**2 - 1. Let z(l) = 11*l**2 - 4*l - 1. Suppose c - 120 = -3*c. Let k(o) = c*w(o) - 5*z(o). Factor k(f).
5*(f - 1)*(f + 5)
Let g(o) be the third derivative of -o**5/270 - 5*o**4/27 - 4*o**3/3 - 4*o**2 + 7*o. Solve g(s) = 0 for s.
-18, -2
Let j be ((-30)/(-10) + (-16)/3)*-6. Let -13*z**2 - 7*z**2 - j*z**2 - 6*z + 31*z**2 - 3 = 0. What is z?
-1
Let p(x) = x**3 + x**2 - x - 1. Let h(k) = 2*k**3 