1, 4
Let n(t) = -16*t**2 - 63*t - 24. Let q(b) = 33*b**2 + 126*b + 49. Let d(v) = -13*n(v) - 6*q(v). Let d(z) = 0. What is z?
-6, -3/10
Let t(d) be the second derivative of 5*d**7/42 + 17*d**6/6 + 79*d**5/4 + 105*d**4/4 - 270*d**3 - 1350*d**2 - 3472*d. Factor t(o).
5*(o - 2)*(o + 3)**3*(o + 10)
Let y(a) be the second derivative of a**7/21 - a**6/3 - a**5/10 + 5*a**4/6 + 202*a. Factor y(h).
2*h**2*(h - 5)*(h - 1)*(h + 1)
Let g(a) be the first derivative of a**4/18 - 14*a**3/3 + 147*a**2 + 57*a - 1. Let b(y) be the first derivative of g(y). Determine n so that b(n) = 0.
21
Let q be 16 + -1 - -6*30917/172. Factor q*m**2 + 162*m + 6.
3*(27*m + 2)**2/2
Let j(z) = 38*z**3 + 74*z**2 - 80*z - 1552. Let f(m) = -12*m**3 - 25*m**2 + 27*m + 515. Let b(p) = 16*f(p) + 5*j(p). What is n in b(n) = 0?
-15, -4, 4
Let u(a) be the second derivative of 5*a**4/12 - 360*a**2 - 592*a. Factor u(l).
5*(l - 12)*(l + 12)
Let f(s) be the second derivative of -8/15*s**6 + 4/3*s**4 + 1/14*s**7 + 0*s**2 + 2*s**3 + 197 - 2*s - 3/4*s**5. Suppose f(j) = 0. What is j?
-1, -2/3, 0, 1, 6
Let q(w) = -w**3 - 6*w**2 + 18*w + 19. Let b be q(-8). Suppose -228*y + 1 - 16*y**4 - 132*y**b - 304*y**2 + 6 - 47 = 0. What is y?
-5, -2, -1, -1/4
Factor -15264*c**2 + 15320*c**2 + 736 - 161*c + 581*c + 536*c - 4*c**3 - 160*c.
-4*(c - 23)*(c + 1)*(c + 8)
Let t(l) = -3*l**2 - 166 + 64 + 71*l + 35*l**2 - 23*l**3 + 22*l**3. Let d be t(34). Factor 0*i - 2/3*i**3 + 0*i**4 + d + 2/9*i**5 + 4/9*i**2.
2*i**2*(i - 1)**2*(i + 2)/9
Let q(i) = 35*i**2 - 31*i - 2. Let x be q(1). Let u(p) be the first derivative of -2/33*p**3 + 23 - 2/11*p**x + 6/11*p. Factor u(n).
-2*(n - 1)*(n + 3)/11
Let p be (-16)/(-10) - (-48)/(-30). Let c(s) be the third derivative of -4/9*s**4 - 16/45*s**5 + 0*s + p - 12*s**2 - 2/9*s**3. Factor c(v).
-4*(4*v + 1)**2/3
Let c be (-269204075)/2093 + 2*-5. Let v = 128785 + c. What is l in -60/13*l**3 - 600/13*l**2 + 0 - v*l - 2/13*l**4 = 0?
-10, 0
Let y = -6605/6 + 2209/2. Find g, given that -1/3*g**4 + 0 + y*g**2 - 2/3*g**3 + 4*g = 0.
-4, -1, 0, 3
Let p(k) be the second derivative of k**6/6 - 23*k**5/4 + 135*k**4/4 - 485*k**3/6 + 95*k**2 - 111*k - 4. Factor p(h).
5*(h - 19)*(h - 2)*(h - 1)**2
Let m = 788 + -779. Let x be -7 - (m + (-260)/16). Solve -x*v**4 + 0 + v**3 + 1/4*v**2 - v = 0 for v.
-1, 0, 1, 4
Let i(m) be the second derivative of -107*m**4/18 + 220*m**3/9 - 4*m**2 + 218*m - 4. Factor i(k).
-2*(k - 2)*(107*k - 6)/3
Let g(q) be the third derivative of -q**7/630 - 67*q**6/90 + 1227*q**2. Let g(c) = 0. Calculate c.
-268, 0
Let b be (-6)/(-4)*12*4/18. Suppose 0 = -b*h + 3*h + a + 51, -206 = -4*h + 5*a. Let 152*i + 10*i**2 - 68*i + 15 - h*i = 0. Calculate i.
-3, -1/2
Suppose -3*i - 3*d = -d - 67, 0 = i + d - 24. Determine z, given that 2*z + 34*z**2 - 34*z**2 + 36*z**4 + 20*z**5 + 28*z**4 + i*z**2 + 57*z**3 = 0.
-2, -1/2, -1/5, 0
Let z(r) = 3*r**3 - 38*r**2 + 74*r - 46. Let t be (1/3 + 3)*27/(-18). Let n(o) = -2*o**3 + 25*o**2 - 49*o + 31. Let k(h) = t*z(h) - 7*n(h). Factor k(b).
-(b - 13)*(b - 1)**2
Let -224/13*m + 16/13*m**4 + 1086/13*m**2 - 128/13 - 20*m**3 = 0. What is m?
-1/4, 1/2, 8
Let p(y) be the second derivative of -y**7/2520 + y**6/45 + 3*y**5/10 + y**4/3 + 25*y**3/6 - 10*y + 1. Let c(v) be the third derivative of p(v). Solve c(n) = 0.
-2, 18
Let t(i) be the third derivative of -8/3*i**3 + 0*i - 21*i**2 + 1/60*i**5 + 1/72*i**6 + 0*i**4 + 0. Let f(a) be the first derivative of t(a). Factor f(o).
o*(5*o + 2)
Find w such that 22*w + 225 - 1154*w**2 + 119*w + 89*w + 1159*w**2 = 0.
-45, -1
Suppose t = -7, -10*t + 52 = 8*v - 14*t. Let a(f) be the first derivative of 1/42*f**4 + 0*f**2 - 8/63*f**v + 0*f - 18. Factor a(g).
2*g**2*(g - 4)/21
Let o be (7 + (-29)/3)*-6. Suppose o*s = 3*s. Factor 9/7*w - 9/7*w**3 + 3/7*w**2 - 3/7*w**4 + s.
-3*w*(w - 1)*(w + 1)*(w + 3)/7
Let a(j) be the third derivative of 2*j**7/105 - 2*j**6/5 + 43*j**5/15 - 10*j**4 + 56*j**3/3 - 42*j**2 + 1. Determine b, given that a(b) = 0.
1, 2, 7
Suppose 0 = 124*l - 72*l + 117*l - 676. Let b(v) be the second derivative of 0*v**2 + 2/15*v**6 + 22*v + 0*v**3 + 1/6*v**l - 9/20*v**5 + 0. Factor b(j).
j**2*(j - 2)*(4*j - 1)
Let -135/2*s - 8 + 17/4*s**2 = 0. What is s?
-2/17, 16
Let f(j) be the first derivative of 6*j**5 - 95*j**4/4 + 5*j**3 + 1177. Determine n, given that f(n) = 0.
0, 1/6, 3
Let z(p) = p**3 - 2*p - 1. Let u(f) = -5*f**4 + 215*f**3 - 475*f**2 + 295*f + 30. Let c(t) = u(t) + 30*z(t). Factor c(i).
-5*i*(i - 47)*(i - 1)**2
Let g(r) be the first derivative of -r**3/12 - 71*r**2/4 - 1707. Factor g(u).
-u*(u + 142)/4
Let p(d) be the third derivative of 0*d**4 + 0*d + 0*d**3 - 1/336*d**8 + 0 + 0*d**5 + 1/105*d**7 - 1/120*d**6 + 49*d**2. What is w in p(w) = 0?
0, 1
Let a(i) be the third derivative of -1/60*i**5 + 8/3*i**3 - 1/4*i**4 + 0 - 75*i**2 + 0*i. Determine o, given that a(o) = 0.
-8, 2
Let l(q) be the third derivative of 5*q**8/112 - 5*q**7/42 - 13*q**6/12 + 23*q**5/6 - 15*q**4/8 - 15*q**3/2 + 957*q**2. Let l(p) = 0. Calculate p.
-3, -1/3, 1, 3
Let v(t) be the first derivative of 1/18*t**3 + 1/36*t**4 - 10 + 1/18*t**2 + 20*t + 1/180*t**5. Let j(a) be the first derivative of v(a). Factor j(k).
(k + 1)**3/9
Let z(p) be the first derivative of p**5/5 - 45*p**4/4 + 604*p**3/3 - 1080*p**2 + 1600*p - 2402. Factor z(y).
(y - 20)**2*(y - 4)*(y - 1)
Find k such that 9/7*k**3 + 144/7 - 12*k + 3/7*k**4 - 72/7*k**2 = 0.
-6, -2, 1, 4
Let l(u) be the second derivative of u**5/420 + u**4/168 - u**3/21 - 33*u**2 + 63*u. Let a(t) be the first derivative of l(t). Factor a(d).
(d - 1)*(d + 2)/7
Let n(m) = 7*m**2 - 1842*m - 1858. Let h(p) = -55*p**2 + 14735*p + 14865. Let o(b) = -3*h(b) - 25*n(b). Solve o(x) = 0 for x.
-1, 371/2
Factor 456*b + 32490 - 183/2*b**2 + 3/2*b**3.
3*(b - 38)**2*(b + 15)/2
Let m(b) be the second derivative of b**6/15 + 37*b**5/5 + 145*b**4/6 + 24*b**3 - 4*b - 1. Factor m(i).
2*i*(i + 1)**2*(i + 72)
Let d(l) be the third derivative of -l**4/12 - 5*l**3/6 + 6*l**2. Let j be d(-5). Factor -x**4 - 12*x**3 + 8*x**2 - j*x**4 + 10*x**4 + 0*x**4.
4*x**2*(x - 2)*(x - 1)
Let r(l) be the third derivative of l**8/112 + 3*l**7/10 - 88*l**2 - 5. Factor r(k).
3*k**4*(k + 21)
Suppose 0 = 630*c - 638*c. Let q(r) be the third derivative of 5/12*r**4 + 0*r**3 + c*r + 0 + 1/12*r**5 - 10*r**2. Let q(a) = 0. What is a?
-2, 0
Let o = 557 - 554. Let n be -6*(-2)/o - (-132)/(-45). Let 0 + 0*h - 8/5*h**3 - 2/3*h**5 - n*h**2 + 12/5*h**4 = 0. What is h?
-2/5, 0, 2
Let v(z) = -8*z**3 - 116*z**2 + 118. Let b(q) = 3*q**3 - 3*q**2 + q + 2. Let k(y) = -4*b(y) - 2*v(y). Determine i so that k(i) = 0.
-61, -1, 1
Let w(t) be the first derivative of -5*t**3/3 - 485*t**2/2 + 990*t - 1858. Factor w(b).
-5*(b - 2)*(b + 99)
Let g be 0 - (314/(-1099))/(24/742). Find z such that 1/6*z**3 - 25/6*z**2 - 9/2 - g*z = 0.
-1, 27
Let f = -8609 + 25828/3. Factor 0 - 4/9*p + 1/9*p**3 + f*p**2.
p*(p - 1)*(p + 4)/9
Suppose 17*k + 13*k - 150 = 0. Let g(l) be the third derivative of 7/9*l**4 + 0*l - 49/90*l**k + 0 - 4/9*l**3 + 6*l**2. Let g(m) = 0. What is m?
2/7
Suppose 13/2*h - 1/6*h**2 + 21 = 0. What is h?
-3, 42
Solve 1/2*i**3 + 0 - 9/2*i + 4*i**2 = 0 for i.
-9, 0, 1
Let z(k) be the third derivative of -k**8/42 + 18*k**7/35 + 7*k**6/15 - 3*k**2 - 22. Let z(u) = 0. Calculate u.
-1/2, 0, 14
Let w(h) = -11 + 13 - 3 + h**4 - 2*h. Let f(o) = -8*o**4 + 5*o**3 - 9*o**2 - 63*o - 99. Let q(a) = 2*f(a) + 18*w(a). Factor q(s).
2*(s - 4)*(s + 3)**3
Find b, given that -64*b**2 + 125*b**2 - 1211 - 2548*b - 73*b**2 + 363 = 0.
-212, -1/3
Determine y, given that 17/4*y**4 - 25 - 421/4*y**2 - 109/4*y**3 + 5/4*y**5 - 100*y = 0.
-5, -2, -1, -2/5, 5
Let s(n) be the second derivative of -n**9/52920 + n**8/5880 - n**7/2205 + 17*n**4/4 - 16*n. Let i(q) be the third derivative of s(q). Factor i(v).
-2*v**2*(v - 2)**2/7
Let n be -9 - (-3 - 6 - (2 - 7)). Let f(g) = 8*g**3 + 14*g**2 - 18*g. Let s(l) = -7*l**3 - 12*l**2 + 17*l. Let t(h) = n*f(h) - 6*s(h). Factor t(q).
2*q*(q - 2)*(q + 3)
Let p(a) be the first derivative of -a**6/1980 + 4*a**5/165 + 17*a**4/132 - 152*a**3/3 - 20. Let w(n) be the third derivative of p(n). Factor w(t).
-2*(t - 17)*(t + 1)/11
Suppose 0 = -25*x + 27*x + u + 3, 0 = 3*x + 3*u + 9. Let l(w) be the first derivative of 0*w + 1/5*w**5 - 26 - 1/2*w**4 +