- -7). Let d = 153 - s. Solve -2/9*l**3 + d*l**4 + 0 - 2/9*l**2 + 2/9*l = 0.
-1, 0, 1
Suppose -3*h + 2 = j, -5*j + h + 11 - 1 = 0. Let x(c) be the second derivative of 1/3*c**3 + 1/18*c**4 + 0 + 2/3*c**j + c. Find i such that x(i) = 0.
-2, -1
Let t be 6/8*(7 + 1). Suppose 6*i - t = 2*i + w, 0 = 5*i + 3*w - 16. Factor 6 + 2/3*m**i + 4*m.
2*(m + 3)**2/3
Let p(t) be the first derivative of -t**6/360 - t**5/36 - 7*t**4/72 - t**3/6 - 11*t**2/2 + 6. Let k(z) be the second derivative of p(z). Factor k(f).
-(f + 1)**2*(f + 3)/3
Let q(x) be the second derivative of 1/2*x**6 - 3/2*x**3 - 9*x + 27/2*x**2 + 0 + 1/14*x**7 + 3/10*x**5 - 7/2*x**4. What is r in q(r) = 0?
-3, -1, 1
Let z(h) be the second derivative of -h**5/10 + 2*h**4/3 - 5*h**3/3 + 2*h**2 + h - 26. Factor z(l).
-2*(l - 2)*(l - 1)**2
Let d(n) = -n**2 - 13*n - 38. Let p be d(-8). Factor m**3 - 3*m**4 + 5*m + 2*m**4 - 2*m + 5*m**p.
-m*(m - 3)*(m + 1)**2
Let q(w) = w**3 + 3*w**2 - 3*w - 1. Let v(h) = -h**2 + h + 1. Let y(l) = -q(l) - 2*v(l). Let z(m) = -m**3 + m**2 - m + 1. Let s(k) = y(k) + z(k). Factor s(o).
-2*o**3
Suppose -5*p - 4*h = -27 - 6, 2*h + 24 = 2*p. Let t be 1 + 2/(6/p). Suppose -2*y**2 + y**3 - y**5 - 3*y**t + 3*y**2 + 2*y**4 = 0. Calculate y.
-1, 0, 1
Let d(t) be the second derivative of -t**6/30 + 7*t**5/4 + 37*t**4/12 - 35*t**3/6 - 18*t**2 + 3*t + 8. Suppose d(y) = 0. What is y?
-1, 1, 36
Let d be -2 + (2 - 5 - 3 - (-144)/18). Determine m, given that 0*m**4 - 2/9*m**5 + 0 - 2/9*m + 4/9*m**3 + d*m**2 = 0.
-1, 0, 1
Let n be 25/45*372/310. Factor 2/3 - 4/3*c + n*c**2.
2*(c - 1)**2/3
Let t(g) be the first derivative of -g**6/200 + 3*g**5/100 - 3*g**4/40 + g**3/10 + 15*g**2/2 + 5. Let c(j) be the second derivative of t(j). Factor c(x).
-3*(x - 1)**3/5
Let h = 4/5 + -11/20. Let r(x) be the first derivative of 0*x + 1/2*x**2 + h*x**4 - 2/3*x**3 + 10. Factor r(l).
l*(l - 1)**2
Factor -20*d - 120 + 5/2*d**2.
5*(d - 12)*(d + 4)/2
Let l(b) be the first derivative of b**6/1800 + b**5/100 + 3*b**4/40 + 19*b**3/3 - 13. Let d(o) be the third derivative of l(o). Suppose d(f) = 0. Calculate f.
-3
Let y = -3239/15 + 216. Let u(c) be the first derivative of y*c**2 + 2/45*c**3 + 0*c - 6. Factor u(f).
2*f*(f + 1)/15
Let o(w) be the third derivative of -1/40*w**4 + 16*w**2 + 0*w**3 + 1/350*w**7 + 3/100*w**5 - 3/200*w**6 + 0*w + 0. Factor o(k).
3*k*(k - 1)**3/5
Suppose 0 = 26*y - 29*y + 114. Factor y*h**3 + 6 + 3*h - 19*h**3 + h - 14*h**2 - 15*h**3.
2*(h - 3)*(h - 1)*(2*h + 1)
Let l(v) be the third derivative of -2*v**4 + 37/75*v**5 + 0*v - 1/15*v**6 - v**2 + 0 + 24/5*v**3 + 2/525*v**7. Factor l(h).
4*(h - 3)**2*(h - 2)**2/5
Factor 64/5*o**2 - 8/5*o**4 + 0 - 128/5*o + 24/5*o**3 - 2/5*o**5.
-2*o*(o - 2)**2*(o + 4)**2/5
Find m, given that 55*m**3 + 5*m**4 - 28*m - 65 + 217*m**2 + 8*m**2 + 225 + 110 + 433*m = 0.
-3, -2
Let d(g) be the first derivative of 2*g**4/3 + 19*g**3/3 - 19*g**2/2 - 8*g/3 + 31. Factor d(j).
(j - 1)*(j + 8)*(8*j + 1)/3
Let o(i) = 68*i**4 - 36*i**4 - 31*i**4. Let m(s) be the first derivative of 12*s**4 + 72*s**3 + 216*s**2 + 324*s - 1. Let p(v) = -m(v) - 4*o(v). Factor p(w).
-4*(w + 3)**4
Let 28/3*i - 26/9*i**2 + 0 + 2/9*i**3 = 0. What is i?
0, 6, 7
Suppose -28 = 3*a - 373. Let w = -113 + a. Solve -3/5*g**w - 12/5 + 12/5*g = 0.
2
Let n(r) be the first derivative of -7*r**6/15 - 12*r**5/5 - 5*r**4 - 16*r**3/3 - 3*r**2 - 4*r/5 - 126. Factor n(a).
-2*(a + 1)**4*(7*a + 2)/5
Let o(f) be the third derivative of -f**7/350 - f**6/200 - 16*f**2. Factor o(i).
-3*i**3*(i + 1)/5
Let j(c) = 6*c**2 - 7*c + 2. Let d(o) = o**2 + o. Suppose -6*q + q - 5 = 0. Suppose 3*f - 5*r = 21, 3*r = f - 0*r - 11. Let w(b) = f*d(b) + q*j(b). Factor w(p).
-(p - 2)*(4*p - 1)
Suppose z + 2*a = 8, a = -4*z + 2*a + 23. Solve -12*o - z - 1 + 17 + 2 + 3*o**2 = 0.
2
Let d = 82 + -73. Suppose 5*f + d = -5*j + 29, 0 = 4*j - 4. Suppose -41/3*v**2 + 15*v**4 + 28/3*v**f - 28/3*v - 4/3 = 0. Calculate v.
-1, -2/5, -2/9, 1
Let y(x) be the second derivative of 2*x + x**3 + 4*x**2 + 0 - 1/6*x**4. Factor y(o).
-2*(o - 4)*(o + 1)
Let a be (1 - 5) + 3 - (-3 - -2). Let d(h) be the second derivative of a*h**2 + 0 - 1/4*h**4 + h - 1/20*h**5 + 2/3*h**3. Factor d(t).
-t*(t - 1)*(t + 4)
Let u(i) be the first derivative of -7*i**3/9 - 22*i**2/3 - 4*i - 232. Suppose u(m) = 0. What is m?
-6, -2/7
Let t(m) be the third derivative of m**6/630 - m**5/105 - m**4/14 + 7*m**3/6 - 6*m**2. Let r(h) be the first derivative of t(h). Factor r(x).
4*(x - 3)*(x + 1)/7
Let d(i) be the first derivative of 1/20*i**4 + 2/15*i**6 - 1/2*i**2 - 2/5*i + 13/15*i**3 - 11 - 11/25*i**5. Solve d(x) = 0.
-1, -1/4, 1, 2
What is y in -27/2*y**2 - 651*y - 144 = 0?
-48, -2/9
Factor 30/11*u + 4/11*u**2 - 2/11*u**3 + 0.
-2*u*(u - 5)*(u + 3)/11
Determine x so that -28*x**2 - 28*x**2 - 814 + 380*x - 12*x**2 + 114 + 4*x**3 = 0.
5, 7
Suppose 16 = 4*p + 4. Let -a**3 - 11*a - a**p + 17*a + 4 = 0. What is a?
-1, 2
Let m(s) be the third derivative of 0*s - 3*s**2 - 5/336*s**8 + 0 + 0*s**3 - 1/6*s**5 + 0*s**4 - 5/24*s**6 - 2/21*s**7. Factor m(q).
-5*q**2*(q + 1)**2*(q + 2)
Let l = -27 + 30. Determine q so that -13 + l*q**3 + 15 - 4 - 9*q - 4 = 0.
-1, 2
Factor -11*q**2 + 4 - 5/3*q**3 - 16/3*q.
-(q + 1)*(q + 6)*(5*q - 2)/3
Let z(x) be the third derivative of 0 - 1/45*x**3 + 19*x**2 + 1/900*x**6 + 0*x - 1/180*x**4 + 1/450*x**5. Factor z(i).
2*(i - 1)*(i + 1)**2/15
Suppose -20 = -11*j + 24. Let m(l) be the third derivative of 0*l - 8*l**2 + 0 - 1/10*l**7 + 0*l**3 + 23/40*l**6 + 1/2*l**j - l**5. Factor m(n).
-3*n*(n - 2)*(n - 1)*(7*n - 2)
Let n = -60521/7 + 8646. Factor 4/7*r + 3/7*r**2 - n*r**3 + 0.
-r*(r - 4)*(r + 1)/7
Let v(m) be the second derivative of m**6/70 - 9*m**5/70 + m**4/28 + 12*m**3/7 + 24*m**2/7 - m - 12. Factor v(i).
3*(i - 4)**2*(i + 1)**2/7
Let b(p) be the second derivative of 14*p**7/9 - 119*p**6/90 - p**5/10 + p**4/4 + 6*p + 5. Determine x so that b(x) = 0.
-1/4, 0, 3/7
Let y(k) be the first derivative of -3*k**2/2 + 6*k + 36. Let l be y(2). Suppose -1/6*h**2 + 1/6*h**3 + 0*h + l = 0. Calculate h.
0, 1
Suppose 5 = 4*k - 3. Let s be 49 + -52 - (-1 + (-5 - -1)). Factor -s*h - 3*h**5 + 6*h**k + 0*h - h - 6*h**4 + 6*h**5.
3*h*(h - 1)**3*(h + 1)
Let d be (-8)/6 + 8/6. Factor 2/5*g**4 - 2/5*g**2 + 2/5*g**3 + d - 2/5*g**5 + 0*g.
-2*g**2*(g - 1)**2*(g + 1)/5
Let y = -12928/33 - -4313/11. Factor 0 - 7/3*a**2 - 5/3*a**4 - 2/3*a - y*a**5 - 3*a**3.
-a*(a + 1)**3*(a + 2)/3
Factor 30*y + 1769*y**2 + 3*y**3 + 1811*y**2 - 3547*y**2.
3*y*(y + 1)*(y + 10)
Determine k so that 30*k**3 - 8*k**4 - 61*k**3 - 4*k - 4*k**5 - 8 + 16*k**2 + 39*k**3 = 0.
-2, -1, 1
Let l(x) be the third derivative of 2*x**7/21 - x**6/2 + 13*x**5/12 - 5*x**4/4 + 5*x**3/6 - 3*x**2 + 27*x. Factor l(y).
5*(y - 1)**2*(2*y - 1)**2
Let i be ((-5)/(-15))/(6/288*8). Solve 1/3 - 2/3*d + 1/3*d**i = 0 for d.
1
Let g be ((-8)/(-10))/((-1)/(-5)). Let h = -4135 + 12407/3. What is u in 2/3*u - 1/3*u**g - h*u**3 + 0 + 1/3*u**2 = 0?
-2, -1, 0, 1
Factor -40*k**3 + 19*k**3 + 6*k**2 + 17*k**3 - 24*k**2 - 7 + k**4 - 20*k.
(k - 7)*(k + 1)**3
Let s be 13/(-1) + (-7365)/(-491). Factor 18 + 0*q**s - 4/3*q**3 - 2/9*q**4 + 12*q.
-2*(q - 3)*(q + 3)**3/9
Let a(g) = 9*g**5 + 24*g**4 - 115*g**3 + 97*g**2 + 127*g - 128. Let o(k) = k**5 + k**3 - k**2 + k. Let x(j) = a(j) - 7*o(j). What is p in x(p) = 0?
-16, -1, 1, 2
Let f = 4842 + -33886/7. Determine u so that -6/7*u**3 + 0 + f*u**5 + 10/7*u**2 - 10/7*u**4 - 2/7*u = 0.
-1, 0, 1/4, 1
Find o, given that 6/5*o**5 - 22/5*o + 48/5*o**3 - 12/5 + 32/5*o**4 + 12/5*o**2 = 0.
-3, -1, 2/3
Let q(f) be the first derivative of 0*f - 4/13*f**2 - 24/65*f**5 - 35/26*f**4 - 10 - 16/13*f**3. Let q(d) = 0. Calculate d.
-2, -2/3, -1/4, 0
Let c = 2391/14 - 1192/7. Let c*r**2 + 3/2*r + 1 = 0. What is r?
-2, -1
Suppose -13*t = -8*t - 260. Factor -t*g**2 + 10*g**5 - 5*g**5 + 62*g**2 - 10*g**4 - 5*g**3.
5*g**2*(g - 2)*(g - 1)*(g + 1)
Let n(m) = m**3 - m**2 - 2*m + 7. Let g(i) = -6*i**2 - i**3 + 13*i**2 + 5*i - 6 - 6*i**2 - 3*i. Let h(s) = -7*g(s) - 6*n(s). Factor h(p).
p*(p - 2)*(p + 1)
Suppose -5*w = -3*p - 22 - 0, -2*w - 3*p = 8. Factor 2*d**2 - 4*d**2 - 2*d**w + 0*d**3 - 4*d**3.
-4*d**2*(d + 1)
Solve -35 + 2*c**3 + 0*c**3 - 1439*c + 170*c**2 + 3841*c - 3663 + 1124*c = 0.
-43, 1
Let r(l) be the third derivative of