 s = -318 - -322. Let a(r) be the third derivative of 0 - 1/42*r**s - r**2 + 0*r**3 + 0*r - 1/210*r**5. Factor a(h).
-2*h*(h + 2)/7
Factor 7605/2*k**2 - 6591/2*k**3 + 375/2 - 2925/2*k.
-3*(13*k - 5)**3/2
Suppose -9*k = -55 - 44. Factor 25*t**2 + 10*t - 34*t**2 + 27*t**2 + k*t - 3*t**3.
-3*t*(t - 7)*(t + 1)
Let p(d) be the second derivative of d**7/231 + 4*d**6/165 + 3*d**5/110 + 38*d. Solve p(i) = 0.
-3, -1, 0
Let y(p) be the third derivative of -p**8/336 + p**7/105 + p**6/24 - p**5/10 - p**2 - 8*p. Solve y(v) = 0.
-2, 0, 1, 3
Let u(v) be the first derivative of 4*v**3/21 - 2*v**2 - 32*v/7 + 28. Factor u(t).
4*(t - 8)*(t + 1)/7
Let s = -59929/9 - -6659. Factor 2/9*a**2 + 0 + s*a.
2*a*(a + 1)/9
Let a(g) be the third derivative of 0 + 0*g + 2*g**3 - 1/3*g**4 - 6*g**2 - 1/15*g**5. Solve a(d) = 0 for d.
-3, 1
Suppose 8*s + 3 = 9*s. Suppose s*f + f = 8. Factor 21 + 11*t + t - 3*t**f - 13 + 7*t**2.
4*(t + 1)*(t + 2)
Suppose -51 = 14*n - 31*n. Let i(m) be the first derivative of 7 - 8/9*m**2 - 8/9*m - 10/27*m**n - 1/18*m**4. Factor i(y).
-2*(y + 1)*(y + 2)**2/9
Suppose 244 - 236 = 4*r. Let a(f) be the third derivative of -4*f**r - 1/105*f**5 + 1/14*f**4 + 0 + 0*f - 4/21*f**3. Determine x so that a(x) = 0.
1, 2
Let 65*l**3 + 0 + 1/3*l**5 + 29/3*l**4 + 0*l - 75*l**2 = 0. What is l?
-15, 0, 1
Let o(v) = -6*v**4 - 3*v**3 - 36*v**2 + 37*v - 5. Let k(l) = l**4 + 3*l**3 - l**2 + l + 1. Let p(i) = -5*k(i) - o(i). Let p(q) = 0. Calculate q.
0, 2, 3, 7
Let y be (-86)/34 - ((-3 - 10) + 10). Factor y - 6/17*h**2 - 8/17*h.
-2*(h + 2)*(3*h - 2)/17
Let m = 14 - 10. Let j be 14/10*m/7. What is y in -2/5*y + 2/5*y**4 - 4/5*y**2 + j*y**3 - 2/5*y**5 + 2/5 = 0?
-1, 1
Let m be 2/21 - 4*9/378. Factor m*b**2 + 0*b + 0 + 0*b**4 - 2/3*b**5 + 2/3*b**3.
-2*b**3*(b - 1)*(b + 1)/3
Let r(p) be the first derivative of -4*p**5/5 + 32*p**3/3 - 64*p + 43. Factor r(d).
-4*(d - 2)**2*(d + 2)**2
Factor 9*d**4 - 34*d + d**5 + 39*d + 2*d**3 + 19*d + 28*d**3 + 44*d**2.
d*(d + 2)**3*(d + 3)
Let p(d) be the first derivative of 4*d**5/5 - 2*d**4 - 44*d**3/3 + 24*d**2 + 144*d + 77. Factor p(c).
4*(c - 3)**2*(c + 2)**2
Let h = -2122 - -2124. Factor 8/11*f + 2/11*f**h + 0.
2*f*(f + 4)/11
Let l(c) be the third derivative of c**6/180 - c**5/18 + 2*c**4/9 - 4*c**3/9 - 228*c**2 - 2. Suppose l(b) = 0. What is b?
1, 2
Let j(x) = 29*x**3 + 28*x**2 - 5*x - 65. Let q(s) = 9*s**3 + 10*s**2 - 2*s - 22. Let g(d) = 4*j(d) - 14*q(d). Factor g(a).
-2*(a + 2)**2*(5*a - 6)
Let s(t) = 2*t**2 - 8*t + 3. Let i be s(4). Suppose 5*j + 3*u = 6, -5*j - u = -i*j - 2. Factor j + 5/2*p**5 + 0*p**2 - 7/2*p**4 + 0*p + p**3.
p**3*(p - 1)*(5*p - 2)/2
Let g(y) = y**2 - 1. Let z(o) = -o**3 + 12*o**2 - 15*o + 4. Let v(d) = 5*g(d) - z(d). Factor v(p).
(p - 3)**2*(p - 1)
Let q(w) be the first derivative of -w**6/57 - 2*w**5/95 + w**4/38 + 2*w**3/57 + 70. Factor q(h).
-2*h**2*(h - 1)*(h + 1)**2/19
Suppose 19*g - 13*g - 60 = -24*g. Factor -8/11*p**4 + 14/11*p**3 + 0 - 4/11*p**g - 2/11*p.
-2*p*(p - 1)**2*(4*p + 1)/11
Let c(q) be the second derivative of 27/10*q**5 + 2/3*q**3 + 10*q + 0*q**2 + 0 + 13/6*q**4 + 23/15*q**6 + 1/3*q**7. Find p, given that c(p) = 0.
-1, -2/7, 0
Let j = -341 - -317. Let f be (j/126)/(12/(-14)). Suppose -f*i**2 - 50/9 + 20/9*i = 0. What is i?
5
Let s(a) = 15*a**3 - 90*a**2 - 115*a. Let m(i) = i**3 + i**2 - i. Let g(k) = 10*m(k) - s(k). Find u, given that g(u) = 0.
-1, 0, 21
Let c(d) be the third derivative of -1/72*d**4 + 1/315*d**7 + 1/45*d**5 - 1/72*d**6 - 3*d**2 + 0*d**3 + 0 + 0*d. Factor c(g).
g*(g - 1)**2*(2*g - 1)/3
Let w = 65 + -193/3. Let p = 358 + -356. Suppose 2/3*v - 1/6*v**p - w = 0. What is v?
2
Let n = 51 + -49. Let j be 102/30 - 6/n. Factor -2/5*x**4 - 2/5*x**3 + j*x**2 + 2/5*x + 0.
-2*x*(x - 1)*(x + 1)**2/5
Let q(r) = -r**3 - 6*r**2 - 8*r - 13. Let f be q(-5). Let y be ((-20)/(-16) + 1)*f/3. Solve -y + 1/4*m**2 + 1/4*m = 0.
-3, 2
Suppose -25*u + 66 = -6 + 22. Solve 0 - m**u + 1/2*m**5 + m**4 + 0*m - 1/2*m**3 = 0 for m.
-2, -1, 0, 1
Factor 5 - 8 + 100*h**2 + 2 - 4*h**3 + 1.
-4*h**2*(h - 25)
Let p be (-1 - (-7)/6) + (68/(-4))/102. Solve -1/11*g**2 + p + 6/11*g = 0.
0, 6
What is t in -14/5*t**2 + 0 + 1/5*t**3 + 13/5*t = 0?
0, 1, 13
Let p be (-3 + 4)/1 + 33/3. Suppose -5*y + 8 = -p. Factor 0*d - 2/3*d**2 + 1/3*d**5 + 0 - 4/3*d**y + 5/3*d**3.
d**2*(d - 2)*(d - 1)**2/3
Let b(d) be the first derivative of -5*d**6/6 + 13*d**5 + 115*d**4/2 + 160*d**3/3 - 476. Determine v, given that b(v) = 0.
-2, -1, 0, 16
Let p(q) = q**3 - 6*q**2 + q + 3. Let j be p(6). Suppose 3 = -2*c + j. Factor 0*r + c*r + 6*r - 6*r**2.
-3*r*(2*r - 3)
Find c such that 4/5*c**4 - 76/5*c**2 + 28/5*c - 28/5*c**3 + 72/5 = 0.
-2, -1, 1, 9
Let n(u) be the second derivative of u**4/6 + 13*u**3/3 - 30*u**2 + 222*u - 2. What is f in n(f) = 0?
-15, 2
Let l(u) = -6*u - 4. Let g(w) = 7*w - 50. Let n be g(7). Let v be l(n). Factor 2/9*o**2 - 4/3*o + v.
2*(o - 3)**2/9
Let l be (-12)/(-5) - 15/(-25). Suppose l*z - 49 = 2*z. Factor z - t**2 + 2*t - 3*t - 49.
-t*(t + 1)
Let t be -2*(-4)/(120/785). Let z = -52 + t. Factor -z*x + 1/6*x**2 + 0.
x*(x - 2)/6
Let w(n) be the third derivative of n**6/90 + 2*n**5/15 + 11*n**4/18 + 4*n**3/3 + 12*n**2 - n. Factor w(t).
4*(t + 1)*(t + 2)*(t + 3)/3
Let y = -9265/4 + 2320. Solve y*u + 5 - 5/4*u**2 = 0 for u.
-1, 4
Let l(r) = r**5 - 2*r**4 + 16*r**3 + 6*r**2 + 7*r. Let w(i) = -i**5 - 15*i**3 - 7*i**2 - 6*i. Let m(p) = -3*l(p) - 4*w(p). Factor m(k).
k*(k + 1)**3*(k + 3)
Let k(t) be the first derivative of -t**4/3 - 8*t**3/3 - 6*t**2 - 12*t + 4. Let y(j) be the first derivative of k(j). Factor y(r).
-4*(r + 1)*(r + 3)
Let w(o) be the third derivative of -o**8/224 + o**7/35 - 3*o**6/80 - o**5/10 + o**4/4 - 154*o**2. Suppose w(x) = 0. Calculate x.
-1, 0, 1, 2
Let d(a) be the second derivative of 1/150*a**5 + a**2 + 4*a + 0 - 1/10*a**4 + 3/5*a**3. Let q(y) be the first derivative of d(y). Solve q(t) = 0 for t.
3
Suppose -5*f + 38 = 3*o + 30, 4*o = 2*f - 24. Let l(a) be the second derivative of 5/72*a**f - 1/120*a**5 - 1/12*a**3 + 0 - 4*a - 3/4*a**2. Factor l(h).
-(h - 3)**2*(h + 1)/6
Suppose 4*l - 4 = -a, -5*l - 5*a + 18 = -7*a. Determine v so that -8 - 3 - 20*v**l + 108*v - 29 = 0.
2/5, 5
Let v(w) be the third derivative of w**7/15 + 11*w**6/20 + 16*w**5/15 - w**4 + 172*w**2. Factor v(x).
2*x*(x + 2)*(x + 3)*(7*x - 2)
Determine c so that -21/2*c + 0 + 3/4*c**2 = 0.
0, 14
Let d(j) be the second derivative of 2/3*j**3 + 0*j**2 - 1/3*j**4 + 13*j + 0. Factor d(s).
-4*s*(s - 1)
Let i(w) be the third derivative of w**6/20 - 64*w**5/15 + 469*w**4/4 - 294*w**3 + 74*w**2. Factor i(t).
2*(t - 21)**2*(3*t - 2)
Let i(z) = 4*z + 34. Let r be i(-7). Let m be (2 - r)*(-4)/8. Factor 0*p - 2/13*p**m + 0 - 2/13*p**3.
-2*p**2*(p + 1)/13
Let h(g) be the third derivative of g**7/3360 - g**5/480 + g**3/3 - 8*g**2. Let j(n) be the first derivative of h(n). Factor j(k).
k*(k - 1)*(k + 1)/4
Let t(o) be the first derivative of -4/27*o**3 - 1/18*o**4 + 7/9*o**2 - 8/9*o + 24. Factor t(v).
-2*(v - 1)**2*(v + 4)/9
Suppose 10*a - 3*v + 21 = 7*a, 4*a = 2*v - 14. Factor -2/7*r + 2/7*r**3 + 0*r**2 + a.
2*r*(r - 1)*(r + 1)/7
Let r(q) be the third derivative of 0 + 0*q**3 + 0*q - 1/42*q**5 + 1/42*q**4 - 1/735*q**7 - 14*q**2 + 1/105*q**6. Factor r(n).
-2*n*(n - 2)*(n - 1)**2/7
Suppose 3*l - 4*l = 22. Let y be l/8 + -3*(-1 - 0). Factor y*n + 1/2 - 1/2*n**2 - 1/4*n**3.
-(n - 1)*(n + 1)*(n + 2)/4
Let g(c) be the second derivative of -11/2*c**2 - 11*c + 1/60*c**4 + 0 + 1/450*c**5 + 2/45*c**3. Let n(w) be the first derivative of g(w). Factor n(t).
2*(t + 1)*(t + 2)/15
Let r(t) be the first derivative of 0*t**2 - 3/4*t**4 + 12*t - 1 - 3*t**3. Solve r(g) = 0.
-2, 1
Let v = 2/7545 - -22631/15090. Let o = 1 + 3. Let -1/4*g**5 - g**o - g**2 + 0 - v*g**3 - 1/4*g = 0. What is g?
-1, 0
Let w(i) be the first derivative of 15*i**4 + 45*i**3 + 0*i**2 - 12*i - 6 - 63/5*i**5. Let w(a) = 0. What is a?
-1, -1/3, 2/7, 2
Let p be (-2)/(-3)*(57/76 + 0). Factor 1/2 + r + p*r**2.
(r + 1)**2/2
Let v(m) be the second derivative of 3/20*m**5 + 1/2*m**4 + 0 + 0*m**2 + 10*m + 0*m**3. Find x, given that v(x) = 0.
-2, 0
Let t(u) be the second derivative of 4*u**2 - 5*u - 1/5*u**5 + 4/3*u**3 + 0 - 1/2*u**4 + 1/15*u**6. Find d such that t(d) = 0.
-1, 2
Let p(j) = -9*j**2 + 3*j - 