1/4*k**4 = 0.
0, 1
Let b(t) be the second derivative of -7/6*t**3 - 1/20*t**5 + 0 - 5/12*t**4 - 3/2*t**2 - 12*t. Factor b(n).
-(n + 1)**2*(n + 3)
Let t = 7051/14122 - -5/7061. Determine a so that t*a**4 + 13/2*a**2 + 18 - 5*a**3 + 30*a = 0.
-1, 6
Let i(u) = 4*u**2 - 4. Let w be i(-2). Factor 0*x**4 + 2 + 2*x**4 + 8*x**2 - w*x**2.
2*(x - 1)**2*(x + 1)**2
Let f(r) = -3*r**3 + 9*r**2 + 22*r - 28. Let c(w) = 3*w**3 - 9*w**2 - 21*w + 27. Let h(k) = -4*c(k) - 3*f(k). Factor h(l).
-3*(l - 4)*(l - 1)*(l + 2)
Let s(r) be the second derivative of -26*r + r**3 + 0 + 4/3*r**2 + 1/30*r**5 + 1/3*r**4. Factor s(o).
2*(o + 1)**2*(o + 4)/3
Let o = -7 + 10. Let s(a) = -136*a - 2038. Let v be s(-15). Find m such that 9/2*m**5 + 0*m + 0 - 3/2*m**v + 15/2*m**4 + 3/2*m**o = 0.
-1, 0, 1/3
Let o = 42829/33 - 3893/3. Determine h, given that -4/11*h + 0 + o*h**2 = 0.
0, 2
Let j(x) be the second derivative of 1/30*x**5 - 4/135*x**6 + 0 + 0*x**4 + 0*x**3 + 1/189*x**7 + 20*x + 0*x**2. Let j(m) = 0. Calculate m.
0, 1, 3
Suppose a - f = -0*a - 9, 2*a - f + 14 = 0. Let u(x) = -x**3 + x**2 - 5*x + 5. Let l(t) = -t + 1. Let k(d) = a*l(d) + u(d). Determine w, given that k(w) = 0.
0, 1
Let n(g) be the second derivative of g**5/60 - 5*g**4/2 - 466*g + 1. Suppose n(o) = 0. Calculate o.
0, 90
Suppose 34*w = 35*w - 21. What is g in -30*g + 5*g**4 - 5*g - 4*g**3 + 11 - 1 - w*g**3 + 45*g**2 = 0?
1, 2
What is r in -189/2*r + 2079/8*r**3 + 123*r**2 + 243/8*r**4 + 12 = 0?
-8, -1, 2/9
Let h be -14*1/(-1)*1. Let r = h - 11. Factor -8*q**3 - r + 8*q**3 + 6*q**2 - 3*q**4.
-3*(q - 1)**2*(q + 1)**2
Let r = 21 - 19. What is b in b + 6 - 5*b**2 - r*b**2 - 2*b + 6*b**2 = 0?
-3, 2
Let l(c) be the first derivative of 1/30*c**5 - 2*c**3 + 0*c**2 + 0*c + 1/12*c**4 + 1/180*c**6 - 3. Let r(s) be the third derivative of l(s). Factor r(m).
2*(m + 1)**2
Factor 127 + 56*u**2 - 18*u**2 + 2*u**3 - 4*u**3 + 109*u + 19*u - 39.
-2*(u - 22)*(u + 1)*(u + 2)
Let j(a) be the second derivative of 5*a - 1/6*a**4 + 0*a**3 + a**2 + 0. Determine h so that j(h) = 0.
-1, 1
Suppose 0*w = 4*w. Suppose w = 4*s - s - 36. Suppose 25 - 6*z + 6*z**2 - 2*z**3 - s - 11 = 0. Calculate z.
1
Let k be 6/(-4) + 1 - (-15)/10. Factor 2*n**4 + 5*n**4 - k + 2*n**2 - 8*n**4.
-(n - 1)**2*(n + 1)**2
Let o(f) be the third derivative of f**7/840 + f**6/40 + 11*f**5/120 - 7*f**4/8 + 49*f**3/24 - 28*f**2 + 2*f. Factor o(r).
(r - 1)**2*(r + 7)**2/4
Factor -8 + 1/4*f**3 + 0*f + 3/2*f**2.
(f - 2)*(f + 4)**2/4
Let c = -67/30 + -171/10. Let r = 20 + c. What is v in -r*v**2 - 4/3*v - 2/3 = 0?
-1
Let v(f) be the second derivative of f**6/120 + 9*f**5/80 + 5*f**4/16 - 25*f**3/24 - 33*f + 2. Factor v(r).
r*(r - 1)*(r + 5)**2/4
Let r(p) be the third derivative of 1/20*p**4 + 53*p**2 + 0 + 0*p + 1/150*p**5 + 0*p**3. Factor r(t).
2*t*(t + 3)/5
Let c(q) = 20*q + 1203. Let l be c(-60). Factor 0 + 2/7*k - 1/7*k**l - 1/7*k**2.
-k*(k - 1)*(k + 2)/7
Let p = 2148 - 2143. Factor -12/7*i**2 - 3/7*i + 0 - 18/7*i**3 - 12/7*i**4 - 3/7*i**p.
-3*i*(i + 1)**4/7
Factor 1/5*i**3 + 1/5*i**2 - 1/5 - 1/5*i.
(i - 1)*(i + 1)**2/5
Let a(s) = -15*s**4 - 17*s**3 + 25*s**2 + 10*s + 3. Let p(r) = -15*r**4 - 18*r**3 + 25*r**2 + 10*r + 2. Let z(x) = -2*a(x) + 3*p(x). Factor z(v).
-5*v*(v - 1)*(v + 2)*(3*v + 1)
Let s(o) be the first derivative of 0*o**2 + 0*o + 7/30*o**4 - 44 - 4/45*o**3. Factor s(g).
2*g**2*(7*g - 2)/15
Solve -6/5*m - 6/5*m**3 - 12/5*m**2 + 0 = 0 for m.
-1, 0
Let u(s) = -10*s**4 - 2*s**3 + 28*s**2 - 22*s - 6. Let h(o) = -21*o**4 - 3*o**3 + 56*o**2 - 45*o - 13. Let z(r) = -6*h(r) + 13*u(r). Let z(n) = 0. Calculate n.
-4, 0, 1
Let o be (-196)/(-35) - (-2)/5. Determine d, given that 14*d**2 - 6*d + o*d**2 + d**2 = 0.
0, 2/7
Suppose 4*m - m = -u + 915, -2*m + 605 = -u. Let l be 1/(-6)*m/(-19). Solve -10/3*t - 2/3*t**2 - l = 0.
-4, -1
Factor 0*l - 1/4*l**4 - 3/4*l**2 + 0 - l**3.
-l**2*(l + 1)*(l + 3)/4
Let a(q) be the second derivative of 2*q**6/15 - 11*q**5/5 + 10*q**4/3 + 15*q - 4. Factor a(s).
4*s**2*(s - 10)*(s - 1)
Suppose -33 + 97 = 2*a. Let k be (284/a - 9)*(-4)/2. Factor -3/8 + 1/8*q**2 + k*q.
(q - 1)*(q + 3)/8
Let p(c) be the first derivative of c**3/3 - 3*c**2/2 - 10*c + 6. Let z be p(5). Factor 1/4*w**2 + z*w + 0.
w**2/4
Let k(c) be the third derivative of -c**7/630 - c**6/120 - c**5/90 + 12*c**2 - 7*c. Suppose k(p) = 0. Calculate p.
-2, -1, 0
Let q(i) be the third derivative of -5*i**8/336 + 5*i**7/21 - 2*i**6/3 - 55*i**2 - 2*i. Let q(j) = 0. What is j?
0, 2, 8
Suppose -4*o - 3*i - 28 = -104, i + 57 = 3*o. Suppose -o = -5*c - 4. Factor -1/4*z**4 + 27/2*z + 5/2*z**c - 9*z**2 - 27/4.
-(z - 3)**3*(z - 1)/4
Let a(o) be the first derivative of -o**3/2 + 75*o**2/2 - 144*o - 325. What is z in a(z) = 0?
2, 48
Suppose 3*i - 22 - 68 = 0. Solve x**2 + 25 + i*x + 4*x**2 + 0*x**2 = 0 for x.
-5, -1
Let y(k) be the first derivative of 2*k**3/3 - 56*k**2 + 1568*k - 262. Factor y(j).
2*(j - 28)**2
Let q(m) be the third derivative of 1/60*m**5 + 1/24*m**4 + 0*m + 5*m**2 + 0 + 0*m**3. Find x such that q(x) = 0.
-1, 0
Let w(k) = 2*k**3 - 9*k**2 - 24*k. Let v(t) = 2*t**3 - 8*t**2 - 24*t. Let b(h) = 7*v(h) - 6*w(h). Determine m, given that b(m) = 0.
-3, 0, 4
Let u(m) be the first derivative of m**4/4 + 2*m**3 - 9*m**2/2 - 14*m + 145. Factor u(l).
(l - 2)*(l + 1)*(l + 7)
Let j = 2747/6 - 35687/78. Find h such that j + 2/13*h**4 - 6/13*h**2 - 2/13*h**3 + 2/13*h = 0.
-1, 1, 2
Let u(w) = 16*w**2 - 56*w - 132. Let c(i) = i**2 - 2*i. Let q(b) = 12*c(b) - u(b). Factor q(g).
-4*(g - 11)*(g + 3)
Let x = -76 - -76. Suppose -3*y + 2*w + x*w = 0, 3*y - w = 0. Factor y*o - 2/5*o**3 + 1/5*o**4 + 0 + 0*o**2.
o**3*(o - 2)/5
Let g(p) be the first derivative of 1/2*p**3 - 4 + 0*p + 3/4*p**2. Factor g(l).
3*l*(l + 1)/2
Let l(a) be the first derivative of -3/2*a + 5/12*a**3 + 13 - 13/8*a**2. Find m such that l(m) = 0.
-2/5, 3
Let j = 4 - 4. Let t be -1*((-21)/84)/((-6)/(-8)). Solve 4/3*i**3 - 5/3*i**2 + j + t*i = 0 for i.
0, 1/4, 1
Let k(i) be the third derivative of 0*i**5 - 1/1260*i**7 + 11*i**2 + 0 + 1/360*i**6 + 0*i**4 + 0*i**3 + 0*i. Factor k(y).
-y**3*(y - 2)/6
Let h be (152/646)/(2/17). What is d in 2/5*d**h - 6/5*d**4 - 2*d + 2*d**3 + 4/5 = 0?
-1, 2/3, 1
Let h = -90 + 75. Let r(o) = 3*o**4 + 9*o**3 + 24*o**2 + 3*o. Suppose -2 = 6*n - 4*n. Let m(y) = -y**2. Let u(a) = h*m(a) + n*r(a). Find t such that u(t) = 0.
-1, 0
Factor 10 + 17 + 60 - 8*q**2 + 196*q + 13.
-4*(q - 25)*(2*q + 1)
Let u = -8 - -14. Let h(g) = -g**4 + g**3 - g**2 - g - 1. Let t = 22 - 20. Let k(s) = 5*s**4 - 9*s**3 + 9*s**2 + s + 3. Let f(w) = t*k(w) + u*h(w). Factor f(j).
4*j*(j - 1)**3
Let v(u) = u**3 + 11*u**2 + 3*u + 7. Let h be v(-11). Let q = 28 + h. Determine f, given that 4/5*f + 1/5 + 1/5*f**4 + 6/5*f**q + 4/5*f**3 = 0.
-1
Let a(o) be the first derivative of 24*o + 2/9*o**3 + 14 - 4*o**2. Solve a(s) = 0.
6
Let d be (-372)/(-27) + 6/27 + -3. Factor d*l**5 - 6*l + 6*l**2 + 9*l**3 + 0*l**5 - 21*l**4 + 3*l**2 - 2*l**5.
3*l*(l - 1)**3*(3*l + 2)
Let j(m) be the second derivative of m**5/170 - 23*m**4/102 + 43*m**3/51 - 21*m**2/17 + m - 144. Let j(u) = 0. What is u?
1, 21
Let l be 4/(-30) - (-1105)/850. Solve -1/6*h**3 + 1/3*h**4 - h**2 - 1/3 + l*h = 0.
-2, 1/2, 1
Let f(h) be the first derivative of -h**3/3 + 29*h**2/2 - 54*h + 222. What is z in f(z) = 0?
2, 27
Let r(p) be the second derivative of p**7/21 - p**6/3 + 7*p**5/10 - p**4/2 + 3*p - 18. Factor r(y).
2*y**2*(y - 3)*(y - 1)**2
Let k(h) = -21*h**3 + 47*h**2 + 9*h. Let c(p) = 22*p**3 - 46*p**2 - 8*p. Let g(v) = -3*c(v) - 4*k(v). Determine z so that g(z) = 0.
-2/9, 0, 3
Let w(s) be the first derivative of -3*s - 3/2*s**3 - 3 + 3*s**2 + 1/4*s**4. Let o(n) be the first derivative of w(n). Factor o(j).
3*(j - 2)*(j - 1)
Let p(x) be the third derivative of 5/3*x**3 - 5/12*x**5 + 38*x**2 + 0*x + 0 + 5/8*x**4. Factor p(r).
-5*(r - 1)*(5*r + 2)
Let d(n) be the second derivative of 12*n + 0*n**2 + 2/3*n**3 - 1/3*n**4 + 0. Factor d(y).
-4*y*(y - 1)
Let h(s) = s**2 + 2*s + 32. Let n be h(-13). Suppose 8 - 59*p**3 + n*p**3 - 12*p**2 + 397*p - 433*p + 84*p**4 = 0. What is p?
-1, 2/7, 1/3
Let p(w) = w**2 - 4*w - 3. Let y be p(5). Suppose 3*d - 9 = -5*s, 3*d + y = 2*s + 5*d. Factor -q - 4*q**3 + 3*q**s - 2*q**2 + 0*q**3.
-q*(q + 1)**2
Let m(h) be the first derivative of 7*h**5 + 605*