).
(a - 1)*(a + 2)/4
Suppose -3*g + 7*g + 2*h - 18 = 0, 4*g - 24 = 4*h. Suppose -a + 4*a = 4*n + 24, 4*a = 3*n + 32. Factor s**2 - a*s**3 + 8*s**2 - s**4 + g*s**4 - 5*s**2.
4*s**2*(s - 1)**2
Let i(x) be the third derivative of -x**7/1680 - 3*x**6/320 - x**5/32 + 25*x**4/192 - x**2 - 6*x. Factor i(t).
-t*(t - 1)*(t + 5)**2/8
Let z(u) be the third derivative of u**5/60 + 5*u**4/4 + 75*u**3/2 + 272*u**2. Factor z(o).
(o + 15)**2
Let p(h) be the second derivative of 1/14*h**4 - 1/7*h**3 - 1/70*h**5 - 4*h + 1/7*h**2 + 0. Factor p(l).
-2*(l - 1)**3/7
Let d be (-3)/3*-24 + 1. Factor 4*m**3 + 4*m + 17*m**2 + 16*m**2 - d*m**2.
4*m*(m + 1)**2
Let w(d) be the first derivative of -d**6/36 + d**5/6 - d**4/6 - 8*d**3/9 + 8*d**2/3 - 8*d/3 - 343. Factor w(f).
-(f - 2)**3*(f - 1)*(f + 2)/6
Let c be ((-72)/20 - -10)*(-45)/(-306). Factor -2/17*z**3 + 8/17 - c*z + 10/17*z**2.
-2*(z - 2)**2*(z - 1)/17
Let x(y) = y**2 - 4*y - 3. Let q be x(5). Let j = 73/27 - 64/27. Let -2/3 + u - j*u**q = 0. What is u?
1, 2
Let w(n) be the third derivative of -n**7/3780 + n**6/810 - n**5/540 + 25*n**3/6 + 29*n**2. Let c(q) be the first derivative of w(q). Find p such that c(p) = 0.
0, 1
Suppose 4*r = 226 - 198. Let u(t) be the third derivative of 0 - 3*t**2 + 0*t + 1/60*t**5 - 1/24*t**4 + 1/120*t**6 + 0*t**3 - 1/210*t**r. Factor u(o).
-o*(o - 1)**2*(o + 1)
Let y(x) be the second derivative of x**8/112 + x**7/35 - x**5/10 - x**4/8 + 21*x**2/2 + 13*x. Let h(w) be the first derivative of y(w). What is u in h(u) = 0?
-1, 0, 1
Let j(w) = -w**2 - 13*w - 20. Let q be j(-6). Factor 2*u**2 + 21*u**3 - q*u**2 - 121*u**3 - 125*u**4.
-5*u**2*(5*u + 2)**2
Suppose 15862*d - 15957*d = 0. Determine o, given that d + 3/4*o**4 + 0*o - 9/4*o**3 - 3*o**2 = 0.
-1, 0, 4
Let o(y) be the second derivative of -1/10*y**5 + 0 + 9*y - 5/6*y**4 - 8/3*y**3 - 4*y**2. Factor o(d).
-2*(d + 1)*(d + 2)**2
Let r = -2 + 2. Suppose 2*i - 32 = 5*w, -i + r*w = w - 2. What is v in -3 - 6*v**2 - 9*v + 18*v - i*v**3 + 2*v**4 + 3*v**4 - 3*v**5 + 4*v**4 = 0?
-1, 1
Let v(h) be the second derivative of h**7/189 - 17*h**6/135 + 8*h**5/45 + h + 1. Factor v(b).
2*b**3*(b - 16)*(b - 1)/9
Let o(i) be the third derivative of 0*i + 0*i**3 - 3/80*i**5 + 1/160*i**6 + 0 - 2*i**2 + 1/16*i**4. Factor o(h).
3*h*(h - 2)*(h - 1)/4
Let z be ((-28)/(-6))/(-7) + (-600)/(-9). Let p = z - 64. Let a**4 + 9/4*a**3 + 0 + 1/4*a + 3/2*a**p = 0. What is a?
-1, -1/4, 0
Let j(x) = x**3 - 6*x**2 + 24*x - 141. Let v be j(6). Factor 58/7*s**v + 85/7*s - 25/7 - 106/7*s**2 + 1/7*s**5 - 13/7*s**4.
(s - 5)**2*(s - 1)**3/7
Let f(i) be the second derivative of -i**4/72 + 115*i**3/36 - 33*i + 6. Factor f(r).
-r*(r - 115)/6
Let k = -5 + 7. Suppose -k*s - 3*s = 2*g - 23, -2*g + 8 = 0. Solve -5*c - 19 - 6*c - 8 + 2*c - s*c**3 + 15*c**2 = 0 for c.
-1, 3
Let 2925 - 5851 + 5*l**2 + 140*l + 2926 = 0. Calculate l.
-28, 0
Let o(p) be the first derivative of -147*p**5/5 - 609*p**4/2 - 897*p**3 - 348*p**2 - 48*p + 108. Suppose o(b) = 0. Calculate b.
-4, -1/7
Let o(s) be the first derivative of -3*s**4/4 + 4*s**3 + 9*s**2/2 - 54*s + 24. Factor o(u).
-3*(u - 3)**2*(u + 2)
Let s be 5/(-10)*(-20)/(-8)*-8. Find m such that -18*m + 2*m**3 + s*m**2 + 2*m + 21*m**2 - 27*m**2 = 0.
-4, 0, 2
Let j(z) be the first derivative of -z**5/5 + z**4/2 + 8*z**3/3 - 9*z**2 + 9*z - 125. Factor j(g).
-(g - 3)*(g - 1)**2*(g + 3)
Let y(b) be the third derivative of b**5/300 - 13*b**4/120 + 2*b**3/5 - 139*b**2. Factor y(g).
(g - 12)*(g - 1)/5
Suppose -73*h + 77*h = 16. Determine u so that u**3 - 6*u**2 - 12*u**3 + 2*u**5 - 83*u**4 + 81*u**h + u**3 = 0.
-1, 0, 3
Let l(h) be the third derivative of -h**5/120 - 25*h**4/48 + 9*h**3/2 - 75*h**2 + 1. What is i in l(i) = 0?
-27, 2
Factor 72*f**2 + 2*f**3 - 5*f + 46*f**2 + 3*f**3 + 52*f**2 - 170.
5*(f - 1)*(f + 1)*(f + 34)
Suppose 0*g - 2*g - 8 = -i, 2*i - 2*g - 12 = 0. Let t(b) = -b**3 + 4*b**2 + 2*b - 5. Let l be t(i). Factor -4*u**4 + 8*u**l + 3*u**2 + 2*u**4 + 5*u**2 + 4*u**4.
2*u**2*(u + 2)**2
Solve 21*l - 28 + 11*l + 625*l**2 - 629*l**2 = 0.
1, 7
Let a be 2975/49 + 2/7. Factor -3*j**3 + 15*j - j**2 - 2*j**2 + 52 - a.
-3*(j - 1)**2*(j + 3)
Determine z, given that -16/3*z - 5/3*z**2 - 1/3*z**5 + 1/3*z**4 + 3*z**3 + 4 = 0.
-2, 1, 3
Let v(s) be the first derivative of 14 + 7/3*s**3 + 13/5*s**5 + 0*s + 1/2*s**2 + 2/3*s**6 + 15/4*s**4. Factor v(u).
u*(u + 1)**3*(4*u + 1)
Let q(n) = n**2 - 20*n - 20 + 0*n**2 - 12*n**2 + 8*n**2. Let x(f) = -80*f**2 - 540*f - 540. Let j(s) = 55*q(s) - 2*x(s). Factor j(h).
-5*(h + 2)**2
Let k(n) be the third derivative of -1/120*n**6 - 1/24*n**4 + 1/30*n**5 + 0*n**3 + 0*n - 25*n**2 + 0. Find w, given that k(w) = 0.
0, 1
Let y(u) be the third derivative of 1/210*u**5 - 3/140*u**6 - 5/1176*u**8 - 13/735*u**7 + 1/42*u**4 + 0 + 0*u**3 - 22*u**2 + 0*u. What is k in y(k) = 0?
-1, 0, 2/5
Let v(x) = -x**2 - 25*x - 84. Let p be v(-4). Let l(k) be the second derivative of p*k**2 - 1/48*k**4 + 0 - k - 1/12*k**3. Factor l(u).
-u*(u + 2)/4
Let k(w) be the second derivative of 1/8*w**4 - 1/12*w**2 + 0 + 24*w - 2/9*w**3. Let k(s) = 0. What is s?
-1/9, 1
Suppose -c**4 + 27*c**2 + 25*c**2 - 51*c**2 - 4*c**3 + 4*c = 0. What is c?
-4, -1, 0, 1
Let h(x) be the first derivative of -x**3/7 - 57*x**2/7 - 58. Determine s, given that h(s) = 0.
-38, 0
Let k(b) = 6*b**3 + 45*b**2 - b + 8. Let d(n) = 5*n**3 + 30*n**2 + 5. Let t(v) = -8*d(v) + 5*k(v). Factor t(r).
-5*r*(r + 1)*(2*r + 1)
Let o(d) = 10*d**2 + 19*d + 1. Let g be o(-2). Let u = 10 - 5. What is x in 84*x**2 - 10*x**4 - 74*x**2 + 2*x**3 + u*x**5 - 7*x**g = 0?
-1, 0, 1, 2
Suppose 11*r = 6*r - 5*a - 10, -2*r - 9 = 3*a. Let q(f) be the first derivative of -5/4*f**4 + 0*f + 5*f**r + 0*f**2 + 5. Factor q(u).
-5*u**2*(u - 3)
Determine r, given that -20/11 - 16/11*r**2 - 38/11*r + 2/11*r**3 = 0.
-1, 10
What is g in 0*g - 59*g + 2*g**2 - 24*g**3 + 27 + 3*g**4 - 31*g + 18*g + 64*g**2 = 0?
1, 3
Let w(v) = 4*v**2 + 16*v + 16. Let d(b) = -4*b**2 - 28*b - 28. Let h(o) = -o - 1. Let u(a) = -d(a) + 12*h(a). Let n(c) = -3*u(c) + 2*w(c). Factor n(m).
-4*(m + 2)**2
Let q(l) be the third derivative of -l**8/30240 - l**7/1260 - l**6/120 - 11*l**5/60 - 9*l**2. Let z(i) be the third derivative of q(i). Factor z(h).
-2*(h + 3)**2/3
Let v be (-10)/(-56) - 0 - (-23)/92. Let m = -136 - -955/7. Factor 3/7*u**2 - v*u**5 + 3/7*u**3 - m*u**4 + 0 + 0*u.
-3*u**2*(u - 1)*(u + 1)**2/7
Let b = -4107 - -4109. Factor 1/2*m**b + m - 3/2.
(m - 1)*(m + 3)/2
Factor -4*m**4 + 5376*m - 9216 + 69*m**3 + 114*m**3 - 71*m**3 - 1168*m**2.
-4*(m - 8)**2*(m - 6)**2
Suppose 0 = -12*k + 567 - 231. Let s be -4 + (k/6 + 2 - 2). Factor -s - 2/3*l**2 - 4/3*l.
-2*(l + 1)**2/3
Let l(d) be the first derivative of d**3/12 - 5. Factor l(k).
k**2/4
Let c be (2*(-698)/24)/(3/26). Let i = c + 505. Factor -8/9 - 2/9*o**3 + 2/9*o**2 + i*o.
-2*(o - 2)*(o - 1)*(o + 2)/9
Determine m, given that -59 + 55 - m**3 + 7*m**2 + 5*m + m**3 - 2*m**3 = 0.
-1, 1/2, 4
Suppose 9*l - 219 = 105. Let b be (-30)/l*1*(-63)/30. Find c, given that 9/4*c**2 - b*c - 1/2 = 0.
-2/9, 1
Let s(q) = 2*q**3 + 2*q**2 - 4*q + 6. Let u(g) = 2*g**3 + 2*g**2 - 2*g + 6. Let t(n) = -4*s(n) + 3*u(n). What is b in t(b) = 0?
-3, 1
Let n(s) be the first derivative of 1/18*s**4 - 4/9*s**2 - 16/9*s + 4/27*s**3 + 43. Find t, given that n(t) = 0.
-2, 2
Let k(p) = -p**3 + 6*p - 4. Suppose 14*s - 16 = 6*s. Let x be k(s). Factor 0 + 1/4*g**3 - 1/4*g**2 + x*g.
g**2*(g - 1)/4
Suppose 61 = 7*k + 47. Factor 0*c**k + 2/9*c**4 - 2/9*c**3 + 0 + 0*c.
2*c**3*(c - 1)/9
Suppose 5*v - 2*z - 17 = 0, 591*v + 2*z = 588*v + 7. Solve -4/5*d**v - 4/5*d - 2/5 + 16/5*d**2 - 14/5*d**4 + 8/5*d**5 = 0 for d.
-1, -1/4, 1
Suppose 79 - 7 = -9*p. Let o be p/(-24) + 35/75. Find b such that -o*b - 4/5*b**2 + 4/5*b**3 + 4/5 = 0.
-1, 1
Suppose -88 + 80 = -2*g. Solve 134*y - 65*y**3 + 7*y**4 - 7*y**5 + 10 - 52*y**g - 3*y**5 - 119*y - 25*y**2 = 0.
-2, -1, 1/2
Let n(c) be the third derivative of c**7/5040 + c**6/720 + c**5/240 + c**4/8 - 14*c**2. Let q(p) be the second derivative of n(p). Solve q(v) = 0 for v.
-1
Find w such that 27117 + 12*w**3 + 24*w - 2*w**4 + 7*w**2 - 27125 - 33*w**2 = 0.
1, 2
Let s(p) be the first derivative of p**5/40 + 3*p**4/16 + p**3/24 - 3*p**2/2 + 2*p + 78. Solve s(r) = 0 for r.
-4, 1
Suppose 2*p = 8 - 2. Facto