
Let t(d) = 2*d**3 + 42*d**2 + 294*d + 693. Let o(v) = -v - 19. Let p be o(-5). Let a(r) = r**3 + 21*r**2 + 147*r + 346. Let i(s) = p*a(s) + 6*t(s). Factor i(x).
-2*(x + 7)**3
Let k(o) be the first derivative of 52/3*o**3 + 0*o - 32*o**5 + 4*o**2 - 15 + 32/3*o**6 + 9*o**4. Let k(c) = 0. What is c?
-1/4, 0, 1, 2
Let k = 27434 - 27429. Factor 0*h + 4/3*h**4 + 0 + 2/3*h**2 + 1/3*h**k + 5/3*h**3.
h**2*(h + 1)**2*(h + 2)/3
Factor 43*l**2 + 79*l - 227*l + 102*l - l**2 - 12*l**3 + 8*l**2 + 12.
-2*(l - 3)*(2*l - 1)*(3*l - 2)
Let k(p) be the third derivative of -p**8/336 + p**7/105 + p**6/15 - 3*p**5/10 + 3*p**4/8 + 24*p**2 + 3*p. Solve k(h) = 0 for h.
-3, 0, 1, 3
Suppose 0 = a - 1 - 1. Suppose -13 - a = -5*u. Solve -2 - 9/2*n**4 - 37/2*n**2 - 15*n**u - 10*n = 0 for n.
-1, -2/3
Let d(j) = -j**4 - 2*j**3 + 2*j**2 + 1. Let c(q) = -9*q**5 - 60*q**4 - 96*q**3 + 12*q**2 + 18. Let t(i) = -c(i) + 18*d(i). Let t(w) = 0. Calculate w.
-2, -2/3, 0
Suppose -22 = -t + 5*s, 2*t - 2*s - 18 = -3*t. Suppose 0 = -2*y - t*y + 144. Factor -6*z**3 + 7*z + 0*z**3 + 34 + 2*z**2 - y - z**3.
-(z - 1)*(z + 1)*(7*z - 2)
Solve -144/13 - 12/13*h + 2/13*h**2 = 0 for h.
-6, 12
Find i such that -96 + 2/3*i**3 - 50/3*i**2 + 112*i = 0.
1, 12
Suppose -3 + 21 = 3*a. Suppose -6 - a = -3*s + 3*g, 2*s - 2 = -4*g. Factor -2*x**2 - s*x**3 + 4*x**3 + 4*x**2.
x**2*(x + 2)
Let r = -144 - -147. Suppose 0 = -8*c + 7*c + 2*d + 11, -c - r*d - 9 = 0. Suppose 0*m - 4/7*m**c - 2/7*m**4 - 2/7*m**2 + 0 = 0. What is m?
-1, 0
Let h(c) = -5*c + 10. Let a be h(2). Find s such that 0*s**2 + 2/15*s**4 + 0*s**3 + a*s + 0 + 2/15*s**5 = 0.
-1, 0
Let l(h) = 11*h**2 + 115*h - 6. Let m(g) = -10*g**2 - 115*g + 5. Let a(c) = 5*l(c) + 6*m(c). Factor a(d).
-5*d*(d + 23)
Let s be (15/(-10))/(1*3/(-6)). Let g(f) be the second derivative of 1/12*f**4 + f**s + 9/2*f**2 + 0 - 4*f. Factor g(h).
(h + 3)**2
Let o(b) = 7 - 4 - 6*b**2 + 1 - 10*b. Let t(p) be the first derivative of 7*p**3/3 + 11*p**2/2 - 5*p + 619. Let m(z) = -5*o(z) - 4*t(z). Factor m(x).
2*x*(x + 3)
Let f(w) be the first derivative of 3*w**4/28 - w**3 + 3*w**2 - 24*w/7 + 1. Factor f(d).
3*(d - 4)*(d - 2)*(d - 1)/7
Let f(n) be the second derivative of -n**6/1260 + 2*n**3/3 - 4*n. Let r(t) be the second derivative of f(t). Factor r(y).
-2*y**2/7
Let h(r) be the second derivative of 1/18*r**4 - 9*r + 0*r**2 + 0 - 1/135*r**6 + 2/27*r**3 + 0*r**5. Suppose h(k) = 0. What is k?
-1, 0, 2
Factor 1/11*y**3 + 0 + 2/11*y**2 - 3/11*y.
y*(y - 1)*(y + 3)/11
Let w(x) = -x**4 + x**2 - x. Let g(z) = -101*z**4 - 5*z**3 + 70*z**2 + 31*z + 4. Let i(t) = -g(t) + w(t). Factor i(y).
(y - 1)*(4*y + 1)*(5*y + 2)**2
Suppose 169*g**5 + 0 + 1/2*g - 520*g**4 + 1509/4*g**3 - 107/4*g**2 = 0. What is g?
0, 1/26, 1, 2
Let o = 6 - 1. Let q(r) = -14 + 7*r**2 - o*r**3 + 14 - 6. Let b(p) = 9*p**3 - 13*p**2 + 11. Let y(w) = 6*b(w) + 11*q(w). What is x in y(x) = 0?
-1, 0
Find v such that -14/3*v - 20/3 - 2/3*v**2 = 0.
-5, -2
Let t = 128 - 173. Let w = t + 181/4. Determine y, given that 9/4*y**2 - 3/4*y**4 + 1/2 + w*y**3 - 9/4*y = 0.
-2, 1/3, 1
Determine u so that -2/11*u**3 + 24*u**2 - 8442/11*u - 17956/11 = 0.
-2, 67
Let f = 24 + -20. Suppose -5 = -f*u - 3*v + 9, 3*u = -5*v + 16. Suppose 0 - 2/9*p**3 + 0*p - 2/9*p**4 + 0*p**u = 0. Calculate p.
-1, 0
Let p = -1/137 + 377/32880. Let w(n) be the third derivative of 1/40*n**5 + 1/12*n**3 + 0 - p*n**6 + 0*n - 1/16*n**4 - 4*n**2. Let w(a) = 0. Calculate a.
1
Let j(q) be the first derivative of -3*q**5/20 + 3*q**4/16 + 2*q**3 - 9*q**2/2 + 452. Solve j(c) = 0.
-3, 0, 2
Let b(m) be the second derivative of 3*m**5/4 + 95*m**4/6 + 775*m**3/6 + 500*m**2 - m - 77. Factor b(q).
5*(q + 5)**2*(3*q + 8)
Let r(z) be the first derivative of 2*z**5/5 + 3*z**4/2 - 4*z**3/3 - 12*z**2 - 16*z + 137. Factor r(s).
2*(s - 2)*(s + 1)*(s + 2)**2
Let h(f) be the first derivative of f**5/10 - 3*f**4/8 + f**3/6 + 3*f**2/4 - f + 131. Factor h(x).
(x - 2)*(x - 1)**2*(x + 1)/2
Factor 19/4*l - 5*l**3 - 5/2 + 1/2*l**2 + 2*l**4 + 1/4*l**5.
(l - 1)**3*(l + 1)*(l + 10)/4
Find r such that 0*r**2 - 4/9*r**3 + 0*r - 2/9*r**4 + 0 + 2/9*r**5 = 0.
-1, 0, 2
Let y(h) be the third derivative of h**5/180 - h**4/3 - 25*h**3/18 - h**2 - 35*h. Factor y(i).
(i - 25)*(i + 1)/3
Solve -51842/5 - 644/5*k - 2/5*k**2 = 0 for k.
-161
Let 39*h**3 + 2011*h**4 + 4 + 120*h**2 - 2008*h**4 - 4 = 0. Calculate h.
-8, -5, 0
Let d be 1/(4/16) - 2. Let r(i) = i**3 + 6*i**2 - 9*i - 10. Let o be r(-7). Solve -2*v + d*v**o + 9*v + 12*v**2 - 6*v**4 + v = 0 for v.
-1, 0, 2
Let f(g) be the first derivative of -2*g**5/5 - 11*g**4/2 - 86*g**3/3 - 69*g**2 - 72*g + 136. Solve f(x) = 0 for x.
-4, -3, -1
Let u(q) be the third derivative of -q**9/483840 - q**5/5 + 16*q**2. Let c(g) be the third derivative of u(g). Suppose c(l) = 0. Calculate l.
0
Let c(t) be the third derivative of t**5/360 + t**4/12 + 11*t**3/36 + 57*t**2. Factor c(l).
(l + 1)*(l + 11)/6
Let x(n) be the second derivative of n**6/150 - 4*n**5/25 + 7*n**4/10 - 4*n**3/3 + 13*n**2/10 - 10*n - 2. Factor x(y).
(y - 13)*(y - 1)**3/5
Suppose -12 = 5*s - 4*k, -s - 2*k + 3 = -3. Let v(i) be the second derivative of -1/42*i**4 + i + s*i**2 + 0 - 1/21*i**3. Solve v(p) = 0 for p.
-1, 0
Let f(b) be the third derivative of -b**8/672 + 3*b**7/140 + 7*b**6/80 - 49*b**5/24 - 1058*b**2. Factor f(k).
-k**2*(k - 7)**2*(k + 5)/2
Let g(w) be the third derivative of -1/21*w**3 - 2/105*w**5 + 5/84*w**4 + 0 + 4*w**2 + 0*w. Let g(b) = 0. What is b?
1/4, 1
Let n = -1/1465 + 887/11720. Let a(s) be the second derivative of 4*s + 1/60*s**6 - 1/84*s**7 - 5/24*s**4 + 0*s**2 + n*s**5 + 1/6*s**3 + 0. Factor a(u).
-u*(u - 1)**3*(u + 2)/2
Let s(u) = 26*u**2 + 4*u + 11. Let m(h) = -5*h**2 - h - 2. Let x(d) = 11*m(d) + 2*s(d). Factor x(o).
-3*o*(o + 1)
Let x = -40933/23 - -1780. Let m = x - -15/253. Factor -2/11*n**2 - m + 6/11*n.
-2*(n - 2)*(n - 1)/11
Let o(n) be the third derivative of -1/3*n**3 + 0*n + 0 - 1/15*n**5 + 1/120*n**6 - 9*n**2 + 5/24*n**4. Solve o(t) = 0.
1, 2
Let d(h) be the second derivative of -h**5/10 + 5*h**4/3 - 16*h**3/3 + 136*h. Factor d(p).
-2*p*(p - 8)*(p - 2)
Let w(k) be the third derivative of -k**7/630 - 7*k**6/360 - k**5/45 + k**4/6 + 5*k**2 - 12*k. Suppose w(s) = 0. Calculate s.
-6, -2, 0, 1
Let c(w) be the second derivative of 1/4*w**5 - 12*w + 10*w**3 + 20*w**2 + 0 + 5/2*w**4. Factor c(y).
5*(y + 2)**3
Let f(t) be the first derivative of t**4/40 + t**3/5 + 11*t**2/20 + 3*t/5 - 141. Factor f(g).
(g + 1)*(g + 2)*(g + 3)/10
Let g(i) be the third derivative of i**8/23520 + i**7/11760 - 3*i**5/10 + 25*i**2. Let v(t) be the third derivative of g(t). What is q in v(q) = 0?
-1/2, 0
Let c = -45 - -47. Let a be ((-4)/c)/((-12)/18). Factor 0 + 1/3*s**a + 1/3*s + 2/3*s**2.
s*(s + 1)**2/3
Let f be 38/(-6) + (-4)/6. Let d = 14 + f. Let d - 5*k**4 - 6 + 2*k - 2*k**3 + 4*k**4 = 0. Calculate k.
-1, 1
Suppose -3*t + i = -4*i - 5, -15 = -5*t + 5*i. Let v = -529 + 2117/4. Find f such that 0*f + 0 + 1/4*f**2 - 1/4*f**4 - 1/4*f**3 + v*f**t = 0.
-1, 0, 1
Let w(u) = u**2 + 9*u. Let l be w(-4). Let r be (8/l)/(3/(-15)). Factor -34*i**3 - 30*i**3 - 16*i**2 - 21*i**4 - r*i**4 - 5*i**4.
-4*i**2*(i + 2)*(7*i + 2)
Let b be 4/(-1) + (-16)/(-2). Suppose 13*w**4 - 38*w**4 - 18*w**4 - 26*w**2 + 7*w**4 + b*w + 54*w**3 = 0. What is w?
0, 1/3, 1/2, 2/3
Let k(s) = -39*s**2 - 567*s - 1146. Let d(j) = -8*j**2 - 113*j - 229. Let f(u) = -24*d(u) + 5*k(u). Determine v so that f(v) = 0.
-39, -2
Let u(n) be the first derivative of -n**4/8 + n**3 - 136. Factor u(t).
-t**2*(t - 6)/2
Let a(g) be the first derivative of g**5/10 + 3*g**4/2 - 24. What is m in a(m) = 0?
-12, 0
Factor 0 - 7*y - 1/2*y**4 - 5*y**3 - 23/2*y**2.
-y*(y + 1)*(y + 2)*(y + 7)/2
Let x(o) = 10*o - 47. Let m be x(7). Let w be m/(-46) - (-94)/60. What is n in -32/15 + w*n - 2/15*n**2 = 0?
4
Let o(u) be the second derivative of -4 + 1/21*u**7 + 0*u**2 - 16/3*u**3 + 8/15*u**6 - 6*u + 3/2*u**5 - 4/3*u**4. Let o(x) = 0. Calculate x.
-4, -1, 0, 1
Let h(s) be the first derivative of s**3/30 - 44*s**2/5 + 3872*s/5 - 85. Factor h(u).
(u - 88)**2/10
Let t = 5872/8763 - 10/2921. Determine x, given that -2/3*x - 2/3*x**2 + t + 2/3*x**3 = 0.
-1, 1
Let l(b) be the first derivative of b**5/10 + 13*b**4/12 + 79*b**3/18 + 25*b**2/3 + 22*b/3 - 19. Solve l(h) = 0 fo