o*(o + 1)/4
Let y(h) be the first derivative of -h**4/10 - 2*h**3/15 + h**2/5 + 2*h + 4. Let a(f) be the first derivative of y(f). Factor a(d).
-2*(d + 1)*(3*d - 1)/5
Let t(k) = k**3 + 10*k**2 + k + 3. Let r be t(-10). Let q = r + 10. Let 15 - 56*b**4 + 90*b**q - 98*b**5 - 15 + 8*b + 56*b**2 = 0. What is b?
-1, -2/7, 0, 1
Let f be -1 + 3 - (-14)/(-8). Factor -1/4*d - 1/2*d**2 + 1/4*d**4 - 1/4*d**5 + f + 1/2*d**3.
-(d - 1)**3*(d + 1)**2/4
Let o(r) be the third derivative of -1/60*r**6 + 1/10*r**5 + 3*r**2 + 0*r + 1/3*r**3 + 0 - 1/4*r**4. Factor o(h).
-2*(h - 1)**3
Let v be -4 + (-8)/(-12)*6. Find o, given that 0*o**3 + 1/4*o**5 + 1/4*o**4 + 0 + 0*o + v*o**2 = 0.
-1, 0
Let x(m) be the second derivative of -1/10*m**5 - 3*m + 0*m**2 + 0 - 1/18*m**4 + 2/9*m**3. Factor x(f).
-2*f*(f + 1)*(3*f - 2)/3
What is l in l**2 + 0 - 2/3*l + 1/3*l**5 + 1/3*l**3 - l**4 = 0?
-1, 0, 1, 2
Let h(r) be the third derivative of -r**5/90 + r**3/9 + 7*r**2. Factor h(n).
-2*(n - 1)*(n + 1)/3
Let c(t) be the second derivative of 0 + 0*t**3 + 1/50*t**5 + 2/105*t**7 + 5*t + 0*t**2 + 0*t**4 - 1/25*t**6. Suppose c(i) = 0. What is i?
0, 1/2, 1
Let s = 106/13 + -411/52. What is v in v**4 + v**2 - s*v - 1/4*v**5 + 0 - 3/2*v**3 = 0?
0, 1
Factor 1/6*y**5 + 0*y**2 + 1/6*y + 0*y**4 - 1/3*y**3 + 0.
y*(y - 1)**2*(y + 1)**2/6
Determine h, given that -8/19*h + 14/19 - 6/19*h**2 = 0.
-7/3, 1
Let g(c) be the third derivative of c**7/105 - 11*c**6/75 + 21*c**5/25 - 9*c**4/5 - 9*c**3/5 - 6*c**2. Factor g(t).
2*(t - 3)**3*(5*t + 1)/5
Let z(x) be the second derivative of 1/60*x**6 + 0*x**4 + 0 + x**2 + x + 1/60*x**5 + 1/210*x**7 + 0*x**3. Let j(a) be the first derivative of z(a). Factor j(n).
n**2*(n + 1)**2
Let u(k) be the second derivative of k**3/6 - 7*k**2/2 - 3*k. Let p be u(11). Factor 2/3*r**p + 4/3*r - 4/3*r**3 + 0*r**2 - 2/3.
2*(r - 1)**3*(r + 1)/3
Let d(i) be the second derivative of 2*i**7/105 - i**6/15 + i**5/15 - 5*i**2/2 + i. Let j(t) be the first derivative of d(t). Determine b so that j(b) = 0.
0, 1
Let t(y) be the second derivative of -y**5/120 + y**4/16 - y**3/6 - 2*y**2 - 4*y. Let b(w) be the first derivative of t(w). Determine u so that b(u) = 0.
1, 2
Let i(a) = 2*a - 4. Let j be i(3). Suppose -4*n + 2*k - j = 0, 10 = -0*n - 5*n + 4*k. Factor -q**3 + 4*q**n + 2*q**3 + q**3 + 2*q.
2*q*(q + 1)**2
Let y = -85 - -85. Factor -4/3*q**2 + 0*q + 0 + y*q**3 + 4/3*q**4.
4*q**2*(q - 1)*(q + 1)/3
Let a(w) be the first derivative of 81*w - 81/2*w**2 + 9*w**3 - 6 - 3/4*w**4. What is l in a(l) = 0?
3
Let c be ((-4)/((-24)/(-14)))/((-26)/39). Suppose -s + 8 - 4 = 0. Solve 9*x**2 + s + c*x**3 + 1/2*x**4 + 10*x = 0 for x.
-2, -1
Let u(k) be the first derivative of k**4/6 + 2*k**3/3 - 8*k/3 + 9. Factor u(f).
2*(f - 1)*(f + 2)**2/3
Let c = 12 + -8. Let x(m) = m**3 - 5*m**2 + 4*m + 3. Let j be x(c). Factor 0*y**3 + 2*y**3 - 4*y - 4*y**2 - j*y**3.
-y*(y + 2)**2
Let n(y) be the third derivative of y**8/336 - y**7/105 - y**6/60 + 2*y**5/15 - 7*y**4/24 + y**3/3 + y**2. Factor n(p).
(p - 1)**4*(p + 2)
Let t(z) = 9*z**4 - 6*z**3 + 18*z**2 + 6*z. Let a = 2 + -9. Let l(b) = -10*b**4 + 5*b**3 - 19*b**2 - 7*b. Let r(x) = a*t(x) - 6*l(x). Factor r(p).
-3*p**2*(p - 2)**2
Let q be (((-44)/(-8))/11)/(1/4). Let t(k) be the second derivative of 4*k - 1/9*k**3 + 0 + 0*k**q + 1/36*k**4. What is y in t(y) = 0?
0, 2
Suppose 4*w - u + 3 = -2, w + 5*u = 25. Let o(y) be the second derivative of 1/4*y**4 + w - y**2 - y + 1/10*y**5 - 1/2*y**3. Suppose o(c) = 0. What is c?
-2, -1/2, 1
Suppose 21 = 5*d - 79. Let v = -20 + d. Factor v + 2/7*y**2 + 2/7*y.
2*y*(y + 1)/7
Let g(p) be the first derivative of p**6/9 - p**4/3 + p**2/3 - 11. Find q, given that g(q) = 0.
-1, 0, 1
Let v = -109 - -109. Let o(g) be the first derivative of -3/10*g**5 + 4 + v*g + 0*g**2 - 1/4*g**4 + 1/6*g**3. What is p in o(p) = 0?
-1, 0, 1/3
Let b be (2/(-6))/(1/(-6)). Let d be (2 - -1) + (-5)/b. Suppose -1/4*z**2 - d*z - 1/4 = 0. Calculate z.
-1
Let v be 8 - 6 - -4*(-4)/8. Let 0*f**2 + 2*f**4 + 0 + v*f + 4*f**5 + 1/4*f**3 = 0. What is f?
-1/4, 0
Let m = 1/2 + 0. Let c(r) be the first derivative of -m*r - 1/8*r**2 + 1/12*r**3 + 2. What is v in c(v) = 0?
-1, 2
Let h = -21119/120 + 176. Let t(f) be the third derivative of 0 - 1/300*f**5 + 0*f + 1/1050*f**7 + 1/600*f**6 - h*f**4 + 0*f**3 - 3*f**2. Factor t(g).
g*(g - 1)*(g + 1)**2/5
Let g(f) be the second derivative of -f**5/40 - f**4/8 + f**2 + 6*f. Factor g(z).
-(z - 1)*(z + 2)**2/2
Determine j so that 2*j**3 + 604*j**2 - 1207*j**2 + 609*j**2 = 0.
-3, 0
Suppose -7 = -4*t + 9. Let h(a) = -a**2 - 6*a + 2. Let j be h(-6). What is k in -2*k**2 + 0*k**j + 2*k**5 - t*k**5 + 2*k**4 + 2*k**3 = 0?
-1, 0, 1
Let u be (-1 - 0) + 20/(-15) - -3. Factor -50/3*x**2 + u*x**5 - 8/3 + 38/3*x**3 - 14/3*x**4 + 32/3*x.
2*(x - 2)**2*(x - 1)**3/3
Let b = -7692 + 346279/45. Let s = b - 26/9. Suppose -1/5*o**3 - 1/5*o**2 + 0*o + 1/5*o**5 + s*o**4 + 0 = 0. What is o?
-1, 0, 1
Let n(t) be the first derivative of -2/9*t**3 + 0*t + 4 + 1/6*t**4 + 0*t**2. Determine i so that n(i) = 0.
0, 1
Let z be 5/(-5) - (1 - 0). Let q be (-78)/(-15) + z/10. Factor -3*i + i**3 + q*i - i - 2*i**2.
i*(i - 1)**2
Let v(d) be the second derivative of -d**6/360 + d**5/90 + d**4/72 - d**3/9 - d**2 - d. Let h(r) be the first derivative of v(r). Determine w so that h(w) = 0.
-1, 1, 2
Suppose -2*q = 2*k + 2*q - 12, 5*q = -k. Let p = k - 6. Factor 1 - 3 - 5*w**4 + p*w**3 + 5*w**4 - 4*w + 2*w**4.
2*(w - 1)*(w + 1)**3
Let u(w) be the first derivative of -w**6/21 + 2*w**5/35 + w**4/14 - 2*w**3/21 + 2. Factor u(g).
-2*g**2*(g - 1)**2*(g + 1)/7
Let h(w) be the third derivative of w**5/150 - w**4/60 + 6*w**2. Find f such that h(f) = 0.
0, 1
Let c(y) be the second derivative of -y**6/30 - 3*y**5/10 - 11*y**4/12 - y**3 - 5*y + 3. Solve c(u) = 0.
-3, -2, -1, 0
Let m be ((-6)/(-15) - -2) + -2. Factor 2/5 - m*y**2 + 6/5*y - 6/5*y**3.
-2*(y - 1)*(y + 1)*(3*y + 1)/5
Let a(u) be the first derivative of -u**4/4 - u**3/3 + 9. Factor a(x).
-x**2*(x + 1)
Factor -77/4*a**2 + 49/4*a**3 - 1 + 8*a.
(a - 1)*(7*a - 2)**2/4
Let n(p) = p - 2. Let l be n(10). Find u, given that l*u**4 - 14*u**4 + 4*u**4 = 0.
0
Let z = -3/511 + 21495/5621. Determine l, given that 72/11*l**5 + z*l**4 - 58/11*l**3 + 0 - 8/11*l - 48/11*l**2 = 0.
-2/3, -1/4, 0, 1
Factor -384*h**2 - 7*h + 3*h + 385*h**2 + 3.
(h - 3)*(h - 1)
Suppose 5 = -2*a - 3*q, 4*a = q + 2*q + 17. Find r such that -4*r**a + 3*r + 5*r**2 - r = 0.
-2, 0
Let f(h) be the second derivative of h**5/180 - h**4/12 + h**3/2 - 2*h**2 + 3*h. Let v(q) be the first derivative of f(q). What is r in v(r) = 0?
3
Suppose 1 = 2*j - 13. Let h(g) = g**2 - 7*g + 4. Let t be h(j). Solve -t*o**2 + 3*o**2 - 2*o**2 + 3*o = 0 for o.
0, 1
Let -1/2*b**2 - 3/2 - 1/2*b**3 + 5/2*b = 0. Calculate b.
-3, 1
Let d(h) be the first derivative of 2*h**5/5 + h**4 + 2*h**3/3 - 7. Let d(i) = 0. Calculate i.
-1, 0
Let n(w) be the second derivative of 0*w**2 + 0 + 0*w**3 + 1/36*w**4 - w. Factor n(p).
p**2/3
Factor -2/3*x - 1/3*x**3 + 0 - x**2.
-x*(x + 1)*(x + 2)/3
Determine f, given that -17*f**2 + 288*f**5 + 2*f + 146*f**3 + 306*f**4 + 45*f**2 + 30*f**4 = 0.
-1/3, -1/4, 0
Factor -169 + 221*c**4 - 131*c - 181*c + 17*c**2 + 24*c**3 - 222*c**4 - 135*c**2.
-(c - 13)**2*(c + 1)**2
Factor 2/7*u**2 + 16/7*u + 0.
2*u*(u + 8)/7
Let f(z) = -5*z**3 + 3*z**2 - 2*z - 1. Let w be f(2). Let j be (-2)/10 + w/(-15). Suppose -3*g + 2*g**3 - j*g**4 + 0*g + 2*g**2 + g = 0. What is g?
-1, 0, 1
Suppose 0 = 5*a - 4 + 29. Let v = a - -11/2. Find c such that 0 - c + v*c**2 = 0.
0, 2
Let g be -2 - 0*(-1)/3. Let n = g + 6. Factor -1/3 - 2*v**2 + 4/3*v**3 + 4/3*v - 1/3*v**n.
-(v - 1)**4/3
Let f(x) be the second derivative of 0*x**2 + 1/30*x**4 - 7*x - 1/5*x**3 + 0. Suppose f(o) = 0. Calculate o.
0, 3
Suppose 5*l - 5 - 5 = 0. Factor -5*q**2 + 2*q + 3*q**l - 8*q - 11 + 7.
-2*(q + 1)*(q + 2)
Suppose -135 = 2*t - 0*k - 3*k, 0 = 5*t + 3*k + 327. Let p be (-2)/12 - 11/t. Factor -2/7*n**3 + 0*n + p*n**2 - 2/7*n**5 + 4/7*n**4 + 0.
-2*n**3*(n - 1)**2/7
Let k(x) be the second derivative of -1/24*x**3 + 2*x + 0 + 0*x**2 + 1/48*x**4. Factor k(y).
y*(y - 1)/4
Let k(p) be the second derivative of p**4/24 - p**3/3 - 23*p. Factor k(u).
u*(u - 4)/2
Let l = -28 - -9. Let v be l/(-7) - (-6)/21. Factor t**4 + v*t**2 + 