e first derivative of -2 + 4/3*d**3 + 7/2*d**m - 2*d. Determine j so that t(j) = 0.
-2, 1/4
Let a = 167 - 164. Solve 2/11*q**2 - 2/11 + 2/11*q - 2/11*q**a = 0.
-1, 1
Let w = -97/3 + 33. Let x be (-3)/(-4)*(-2 - -6). Determine o so that w + 7/3*o**2 - x*o = 0.
2/7, 1
Let y(f) be the second derivative of f**6/1440 - f**5/480 - f**4/48 - f**3/6 + 3*f. Let q(g) be the second derivative of y(g). Factor q(v).
(v - 2)*(v + 1)/4
Let p be 120/65 - (-6)/39. Factor 0 + 1/4*o**p + 0*o + 1/4*o**3.
o**2*(o + 1)/4
Let u(v) = -14*v**3 - v**2 + 29*v - 6. Let o(b) = -85*b**3 - 5*b**2 + 175*b - 35. Let p(d) = -4*o(d) + 25*u(d). What is s in p(s) = 0?
-2, 1/2, 1
Let x = -2/181 - -2926/2715. Let i = x - 2/5. Factor -i*d - 1/3 - 1/3*d**2.
-(d + 1)**2/3
Factor -3*i**5 + 9*i**3 - 3*i - 27*i**3 - 12*i**4 - 5*i**2 - 7*i**2.
-3*i*(i + 1)**4
Suppose 7*l = 8*l - 3. Factor -35*u**2 + 11*u**4 + 24*u - 59*u**4 - 3 - 37*u**2 + 124*u**3 - 28*u**l.
-3*(2*u - 1)**4
Let u be 15/25*30/297. Let k(s) be the first derivative of 1/22*s**4 + 2/11*s**5 + 1/11*s**6 + 0*s + 2 + 0*s**2 - u*s**3. Solve k(b) = 0 for b.
-1, 0, 1/3
Let k(j) be the first derivative of j**6/2 - 12*j**5/5 + 15*j**4/4 - 2*j**3 + 2. Let k(l) = 0. Calculate l.
0, 1, 2
Let o(n) = n**3 + 7*n**2 - 10*n. Let p be o(-8). Suppose w - p = -3*w. Suppose 2*c**5 + 2*c + 4*c - w*c - 4*c**3 = 0. Calculate c.
-1, 0, 1
Suppose 4 = -2*h - 0*h. Let z be (-1)/((-7)/3 - h). Find t such that 6*t**2 - 5*t**2 + 3 - 4 + t - t**z = 0.
-1, 1
Determine t, given that -160*t**3 - t**4 + 40*t**4 + 10*t**4 - 10*t + 26*t**4 + 95*t**2 = 0.
0, 2/15, 1
Let q(s) be the first derivative of 3 + 3/2*s**2 - 1/180*s**5 + 0*s - 1/2*s**3 - 1/12*s**4. Let w(v) be the second derivative of q(v). Factor w(d).
-(d + 3)**2/3
Let g(c) be the second derivative of -c + 0*c**3 + 0*c**2 + 0*c**4 + 0 - 1/90*c**5 - 1/189*c**7 + 2/135*c**6. Factor g(b).
-2*b**3*(b - 1)**2/9
Let s(k) be the first derivative of k**3 - 3*k**2 + 3*k - 1. Factor s(h).
3*(h - 1)**2
Let 2/11*v**2 - 4/11*v + 2/11 = 0. Calculate v.
1
Let o(f) be the second derivative of -1/60*f**6 + 1/20*f**5 + 0 + 1/4*f**2 - 1/6*f**3 + f + 0*f**4. Find c such that o(c) = 0.
-1, 1
Factor -3/4*k + 0*k**2 + 1/2 + 1/4*k**3.
(k - 1)**2*(k + 2)/4
Suppose 3*r - 2*r = 3. Suppose j + 5 = 29. Solve -8 + j*x - 2*x**3 - 22*x**2 + 4*x + 7*x**r = 0.
2/5, 2
Let m(o) = 2*o**2 + 3*o - 5. Let v be m(5). Factor -6 - 18 + 4*t**2 + 24*t + v.
4*(t + 3)**2
Factor 3*k**4 - k**2 - 4*k - 5*k**3 + 14*k - 5*k - 2.
(k - 1)**2*(k + 1)*(3*k - 2)
Suppose 2*n + 3 = 5*n. Suppose -n = o - 4. Suppose -13*m - 2*m**3 - 9*m**2 - o + 4*m - m**3 = 0. What is m?
-1
Suppose 4*l = 22 - 6. Suppose 4*a + 3*p - 3 = 0, -3*p + 3 = -a - l*a. Factor 1/3*h**4 + 0 + 2/3*h**3 + a*h + 1/3*h**2.
h**2*(h + 1)**2/3
Let d(g) be the first derivative of 5*g**3/3 + 5*g**2/2 - 10*g + 50. Suppose d(c) = 0. Calculate c.
-2, 1
Let f = -9 + 15. Let 0*y + 0*y**5 - 3*y - 8*y**4 + 2*y**4 + f*y**2 + 3*y**5 = 0. What is y?
-1, 0, 1
Factor 0*i - 2/15*i**4 - 2/15*i**2 + 0 - 4/15*i**3.
-2*i**2*(i + 1)**2/15
Let z = 937/6 - 156. Solve 1/2*t**3 + 1/3*t**2 - z*t + 0 = 0.
-1, 0, 1/3
Let o be 110/56 + (-114)/(-399). Factor -o*g**2 + 3/2*g + 3/4*g**3 + 0.
3*g*(g - 2)*(g - 1)/4
Factor -7 - 25*y - 2 - 5*y - 2*y**2 - 7*y**2.
-3*(y + 3)*(3*y + 1)
Let g(z) = -3*z**4 - 5*z. Let r(d) = -2*d**4 - 3*d. Let n = -1 + 4. Let y(o) = n*g(o) - 5*r(o). Factor y(j).
j**4
Suppose -2*b + 6*v = 3*v - 3, -1 = 4*b + v. Factor 0*w + 2/5*w**4 + 0*w**3 + b - 2/5*w**5 + 0*w**2.
-2*w**4*(w - 1)/5
Factor -3*d**2 + 0*d**2 - 101*d**4 + 104*d**4 - 9*d**2.
3*d**2*(d - 2)*(d + 2)
Let o = 37/129 + 2/43. Let h = 9 + -7. Factor -o*j + 1/6*j**h + 0 + 1/6*j**3.
j*(j - 1)*(j + 2)/6
Let y(d) = -d**3 - 10*d**2 + d + 12. Let f be y(-10). Suppose -k = 4, -5*k - 19 = 2*r - 3. Determine i so that -i**2 - i**f + 3*i + 6*i**r - i**2 = 0.
-1, 0
Let l = -10 + 20. Let k be 12/20 - 2/l. Solve k*h - 2/5*h**2 + 4/5 = 0 for h.
-1, 2
Suppose 45 = -3*u - 2*u. Let y be (1 + -4)/u*6. Factor l**4 - l**2 + y - l**2 - 1.
(l - 1)**2*(l + 1)**2
Let s(l) = -7*l**2 - 10*l + 4. Let v(b) = -36*b**2 - 51*b + 21. Let m(c) = -21*s(c) + 4*v(c). Factor m(k).
3*k*(k + 2)
Let x(y) be the first derivative of -1/12*y**6 + 1/8*y**4 - 4 + 0*y + 1/6*y**3 + 0*y**2 - 1/10*y**5. Let x(o) = 0. What is o?
-1, 0, 1
Let n(y) be the third derivative of -y**6/72 - y**5/30 + 2*y**2. Factor n(q).
-q**2*(5*q + 6)/3
Suppose -5*h - d - 3 = 0, d + 3 = 2*h - 0*h. Let u(c) be the second derivative of h*c**2 - 1/6*c**3 - 1/12*c**4 + 0 - 2*c. Factor u(q).
-q*(q + 1)
Let m(l) be the third derivative of -4/27*l**3 - 1/54*l**5 + 0*l - 2/27*l**4 - 1/540*l**6 - 2*l**2 + 0. Find h, given that m(h) = 0.
-2, -1
Let n(f) = -f**2 + 2*f + 3. Let x be n(3). Let u = 0 - x. Factor 1/2*h**3 + h**2 + 0*h + u.
h**2*(h + 2)/2
Let d(k) = -k**3 + 8*k**2 + 9*k + 2. Let z be d(9). Determine l, given that -3*l**2 + 4*l**z + l + 5*l**2 - 2*l**2 = 0.
-1/4, 0
Factor 70*u**2 - 10*u**3 - 117*u**2 - 8*u + 65*u**2.
-2*u*(u - 1)*(5*u - 4)
Let p(c) be the second derivative of -1/20*c**5 - c**2 + 1/6*c**4 - 2*c + 0 + 1/6*c**3. Factor p(z).
-(z - 2)*(z - 1)*(z + 1)
Let y(r) = 26*r**3 + 40*r**2 + 66*r + 20. Let d(z) = -5*z**3 - 3*z**2 + 2*z**2 - 2*z**2 - 5*z**2 - 4 - 13*z. Let k(c) = -16*d(c) - 3*y(c). Factor k(g).
2*(g + 1)**2*(g + 2)
Let o(y) = -y**5 + y**3 + 2. Let i(d) be the second derivative of 4*d**7/21 + d**6/30 - 9*d**5/20 - 17*d**2/2 - 3*d. Let s(w) = 6*i(w) + 51*o(w). Factor s(j).
-3*j**3*(j - 1)**2
Let w(g) be the first derivative of -2*g**5/25 + g**4/5 - 2*g**3/15 - 33. Determine u so that w(u) = 0.
0, 1
Suppose -27 + 123 = 6*f. Suppose -4*t + 3*n + 29 = -12, -t + 20 = -4*n. Determine w so that -6*w + t*w + f*w + 0 - 27 - 3*w**2 = 0.
3
Let k(j) = -7*j**5 + 10*j**4 - 15*j**3 + 15*j**2 - 5*j - 3. Let c(d) = 4*d**5 - 5*d**4 + 7*d**3 - 7*d**2 + 2*d + 2. Let p(y) = -5*c(y) - 3*k(y). Factor p(n).
(n - 1)**5
Let p = -31 + 43. Solve 2*q + 4*q + p*q**2 + 12*q + 2*q**3 = 0 for q.
-3, 0
Let q(u) = -u**3 + 18*u**2 + 18*u + 19. Let d be q(19). Determine m, given that -2/5*m**3 + 2/5*m + d*m**2 + 0 = 0.
-1, 0, 1
Let c(w) be the third derivative of w**5/30 + 5*w**4/12 - 2*w**3 - 22*w**2. Factor c(l).
2*(l - 1)*(l + 6)
Suppose -3*b + 12 = 3. Find m such that -b*m**3 - m**2 + 4*m**3 + 3*m**2 + m = 0.
-1, 0
Let a(h) be the first derivative of h**4/36 + 2*h**3/9 + h**2/2 + 7*h + 4. Let u(c) be the first derivative of a(c). Suppose u(f) = 0. Calculate f.
-3, -1
Let n(r) = r**3 - 5*r**2 - 6*r + 3. Let b be n(6). Suppose -3*g + b = -9. Factor 7*i**2 + i**5 - 3*i**g - 2*i**3 + i**5 - 1 - 3*i**2.
(i - 1)**3*(i + 1)*(2*i + 1)
Let z(a) = 23 - a**2 + 8*a**2 + 0*a**2 + 17*a. Let q(n) = 4*n**2 + 9*n + 12. Let y(i) = -10*q(i) + 6*z(i). Factor y(c).
2*(c + 3)**2
Find f such that 0 - 3*f + 27/2*f**2 = 0.
0, 2/9
Let t be (24/(-400))/((-6)/8). Let w(n) be the first derivative of 0*n - 1/15*n**6 - 2 - 2/15*n**3 + t*n**5 + 1/10*n**4 + 0*n**2. Suppose w(g) = 0. What is g?
-1, 0, 1
Suppose 4*v - 5 = 3*v. Suppose 5*a = 15, -2*s + v*a - 15 = -0*a. Factor -2*i**2 + s + 7 + 2*i**3 - 5 - 2*i.
2*(i - 1)**2*(i + 1)
Let j(k) be the third derivative of 0 - 1/24*k**4 + 1/60*k**5 + 0*k - 1/3*k**3 + k**2. Factor j(b).
(b - 2)*(b + 1)
Let g(z) be the first derivative of z**4/4 - 3*z**2/2 - 2*z - 3. Factor g(k).
(k - 2)*(k + 1)**2
Suppose 5*n + 2*m = 121, -5*n + m + 118 = 2*m. Suppose -n = -5*l + 4*z, -4*l - 2*z = z - 6. Suppose -1/5*r**l + 0 - 1/5*r + 2/5*r**2 = 0. Calculate r.
0, 1
Let t(h) = h**4 + h**3 - h**2 + h. Let i(f) = 5*f - 6*f**3 + 6*f - 11*f. Let y(x) = -i(x) - 3*t(x). Factor y(w).
-3*w*(w - 1)**2*(w + 1)
Let x(j) be the first derivative of -2197*j**6/30 + 5408*j**5/25 - 4381*j**4/20 + 1334*j**3/15 - 86*j**2/5 + 8*j/5 - 22. Factor x(t).
-(t - 1)**2*(13*t - 2)**3/5
Suppose n - 4*t + 26 = 3*n, 4*n - 5*t = 0. Let q be (2/(-5))/(4/(-5)). Let 0*z**4 - q*z**n + 1/2*z**3 + 0*z**2 + 0*z + 0 = 0. Calculate z.
-1, 0, 1
Let a(w) = -7*w**2 - 13*w - 10. Let i(s) = 85*s**2 + 155*s + 120. Let p(k) = 25*a(k) + 2*i(k). Factor p(t).
-5*(t + 1)*(t + 2)
Factor 1/4 + 1/2*n + 1/4*n**2.
(n + 1)**2/4
Let a(u) = 0*u**3 + u**2 - 3*u**3 + 5 + 4*u**3 + 0*u**3. Let l be a(0). Factor 0*p**3 + 2/9*p**l + 0 + 0*p + 0*p**4 + 0*p**2.
2*p**5/9
Let b be -1 + (4 - 7) - -9. Let 