 9 = 0. Let x = k + 4. Determine a so that -4*a**3 - 10*a + 3 - 8*a**3 + 18*a**2 - 4*a + x*a**4 + 2*a = 0.
1
Factor -24*q - 54*q + 12*q**2 - 45*q + 33 - 12*q.
3*(q - 11)*(4*q - 1)
Suppose 9*p = 8*p - 10. Let c = -8 - p. Factor 3/2*h + 1/2*h**c + 1.
(h + 1)*(h + 2)/2
Suppose -v + 3*k - 6 = 0, v + 6*k - 2*k = 1. Let f(x) = -2*x - 4. Let n be f(v). Find a such that 4*a - 4*a**2 + 4*a**2 - 7*a**n + 5*a**2 = 0.
0, 2
Let o(h) be the second derivative of -h**6/40 + 3*h**5/20 - 3*h**4/8 + h**3/2 + 5*h**2 - 9*h. Let f(r) be the first derivative of o(r). Factor f(j).
-3*(j - 1)**3
Suppose 0 = -4*k - 3*v + 15, 2*k - 2*v + 6*v = 10. Suppose 64*g + 13*g**4 - 134*g + 69*g - 15*g**k + 7*g**2 - 4*g**5 = 0. What is g?
0, 1/4, 1
Let x = -7/16 - -113/112. Let y = 13/28 - -3/28. Determine u, given that -y - 1/7*u**2 + x*u = 0.
2
Let q = 1398 + -18159/13. Let r = q - -29/65. Factor 2/5*j**4 + r*j**3 + 0 + 2*j**2 + 4/5*j.
2*j*(j + 1)**2*(j + 2)/5
Let m(r) = 5*r**2 - 1. Let l(c) = 9*c**2 - c + 1 + 3 - 5. Let b(w) = 4*l(w) - 7*m(w). Suppose b(u) = 0. Calculate u.
1, 3
Let t = 3690 + -3687. Factor 0 + 1/5*p - 1/5*p**5 + 2/5*p**2 + 0*p**t - 2/5*p**4.
-p*(p - 1)*(p + 1)**3/5
Let a be 41/(-9) + (0 + -10)*9/(-18). Determine n, given that 2/3 - 2/9*n**2 - a*n = 0.
-3, 1
Suppose -16*f - 6 = -19*f. Let r be 155/(-217)*f/(-5). Suppose r*a**4 + 4/7 + 2/7*a - 2/7*a**3 - 6/7*a**2 = 0. What is a?
-1, 1, 2
Let d be 65 - 4/(-6)*42/(-28). Let -119*w**2 + 123*w**2 + 6 + 250 + d*w = 0. Calculate w.
-8
Let t = 12462/7 + -1780. Let 6/7*i**2 + 0 + t*i**4 + 2/7*i + 6/7*i**3 = 0. Calculate i.
-1, 0
Let j(a) = a**3 + a. Let f be j(0). Let q be f - 3 - 46/(-14). Suppose 0 + 8/7*p**4 - 2*p**3 + q*p + 4/7*p**2 = 0. Calculate p.
-1/4, 0, 1
Let q = -41 + 38. Let m be (-1 - 2/(-4))/(q/9). Factor m*v**2 + 1 + 7/2*v.
(v + 2)*(3*v + 1)/2
Let f(h) be the first derivative of 0*h + 0*h**2 + 30 + 2*h**3 + 3/5*h**5 + 9/4*h**4. Factor f(p).
3*p**2*(p + 1)*(p + 2)
Let n(i) be the second derivative of i**6/6 - 3*i**5/2 + 10*i**4/3 + 2*i + 112. Factor n(q).
5*q**2*(q - 4)*(q - 2)
Factor -1 - 5 + 25*i - 20*i**2 - 11 + 7 + 5*i**3.
5*(i - 2)*(i - 1)**2
Suppose 4*l - 1116 = a - 1103, -4*a - 20 = 0. Find s such that 4/9*s**l + 0 - 16/9*s = 0.
0, 4
Let g(w) = -8*w**3 + 11*w**2 - 2*w - 5. Let d(q) = -q**3 - q - 2. Let s(n) = -2*d(n) + 2*g(n). Let s(t) = 0. What is t?
-3/7, 1
Let c be -40 - -43 - 114/40. Let v(g) be the second derivative of -2*g + 1/28*g**7 + 9/40*g**5 + 0 + 0*g**3 - c*g**6 + 0*g**2 - 1/8*g**4. What is h in v(h) = 0?
0, 1
Let n = 224/555 - 10/37. Let u(b) be the third derivative of -1/6*b**4 + 0 - n*b**5 + 0*b + 9*b**2 - 1/30*b**6 + 0*b**3. Factor u(f).
-4*f*(f + 1)**2
Factor 3/2*i**4 + 27/4*i - 1/4*i**5 - 1/2*i**3 - 5/2 - 5*i**2.
-(i - 5)*(i - 1)**3*(i + 2)/4
Let q be 1*(3 + (-2 - 0))*0. Let s(f) be the third derivative of q*f**3 + 0*f - 1/525*f**7 + 0*f**5 + 0*f**6 + 0*f**4 + 0 - f**2 + 1/1680*f**8. Factor s(b).
b**4*(b - 2)/5
Factor 34/9*r + 2/9*r**2 + 32/9.
2*(r + 1)*(r + 16)/9
Suppose -16 = -5*g - 1. Factor g + 7*i - 7*i**4 + 15*i**2 + 13*i**3 - 2 + 11*i**4.
(i + 1)**3*(4*i + 1)
Let s = 274 - 272. Let r be (-1)/(-3) - 8/(-3). Suppose 2/9*v**r + 0*v**s - 2/9*v + 0 = 0. Calculate v.
-1, 0, 1
Suppose o - 2*d = 11, 2*o + d + 4 = 21. Suppose -270 = -o*g + 4*g. Determine z so that g - 2*z**2 + 10 - 32*z + z**2 + 5*z**2 = 0.
4
Let o(q) = 7*q**2 - 12*q + 9. Let k(f) = f**2 - f. Let h(t) = -30*k(t) + 5*o(t). Factor h(l).
5*(l - 3)**2
Let u(x) = -2 - 4*x - 3*x + 4*x**2 + 3. Let l(q) = 4*q - 48. Let o be l(11). Let v(g) = -3*g**2 + 6*g - 2. Let a(i) = o*u(i) - 6*v(i). Factor a(f).
2*(f - 2)**2
Let n(w) be the first derivative of w**6/7 - 4*w**5/35 - 13*w**4/14 + 16*w**3/21 + 4*w**2/7 - 286. Determine m, given that n(m) = 0.
-2, -1/3, 0, 1, 2
Factor 38 - 78 + 40 - 5*b**2 + 20*b + b**2.
-4*b*(b - 5)
Suppose 0 = 5*k - 597 - 3848. Let n = -38 + 40. Let k - 3*z**5 + 3*z**3 - 889 + 6*z**n - 6*z**4 = 0. Calculate z.
-2, -1, 0, 1
Suppose 2*q + 4 = i, 3*i = 3*q - 0*q + 9. Suppose -130*j**3 - 72*j - 16*j**4 + 16*j + 80*j**3 - 16 - 76*j**i - 2*j**5 = 0. Calculate j.
-2, -1
Factor 200/23 - 296/23*o - 6/23*o**2.
-2*(o + 50)*(3*o - 2)/23
Let l(i) be the second derivative of -3 - 6*i**2 + 2/3*i**3 - 1/5*i**5 + i**4 - i. Find o such that l(o) = 0.
-1, 1, 3
Let o be ((-6)/5)/(((-448)/240)/7). Factor -o*f**2 - 2*f**3 + 0 - f.
-f*(f + 2)*(4*f + 1)/2
Let m be 2/5*(17 - 12). Let x = 487 + -4381/9. Factor -4/3*s + x*s**2 + m.
2*(s - 3)**2/9
Solve -6706*h**2 + 32*h**3 - 4*h**3 - 4*h**4 + 6658*h**2 = 0.
0, 3, 4
Let c = -175 + 173. Let g(p) = -p**2. Let k(m) = 6 - 3 - 14*m + 1 + 7*m**2. Let l(d) = c*k(d) - 2*g(d). Factor l(i).
-4*(i - 2)*(3*i - 1)
Let l be -6*31/2*(-2)/(-483). Let n = l + 22/23. Determine v, given that -16/7*v - n*v**3 + 0 + 16/7*v**2 = 0.
0, 2
Let z(t) be the first derivative of -t**6/21 + 2*t**5/35 + 72. Factor z(s).
-2*s**4*(s - 1)/7
Let r(j) be the third derivative of -2/5*j**6 + 3*j**2 + 0 - 1/4*j**4 + 0*j + 11/20*j**5 + 0*j**3 + 1/10*j**7. Factor r(i).
3*i*(i - 1)**2*(7*i - 2)
Factor -3 + 3*b - 3/4*b**4 - 3/2*b**3 + 9/4*b**2.
-3*(b - 1)**2*(b + 2)**2/4
Let t(x) be the second derivative of x**8/120 - 29*x**7/1260 - x**6/360 + x**5/30 + 7*x**4/12 - 14*x. Let c(l) be the third derivative of t(l). Factor c(m).
2*(m - 1)*(4*m + 1)*(7*m - 2)
Suppose -s - 41 = 3*k, -5*k + 3*k - 2*s = 34. Let z be 7/(17 - 3)*k/(-2). Determine j, given that 0*j - 2/5*j**2 - 2/5*j**z + 0 = 0.
-1, 0
Let a(r) be the third derivative of 5*r**2 - 1/120*r**6 + 8/3*r**3 + 3/20*r**5 + 0*r + 0 - r**4. Factor a(p).
-(p - 4)**2*(p - 1)
Let n(w) be the second derivative of -w**6/900 - w**5/60 - w**4/15 - 23*w**3/6 + 22*w. Let o(b) be the second derivative of n(b). Factor o(d).
-2*(d + 1)*(d + 4)/5
Suppose 3*v = -5*r + 22, -416 = -r - 5*v - 394. Factor 2/3*m**4 + 2/3*m**3 + 0*m**r + 0 + 0*m.
2*m**3*(m + 1)/3
Let q(i) = -i**3 - 28*i**2 - 19*i + 18. Let p(a) = -9*a**2 - 6*a + 6. Let m(b) = 10*p(b) - 3*q(b). Factor m(l).
3*(l - 2)*(l - 1)*(l + 1)
Let d = -524 + 530. Let i(s) be the third derivative of -1/1050*s**7 + 0 - 12*s**2 + 0*s + 1/60*s**4 + 1/300*s**5 - 1/300*s**d + 0*s**3. Solve i(k) = 0.
-2, -1, 0, 1
Let v(d) = -2*d**2 - d + 1. Let p(o) = 4*o**2 - 5*o - 9. Let z(b) = p(b) + v(b). Solve z(r) = 0 for r.
-1, 4
Let 2/3*d**5 + 4/9*d + 10/3*d**2 - 16/9 - 14/9*d**4 - 10/9*d**3 = 0. What is d?
-1, 1, 4/3, 2
Suppose 4*j - 5 = 3*j. Suppose -5*m = 5*z - 10, -4*z = -z - 2*m - 1. Let -w**4 - w**5 - 2*w**2 - w + 7*w**4 + 2*w**3 + z - j*w**4 + 0*w = 0. Calculate w.
-1, 1
Suppose 93 = 2*i - 5*f - 69, -3*i = 2*f - 281. Let l = i - 89. Factor 0 - 6/7*z**3 + 2/7*z**l + 4/7*z.
-2*z*(z - 1)*(3*z + 2)/7
Let y be ((-6)/10)/((-162)/108). Factor -6/5*a + y*a**3 + 4/5*a**2 + 0.
2*a*(a - 1)*(a + 3)/5
Factor -22*j**3 - 220*j + 2*j**4 + 141*j**2 - 69 - j**4 + 169.
(j - 10)**2*(j - 1)**2
Suppose 0 = 3*y + y. Suppose y = -n - 2*n + 6. Determine i, given that -15 + 19 - 2*i**n + i**2 = 0.
-2, 2
Suppose -18*b + 34 = -b. Let q(u) be the first derivative of -4 + 2*u**b + 0*u - 2/3*u**3. Let q(v) = 0. What is v?
0, 2
Let x(t) be the second derivative of -5*t**7/42 - 5*t**6/2 - 27*t**5/2 - 50*t**4/3 - 530*t. Solve x(g) = 0 for g.
-10, -4, -1, 0
Solve -11 - 7 - 3*l**2 - 18*l - 6 = 0.
-4, -2
Let p(c) be the first derivative of c**7/42 - c**6/10 + 3*c**5/20 - c**4/12 + 13*c + 15. Let j(x) be the first derivative of p(x). Factor j(y).
y**2*(y - 1)**3
Let z(w) = -w**2 - 2*w + 2. Let o be z(-2). Suppose 0 = 3*v + 15*v - 36. Solve 2*h**v + 4*h**o - 7 + 4 - 3*h**4 = 0 for h.
-1, 1
Let j(h) = h**3 - 11*h**2 - 7*h - 1. Let x be j(12). Let l = 237/4 - x. Factor 0 + 0*d + 0*d**4 - 1/4*d**5 + 0*d**2 + l*d**3.
-d**3*(d - 1)*(d + 1)/4
Factor 66*f - 150 + 31*f + 3*f**2 - 2*f + 17*f**2.
5*(f + 6)*(4*f - 5)
Let l be (11 + 19)*(-5)/(-20). Find g, given that -9/2 + 3/2*g**3 + 21/2*g - l*g**2 = 0.
1, 3
Let d(z) = -33*z**4 + 52*z**3 - 53*z**2 + 10*z + 24. Let c(m) = -m**4 - m**3 - m**2 + 3. Let f(s) = 8*c(s) - d(s). Find h such that f(h) = 0.
0, 2/5, 1
Let i(d) be the second derivative of -d**6/30 - 17*d**5/20 + 3*d**4/2 + 144*d**3 - 432*d**2 + 21*d - 1. Factor i(j).
-(j - 6)*(j - 1)*(j + 12)**2
Let a(i) be the first derivative of 0*i - 3/20*i**5 + 0*i**2 - 4 + 0*i**3 + 3/16*i**4. Solve a(x) 