*(s - 1)**2/13
Let t(o) = 11*o**3 - 31*o**2 - 452*o - 1064. Let p(n) = 45*n**3 - 125*n**2 - 1810*n - 4260. Let u(s) = -6*p(s) + 25*t(s). Let u(z) = 0. What is z?
-4, 13
Let f be (-90)/(-72) - 94/88. Determine c, given that -10/11*c + 12/11 - f*c**2 = 0.
-6, 1
Let p = 7911 - 7911. Factor 2*z**4 + 0*z + 0*z**2 + p - 2/3*z**5 - 4/3*z**3.
-2*z**3*(z - 2)*(z - 1)/3
Let o(i) be the first derivative of 1/420*i**6 + 0*i**3 + 3/2*i**2 - 1/42*i**4 + 1/210*i**5 + 2 + 0*i. Let k(l) be the second derivative of o(l). Factor k(h).
2*h*(h - 1)*(h + 2)/7
Let q = -84146/9 + 9350. Factor 0*a**2 - 2/9*a**3 + 2/3*a + q.
-2*(a - 2)*(a + 1)**2/9
Find g such that g**2 + 196 - 2*g**3 + 158*g - 11*g**2 - 21*g**2 - 200*g + 7*g**2 = 0.
-7, 2
Let b(h) be the third derivative of -h**6/120 - h**5/60 + h**4/6 + 2*h**3/3 - 2*h**2 + 43*h. Factor b(f).
-(f - 2)*(f + 1)*(f + 2)
Let h(r) be the first derivative of r**6/2 + 9*r**5/5 - 27*r**4/4 + 5*r**3 + 399. Solve h(b) = 0.
-5, 0, 1
Suppose -15 = -2*a - 3*a. Let r = 1 + a. Determine c, given that 3*c**r + 2*c + 0*c**3 - 12*c**3 - 2*c + 12*c**2 = 0.
0, 2
Let w(m) be the third derivative of 0 - m**2 + 0*m + 0*m**3 + 1/180*m**5 - 1/72*m**4. Factor w(h).
h*(h - 1)/3
Let c(z) = 3*z**2 - 11*z - 14. Let k(y) = 15 + 11*y - 10*y + 0*y**2 - 3*y**2 + 11*y. Let u(m) = 3*c(m) + 2*k(m). Let u(t) = 0. Calculate t.
-1, 4
Let t(a) be the second derivative of 0 - 4*a - 4/5*a**2 - 1/100*a**5 + 1/30*a**4 + 2/15*a**3. Factor t(w).
-(w - 2)**2*(w + 2)/5
Let f = -9 - -12. Suppose f*v - 5*l = -4 - 0, 0 = 5*v - 5*l. Factor -11*n**2 + 3*n**v + 7*n**2 - n - n**3 + 1 + 2*n**3.
(n - 1)**2*(n + 1)
Let b = 9791 + -9787. Factor -8/3*j + 1/6*j**5 + 4/3*j**2 - 8/3 + 7/6*j**b + 8/3*j**3.
(j - 1)*(j + 2)**4/6
Let k(j) be the third derivative of 11449*j**6/420 - 107*j**5 - 71*j**4/7 - 8*j**3/21 - 406*j**2. Determine l so that k(l) = 0.
-2/107, 2
Suppose 0 = i - 3*h - 9, 0 = -3*i - 0*i - 5*h - 1. What is x in -5*x**2 + i*x**3 - 6*x**4 + 3*x**4 - 2*x**4 - 13*x**3 = 0?
-1, 0
Let a(i) = -i**5 + i**3 - 8*i**2 + 4*i. Let s(q) = 0*q**5 + 7*q**2 - q**3 + q**5 - 44*q - q**4 + 41*q. Let c(j) = 3*a(j) + 4*s(j). Let c(b) = 0. What is b?
-1, 0, 1, 4
Find h, given that -1/3*h**2 + 70/3 + 11*h = 0.
-2, 35
Let a(v) be the first derivative of v**4/48 + v**3/12 + v**2/8 - v + 13. Let g(i) be the first derivative of a(i). Suppose g(j) = 0. What is j?
-1
Let k = -165 - -160. Let y be (-4 - -6) + k - -6. Factor 0 - 2/9*x**y + 4/9*x**2 + 0*x.
-2*x**2*(x - 2)/9
Let p(s) be the first derivative of 0*s + 3/4*s**4 + 0*s**2 + 3/5*s**5 + 0*s**3 + 3. Solve p(w) = 0 for w.
-1, 0
Suppose 21*l = 18*l - 2*g + 11, -l - 1 = 3*g. Let d(o) be the third derivative of 1/20*o**l + 2/3*o**3 + 0*o - 6*o**2 + 1/4*o**4 + 0 + 1/240*o**6. Factor d(s).
(s + 2)**3/2
Let a = -4 - -9. Let p(d) = 8*d**2 + 2*d. Let t(z) = -7*z**2 - 3*z. Let f(o) = a*p(o) + 6*t(o). Factor f(x).
-2*x*(x + 4)
Suppose -20*o + 31*o = 0. Let m(q) be the third derivative of o + 2/33*q**3 - 1/165*q**5 - 7*q**2 - 1/44*q**4 + 1/220*q**6 + 0*q. Factor m(t).
2*(t - 1)*(t + 1)*(3*t - 2)/11
Let o = -25 - -52. Let s = -25 + o. Solve 24/5*b + 2/5*b**3 + 16/5 + 12/5*b**s = 0 for b.
-2
Let s = -455 + 457. Let d(o) be the first derivative of 0*o**2 + 1/12*o**4 + 0*o**3 + s + 0*o + 1/15*o**5. What is n in d(n) = 0?
-1, 0
Let q(d) be the first derivative of 5*d**6/3 - 14*d**5/5 - 64*d**4 - 136*d**3/3 + 48*d**2 - 287. Find r, given that q(r) = 0.
-4, -1, 0, 2/5, 6
Let b(i) be the third derivative of i**8/84 - i**6/30 - 35*i**2 + i. Let b(k) = 0. Calculate k.
-1, 0, 1
Let l(v) be the first derivative of 0*v + 21 - 2/3*v**3 + 0*v**2. Find s, given that l(s) = 0.
0
Suppose 5*k - 122 + 112 = 0. Let g(q) = q**2 - 18*q + 32. Let j be g(k). Factor -4/5*r**3 + 8/5*r**2 + j - 4/5*r.
-4*r*(r - 1)**2/5
Let w(r) be the first derivative of -r**2/2 + 7*r + 8. Let h be w(3). Factor -2*i - 2*i**5 + 5*i**5 + 2*i**5 - 4*i**4 + h*i**2 - 3*i**5.
2*i*(i - 1)**3*(i + 1)
Let w(n) be the first derivative of n**4/5 - 32*n**3/15 - 38*n**2/5 - 8*n - 683. Factor w(x).
4*(x - 10)*(x + 1)**2/5
Factor 0 + 10*w + 1/5*w**2.
w*(w + 50)/5
Factor 32/21 + 688/7*k + 11094/7*k**2.
2*(129*k + 4)**2/21
Let u be ((-1)/((-18)/8))/(32 - (-7436)/(-234)). Solve -1/3*r**u - 2 + 5/3*r = 0 for r.
2, 3
Suppose -43*j = 56 - 271. Let s(y) be the first derivative of -2/3*y**3 + 0*y**4 + 6 + 0*y + 2/5*y**j + 0*y**2. Factor s(r).
2*r**2*(r - 1)*(r + 1)
Let t = 33 - -301. Let w = 2362/7 - t. Suppose 16/7 - w*f**3 + 52/7*f**2 + 4/7*f**4 - 48/7*f = 0. What is f?
1, 2
Let z = -848 + 848. Let a be (-16)/(-20) + 4/(-10). Factor 0*f**2 + 3/5*f**4 - 1/5*f**5 - a*f**3 + z*f + 0.
-f**3*(f - 2)*(f - 1)/5
Let r be (-6)/21 + 3/(21/16). Let h be (-5)/(-2) + 1/r. Determine t so that -2/5*t**h + 6/5*t**2 - 6/5*t + 2/5 = 0.
1
Let p(m) be the third derivative of m**6/200 + 7*m**5/100 - m**4/5 + m**2 - m. Suppose p(x) = 0. Calculate x.
-8, 0, 1
Let w(y) = -y**3 + 4*y**2 - 4*y + 3. Let h be w(3). Let u be h/(1 + (0 - 3)). Factor -4 + u*b**2 - 3*b + 5*b + 4*b - 2*b**2.
-2*(b - 2)*(b - 1)
Let q = 4 + -4. Suppose -54*i = -5*c - 53*i + 12, -i = -4*c + 10. Factor 8/3*l + q + 12*l**c.
4*l*(9*l + 2)/3
Let t(d) be the third derivative of -d**6/600 - 11*d**5/300 - 13*d**4/40 - 3*d**3/2 - 326*d**2. Factor t(m).
-(m + 3)**2*(m + 5)/5
Determine f so that -39*f**3 + 10*f**2 + 4*f**4 + 5*f**2 + 2*f**4 + 3*f**5 + 15*f**2 = 0.
-5, 0, 1, 2
Determine i so that -84*i**2 + 25521 + 316*i - 557 + 85*i**2 = 0.
-158
Let t = 995 - 990. Let y(i) be the second derivative of 6*i**2 - 16/3*i**3 - 2/15*i**6 + 0 + 0*i**t + 2*i**4 - 4*i. Factor y(q).
-4*(q - 1)**3*(q + 3)
Let t(g) be the second derivative of 1/2*g**4 + 0*g**2 - 1/5*g**6 - 2/9*g**3 + 4/63*g**7 - 1/15*g**5 - 4*g + 0. Solve t(r) = 0 for r.
-1, 0, 1/4, 1, 2
Factor 1/2*r**2 - 9/2 + 4*r.
(r - 1)*(r + 9)/2
Suppose -5*v + 8 = -2. Determine w so that 6*w**3 + 9*w**4 - 24*w - 16 + 12*w**4 - 19*w**4 - 4*w**v = 0.
-2, -1, 2
Let i(h) be the third derivative of -h**6/120 + 19*h**5/60 - 14*h**4/3 + 32*h**3 - 21*h**2 + 1. Factor i(w).
-(w - 8)**2*(w - 3)
Let o = -1169 + 12867/11. Let 5/11*u**3 + o*u**2 + 4/11*u + 0 + 1/11*u**4 = 0. What is u?
-2, -1, 0
Find u, given that -6*u - 27/8*u**2 + 3/2 = 0.
-2, 2/9
Factor -2*h**2 - 410 - 119 + h**2 - 44*h + 45.
-(h + 22)**2
Let v(p) be the second derivative of -p**4/66 + 7*p**3/33 - 6*p**2/11 + 34*p - 1. Factor v(l).
-2*(l - 6)*(l - 1)/11
Let 3*q + 3/2*q**2 + 3/2*q**5 - 3/2*q**4 - 9/2*q**3 + 0 = 0. What is q?
-1, 0, 1, 2
Suppose 2*o - 10 - 4 = 0. Let r = o + -5. Factor -3*d**r - 4*d - 14*d**3 + d + 17*d**3 + 3.
3*(d - 1)**2*(d + 1)
Determine v so that 6883*v**2 + 98*v**3 - 26*v**3 + 15*v**4 - 6778*v**2 + 36*v - 12 = 0.
-2, -1, 1/5
Let n(b) be the third derivative of 0*b**3 - 1/840*b**6 + 4*b**2 + 0*b + 0 - 1/84*b**4 + 1/140*b**5. What is u in n(u) = 0?
0, 1, 2
Let u(r) be the first derivative of 2*r**3/27 - 17*r**2/9 + 32*r/9 + 10. Let u(g) = 0. Calculate g.
1, 16
Suppose -2*m + 7*m = 50. Suppose 0 = -m*d + 31 - 11. Find o such that 1/3*o**3 + 4*o - 2*o**d - 8/3 = 0.
2
Let r(p) = -p**3 - 4*p**2 - 13*p. Let y(i) = -2*i**3 - 8*i**2 - 14*i. Let q(u) = -2*r(u) + 3*y(u). Let q(z) = 0. What is z?
-2, 0
Suppose -r + t = -2*t - 3, -4*t + 15 = 5*r. Factor -i**2 + 952 - 952 + i**r.
i**2*(i - 1)
Let q(r) be the first derivative of -r + 10 + 1/66*r**4 + 2/33*r**3 - 3/11*r**2. Let c(m) be the first derivative of q(m). Factor c(x).
2*(x - 1)*(x + 3)/11
Let r be (-18)/54 - (-1582)/4710. Let o = 1254/785 + r. Factor o*n - 8/5 - 2/5*n**2.
-2*(n - 2)**2/5
Suppose 2*u = 3*u. Suppose 25*c - 19*c - 12 = 0. Determine q so that -4*q**4 - c*q + u*q - 2*q**4 + 6*q**2 - q + 3*q**5 = 0.
-1, 0, 1
Let z(c) be the second derivative of 5*c**7/14 + 16*c**6/5 + 111*c**5/20 + 5*c**4/2 - 769*c - 2. Determine q, given that z(q) = 0.
-5, -1, -2/5, 0
Let 0*u + 0 - 10/3*u**4 - 2/3*u**5 + 8/3*u**3 + 40/3*u**2 = 0. What is u?
-5, -2, 0, 2
Let c(i) = -i**3 + i**2 - i + 2. Let j(l) = -l**3 + 13*l**2 + 2*l - 4. Let y(w) = 2*c(w) + j(w). Solve y(o) = 0 for o.
0, 5
Let o(v) = 7 - v**2 + 8*v**2 + 2 + 4*v**2 + v**3 + 19*v. Let t be o(-9). Determine w so that t - 1/2*w + 1/2*w**3 + 0*w**2 = 0.
-1, 0, 1
Let p(u) be the first derivative of -u**7/840 - u**6/240 + u**5/80 + u**4/24 - u**3/6 - 17*u**2/2 + 16. Let b