0, 2, 3
Let i(m) = 5*m**4 + 69*m**3 + 226*m**2 + 260*m. Let y(z) = -4*z**4 - 64*z**3 - 226*z**2 - 261*z. Let f(b) = 3*i(b) + 4*y(b). Factor f(l).
-l*(l + 2)*(l + 3)*(l + 44)
Suppose 96*i + 12*i - 9*i - 390 = -31*i. Solve -6/7*f**2 - 5/7*f + 0 - 1/7*f**i = 0 for f.
-5, -1, 0
Suppose -2*r - 15816 = 3*a - 15851, -5*r + 80 = 5*a. Factor 2/3*m**a + 26/3*m**2 + 0 + 0*m.
2*m**2*(m + 13)/3
Let -2*i**2 - 69935 - 54711 - 73743 - 133387 - 2*i**2 - 2304*i = 0. What is i?
-288
Let w(a) be the first derivative of 2/3*a**3 - 15/2*a**2 + 5 + 1/12*a**4 + 0*a - 1/30*a**5. Let v(z) be the second derivative of w(z). Factor v(n).
-2*(n - 2)*(n + 1)
Let a = 317025/16 + -19814. Let g(f) be the first derivative of -18 + 1/20*f**5 + 0*f - 1/12*f**3 + a*f**4 - 1/8*f**2. Let g(o) = 0. Calculate o.
-1, 0, 1
Let l(i) = -i**2 + 29*i - 200. Let s be l(12). Let c(z) be the second derivative of 1/12*z**5 + 6*z + 0 - 5/6*z**2 + 5/6*z**3 - 5/12*z**s. Solve c(m) = 0 for m.
1
Let a be (-6 + 376/35)*310/32. Let h = a - 347/8. Suppose 12/7*w**2 + 0*w + 0 + 30/7*w**3 + h*w**4 = 0. What is w?
-1, -2/3, 0
Find t such that -t**4 + 8*t**3 + t**5 + 23*t**4 - 34*t**3 + 3*t**4 = 0.
-26, 0, 1
Let v(c) be the second derivative of -c**6/120 - 17*c**5/40 - 241*c**4/48 + 23*c**3/2 - 5308*c. Factor v(u).
-u*(u - 1)*(u + 12)*(u + 23)/4
What is y in 124/3*y - 56/3*y**3 + 38/3*y**2 + 16 = 0?
-3/4, -4/7, 2
Let s be (2 - (-9)/6)/(9/(-18)). Let h be 2 + (-2 - (5 + s)). Suppose -1/4*o**h + o + 5/4 = 0. What is o?
-1, 5
Find m such that 2/3*m**3 + 20436626/3 + 94178*m + 434*m**2 = 0.
-217
Let o(h) = -h**2 + 1. Let y = -21 + 26. Let a(n) = y*n**3 - 4 - 5*n**3 + 3*n**3 + 3*n**2 - 6*n + 4*n**2. Let g(u) = a(u) + 4*o(u). Let g(j) = 0. What is j?
-2, 0, 1
Let u(p) be the second derivative of -p**4/60 + 268*p**3/15 - 107*p**2/2 + 105*p + 12. Factor u(x).
-(x - 535)*(x - 1)/5
Determine v, given that 1/6*v**2 + 67/6*v + 42 = 0.
-63, -4
Let y be (-2*3/33)/(15860/(-440) - -36). Solve -2268*p - 55/3*p**3 - 1944 - 1/3*p**y - 342*p**2 = 0.
-18, -1
Let b = -563 - -788. Let r be (25/b)/((-5)/(-60)). Find s such that r + 2/3*s**4 + 2/3*s - 2*s**2 - 2/3*s**3 = 0.
-1, 1, 2
Let j = 25 + -23. Suppose 0*n + j*n + x = 29, 2*x - 22 = -n. Factor -9*g**2 - 15*g - 4*g**5 + 23*g + n*g**3 - 5*g**2 - 6*g**2 + 4*g**4.
-4*g*(g - 1)**3*(g + 2)
Let g(u) be the third derivative of -u**6/720 - 7*u**5/40 + 43*u**4/48 - 119*u**3/6 + 44*u**2. Let j(y) be the first derivative of g(y). Factor j(l).
-(l - 1)*(l + 43)/2
Let t be (90/14 - 1) + ((-2400)/(-105))/40. Factor 2/7*w**3 - 20/7 + t*w - 24/7*w**2.
2*(w - 10)*(w - 1)**2/7
Suppose 143*v = 151*v - 16. Let w(k) be the first derivative of -5/8*k**4 - 18 + 0*k**3 + 0*k + 0*k**v - 1/2*k**5. Let w(p) = 0. What is p?
-1, 0
Suppose 0 = -4*t - 2*z + 398, 20*t + 4*z - 103 = 19*t. Suppose 92*y = t*y - 14. What is m in 1/6*m - 1/6*m**3 + 1/3*m**y - 1/3 = 0?
-1, 1, 2
Factor 101*k**2 + 603 - 73*k**3 + 178*k - 33*k**4 + 472 - 1215 + k**5 - 34*k.
(k - 35)*(k - 1)**2*(k + 2)**2
Let g = 660 + -660. Let s(r) = 3*r**2 + 3*r + 2. Let j be s(g). Suppose -10/9*b**4 + 8/9*b**j + 0 + 0*b + 16/9*b**3 = 0. What is b?
-2/5, 0, 2
Suppose -9*i - 38*i**2 + 30*i + 67*i**2 + 54 - 32*i**2 = 0. What is i?
-2, 9
Let z(h) be the first derivative of -h**4/26 - 734*h**3/39 - 3491. Solve z(q) = 0.
-367, 0
Factor -351897*r - r**4 + 351897*r - 44*r**3 - 484*r**2.
-r**2*(r + 22)**2
Suppose 10*j + 40 = 290. Factor -5*y**4 + 44*y - 39*y - 40*y**2 + j*y**3 + 15*y.
-5*y*(y - 2)**2*(y - 1)
Let m be -2*(14/(-5) + 3)*-5. Determine c so that 4*c**2 - 7*c - 16*c**4 - 5*c**3 + 5*c**2 + m + 17*c**4 = 0.
1, 2
Let j = 1713 + -1724. Let c be -1 - j/(1144/120). Factor -c*g**2 + 12/13*g - 16/13.
-2*(g - 4)*(g - 2)/13
Suppose 18*j - 20*j - 4*q = -12, 2*q - 14 = -5*j. Factor -15*y**3 + y**2 - 117*y**4 - y**j + 122*y**4.
5*y**3*(y - 3)
Factor -242064*x + 19849248 + 984*x**2 - 4/3*x**3.
-4*(x - 246)**3/3
Let c(a) be the first derivative of -2*a**7/21 - 4*a**6/15 + 3*a**5/5 + 4*a**4/3 - 8*a**3/3 + 43*a + 2. Let f(x) be the first derivative of c(x). Factor f(g).
-4*g*(g - 1)**2*(g + 2)**2
Let u(s) be the first derivative of 1/3*s**2 - 72 + 7/9*s**3 + 1/3*s**4 - 4/15*s**5 + 0*s. Find q such that u(q) = 0.
-1/2, 0, 2
Let i(v) = v**3 - 10*v**2 + 9*v + 3. Let a be i(9). Solve -8*h**2 + 16*h**3 - 6*h + 7*h**a - 21*h**3 + 14*h = 0.
0, 2
Suppose -15/2*i - 18 + 3/4*i**4 + 15/2*i**3 + 69/4*i**2 = 0. Calculate i.
-6, -4, -1, 1
Let u be (-84)/189 + (-148)/(-9). Solve u*t**2 + 8*t**5 - 19*t**3 - 4*t**5 + t**4 - 6*t**4 + 3*t - 23*t**2 = 0.
-1, 0, 1/4, 3
Let a(q) be the second derivative of -3*q**5/80 + 21*q**4/16 + 3337*q. Factor a(f).
-3*f**2*(f - 21)/4
Let h = -392 + 389. Let m be ((-6)/42)/(-4 - h). Solve -1/7*u**3 + 1/7*u**2 + 1/7*u + 0 - m*u**4 = 0.
-1, 0, 1
Let v(n) be the third derivative of n**6/480 + 3*n**5/32 - 17*n**4/16 + 229*n**3/6 + 69*n**2 + 1. Let p(b) be the first derivative of v(b). Solve p(g) = 0.
-17, 2
Let p(g) be the third derivative of -g**6/180 - 11*g**5/90 + 10*g**4/9 - 28*g**3/9 - 8*g**2 - 64*g. Suppose p(j) = 0. Calculate j.
-14, 1, 2
Suppose 8/3 + 4/9*g**4 - 28/9*g**2 + 2/9*g**5 + 22/9*g - 8/3*g**3 = 0. Calculate g.
-4, -1, 1, 3
Determine g so that 262/7*g**2 + 54/7*g - 4 - 120/7*g**3 = 0.
-2/5, 1/4, 7/3
Let f be 19 + (-1725)/92 - -5. Solve 9*g**2 - 27/4*g**3 - f*g**4 + 0 + 3*g = 0 for g.
-2, -2/7, 0, 1
Let g = -206 + 208. What is a in 18*a**g + 3*a**3 - a**4 - 25*a**2 + 11*a**2 = 0?
-1, 0, 4
Let f(c) be the first derivative of -1/15*c**6 + 0*c**5 + 0*c**2 - 29 + 2/5*c**4 + 0*c + 0*c**3. Find o, given that f(o) = 0.
-2, 0, 2
Suppose -562*o = -546*o - 96. Let j(s) be the second derivative of 0*s**3 - 2/5*s**o - 2/21*s**7 - 2/5*s**5 + 15*s + 0*s**4 + 0*s**2 + 0. Factor j(r).
-4*r**3*(r + 1)*(r + 2)
Suppose -394 - 626 = -34*d. Suppose d*a = 36*a. Factor 4/3*n**4 + 4*n**3 + 0*n + a + 8/3*n**2.
4*n**2*(n + 1)*(n + 2)/3
Let v(g) be the first derivative of -g**4/22 + 28*g**3/11 - 441*g**2/11 - 1588. Factor v(b).
-2*b*(b - 21)**2/11
Suppose 8*h = 64 - 16. Suppose 164 = h*x + 152. Solve 8/5 - 14/5*j + 6/5*j**x = 0.
1, 4/3
Let n(s) be the third derivative of -229*s**2 + 1/4*s**6 + 0*s - 1/42*s**7 - 5/12*s**5 + 0 + 0*s**3 + 0*s**4. Factor n(a).
-5*a**2*(a - 5)*(a - 1)
Let m(f) = -f**3 + 7*f**2 - 9*f + 5. Let v be m(6). Let i = v - -17. Factor 9*a**4 + 81*a**5 + 10*a**i + 11*a**4 + 4*a**3 + 6*a**4.
a**3*(9*a + 2)**2
Let p(x) = 4*x**2 + 115*x + 676. Let b(t) = 83 + 391*t + 0*t**2 + 86 + t**2 - 362*t. Let w(h) = -22*b(h) + 6*p(h). Solve w(g) = 0.
-13
Let a(o) = 6*o + 33. Let g be a(-5). Factor -5*n**4 - 808*n + 22 + 60*n**g - 20*n**2 - 152*n - 1302.
-5*(n - 8)**2*(n + 2)**2
Find s, given that -549/2 - 3/4*s**3 - 165/4*s + 93/2*s**2 = 0.
-2, 3, 61
Let o = 477665/714 - 4015/6. Let h = 418/1071 + o. Determine k, given that -4/9 - h*k + 2/9*k**2 = 0.
-1, 2
Let z(w) be the second derivative of -6*w**3 + 0*w**2 + 13/6*w**4 + 4 - 2/9*w**5 - 4*w + 1/135*w**6. Factor z(n).
2*n*(n - 9)**2*(n - 2)/9
Determine n, given that 8/5*n**3 - 1224/5*n + 324 - 4/5*n**4 + 48*n**2 = 0.
-9, 3, 5
Let y be 0/(-12)*(-2)/4. Suppose y*o = w + o - 125, o = 0. Factor 15*c**2 - 9*c + 7*c + w + 77*c + c**3 + 0*c**3.
(c + 5)**3
Suppose 2*b = 4*o - 14, 0 = -b + 4*b - 2*o + 1. Let f be -5*(-84)/(-150)*(-10)/8. Suppose -5/2*n**2 - 3/2 - 1/2*n**b - f*n = 0. Calculate n.
-3, -1
Suppose 48 = 4*v + 4*h, 2*v - 46 = -5*h - 10. Factor 22 + v + 7*y**3 - 28*y**3 - 90*y**2 + 81*y.
-3*(y - 1)*(y + 5)*(7*y + 2)
Let a(z) be the second derivative of -3/20*z**5 - 3 - 7*z + 1/30*z**6 - 17/6*z**3 - 3*z**2 - 5/4*z**4. Find t such that a(t) = 0.
-1, 6
Let w(k) be the third derivative of 0 - 4/3*k**3 - 1/3*k**4 + k**2 + 68*k - 1/30*k**5. Find r, given that w(r) = 0.
-2
Let k be ((-17 - -13) + 52)/10*(-30)/(-22). Factor 14/11*b**2 - k + 248/11*b.
2*(b + 18)*(7*b - 2)/11
Let w be -3*(5000/(-150))/50. Suppose 32/7 + 20/7*g**5 - 136/7*g**4 - 328/7*g**w + 332/7*g**3 + 80/7*g = 0. What is g?
-1/5, 1, 2
Let s(c) be the second derivative of c**6/1620 - c**5/27 - 11*c**4/27 + c**3/6 + 11*c**2 - 6*c - 2. Let q(z) be the second derivative of s(z). Factor q(a).
2*(a - 22)*(a + 2)/9
Suppose 2 = 3*p - 53289*y + 53293*y, 0 = y + 1. Factor -24/19 - 26/19*c - 2/19*c**p.
-2*(c + 1)*(c + 12)/19
Let g(k) = 10*k**2 + 11*k +