1
Factor 145*z**2 + 15503*z - 3*z**3 + 1735595 - 77504*z + 602*z**2 - 20234.
-3*(z - 83)**3
Let d(n) be the third derivative of -1/240*n**5 - 1/720*n**6 + 1/2*n**3 + 0*n**4 + 0*n - n**2 + 0. Let x(m) be the first derivative of d(m). Factor x(u).
-u*(u + 1)/2
Let r(q) be the third derivative of -13*q**6/30 + q**5/30 + 6*q**2 - 5*q. What is j in r(j) = 0?
0, 1/26
Find c such that -82/17*c**2 + 6/17*c**3 + 266/17*c + 98/17 = 0.
-1/3, 7
Let d be 3 + 27/(-5) + 3. Let c = 18/193 + 2226/965. Find l, given that 0 + 27/5*l**3 - c*l**4 + d*l - 18/5*l**2 = 0.
0, 1/4, 1
Let h(w) = 3*w**2 - 716*w - 737. Let f(o) = -65*o**2 + 15745*o + 16215. Let t(x) = -2*f(x) - 45*h(x). Factor t(q).
-5*(q - 147)*(q + 1)
Let w(z) be the first derivative of z**4/8 + 16*z**3/3 - 601. Factor w(y).
y**2*(y + 32)/2
Let l(q) = -3*q**3 - 4*q**2 + q. Let w(o) = 16*o**3 + 21*o**2 - 4*o. Suppose -3*d + 6*d = 99. Let u(s) = d*l(s) + 6*w(s). Determine y so that u(y) = 0.
-3, 0, 1
Solve 1537 - 768 - 762 - w**2 - 6*w = 0 for w.
-7, 1
Let o(r) be the first derivative of -r**4 + 8*r + 2*r**2 - 36 - 8/3*r**3. Let o(v) = 0. What is v?
-2, -1, 1
Let r = 16 - 210. Let g = r - -199. Factor 4/7*u**3 + 0 + 0*u**2 + 0*u**4 - 2/7*u**g - 2/7*u.
-2*u*(u - 1)**2*(u + 1)**2/7
Let v(s) be the second derivative of -4*s**3 - 1/3*s**4 + 20*s + 0 - 16*s**2. Factor v(j).
-4*(j + 2)*(j + 4)
Let s(b) = 25*b**2 - 32*b - 14. Let c(n) = 76*n**2 - 92*n - 40. Let f(m) = 3*c(m) - 8*s(m). Factor f(o).
4*(o - 1)*(7*o + 2)
Let o(a) be the second derivative of -a**7/294 - a**6/35 + 3*a**5/28 - 2*a**4/21 - a - 29. Find k, given that o(k) = 0.
-8, 0, 1
Let n(x) be the third derivative of -1/3*x**3 + 1/60*x**5 + 11*x**2 + 0*x + 0 + 1/24*x**4. Solve n(i) = 0.
-2, 1
Let 28*r**4 - 232/3*r + 16 - 262/3*r**3 + 124*r**2 - 10/3*r**5 = 0. What is r?
2/5, 1, 2, 3
Let j be 54/21 - 15/(-35). Find u, given that -u**4 - 3*u**2 - 5*u + u**3 + 3*u**j + u - 7 + 11 = 0.
-1, 1, 2
Let g(c) = -11*c - 7. Let m be g(-1). Determine t, given that 2*t + 190 + 72*t**2 + 48*t**5 + 2*t - 112*t**4 + 198 - m*t**3 - 396 = 0.
-1/2, 1/3, 1, 2
Let j(n) = -7 - 21*n - 24*n + 39*n. Let r be j(-9). Solve 2*a - 23*a**3 + r*a**3 + a**2 - 25*a**3 = 0.
-1, 0, 2
Suppose 0*t**2 - 4*t**2 + 108*t - 46 - 8 - 14 - 36 = 0. What is t?
1, 26
Suppose -1/2*g**5 + 1/2*g**3 - 11/2*g**2 + 3/2*g**4 - 2 + 6*g = 0. What is g?
-2, 1, 2
Let x = 257 + -257. Suppose -3/4*v**3 - 3*v + x + 15/4*v**2 = 0. What is v?
0, 1, 4
Find j such that -15*j**4 + 100*j**2 - 57*j**4 + 260*j**3 - 44*j**4 + 12*j**5 = 0.
-1/3, 0, 5
Let q(r) be the first derivative of r**4/20 + r**3/5 - 2*r**2/5 + 788. Factor q(u).
u*(u - 1)*(u + 4)/5
Let u be (0 - 42/12)*(-3 - (-165)/70). Determine q so that -3/4*q**2 + 0 + u*q = 0.
0, 3
Let z be (-8 - -15) + (0 - 7). Let s(x) be the second derivative of z - 1/3*x**3 - 1/6*x**4 + 3*x + 2*x**2. Solve s(f) = 0 for f.
-2, 1
Let -75/2 - 69*q**2 - 3/2*q**4 + 18*q**3 + 90*q = 0. Calculate q.
1, 5
Suppose 4*h + 2 = 5*h. Let t be -6 + -1 + (-851)/(-111). Factor t*d**h + 0 - 2/3*d**4 - 2/3*d**3 + 2/3*d.
-2*d*(d - 1)*(d + 1)**2/3
Let c(l) be the first derivative of 15/2*l**2 - 10 - 10*l - 5/3*l**3. Suppose c(s) = 0. What is s?
1, 2
Let n(u) be the first derivative of 1/12*u**3 + 1/2*u - 3/8*u**2 + 12. What is z in n(z) = 0?
1, 2
Let b(s) = 3*s**5 + 15*s**4 - 15*s**3 - 3*s**2 + 12*s + 6. Let m(y) = y**4 - y**3 + y**2 + y. Let z(n) = b(n) - 9*m(n). Determine q, given that z(q) = 0.
-2, -1, 1
Suppose 4*u - 14 = -w, 3*w + 2 - 8 = -3*u. Let z be ((-104)/(-10))/((-174)/(-145)) + -2. What is x in -u*x - z*x**2 + 8/3 = 0?
-1, 2/5
Let d be (5/(30/4) - 2) + 32 + -30. Determine n so that 0 - d*n**3 + 4/3*n**2 - 2/3*n = 0.
0, 1
Suppose 0 = -2*h - 2*n + 2, -2*h + 19 = -2*n + 1. Let b = -2 + 6. Determine w, given that -8*w**5 + 2*w**h - 2*w**4 + 4*w**b + 3*w**3 + w**4 = 0.
-1/2, 0, 1
Let s(b) be the first derivative of 3/14*b**4 - 1/7*b**2 + 43 - 4/21*b**3 + 0*b. Factor s(x).
2*x*(x - 1)*(3*x + 1)/7
Let s(r) be the first derivative of 0*r - 4/15*r**3 - 1/10*r**2 + 13 - 1/30*r**6 - 4/25*r**5 - 3/10*r**4. Solve s(y) = 0 for y.
-1, 0
Let w(a) be the first derivative of 0*a**4 + 3/2*a**2 + 1/60*a**5 + 0*a + 5 - 1/6*a**3. Let d(h) be the second derivative of w(h). Find c such that d(c) = 0.
-1, 1
Factor -14 + 6*v**2 - 4 + 13*v**2 + 8*v - 11*v**2 + 62*v.
2*(v + 9)*(4*v - 1)
Let q(m) be the first derivative of -m**4/16 - 57*m**3/4 - 9747*m**2/8 - 185193*m/4 - 247. Factor q(w).
-(w + 57)**3/4
Let y(m) be the third derivative of -9/10*m**5 - 4*m**2 - 108*m**3 + 0*m - 1/40*m**6 - 27/2*m**4 + 0. Factor y(n).
-3*(n + 6)**3
Suppose -6*o - 14*o + 84 - 8*o**2 - 60 + 4*o**3 = 0. Calculate o.
-2, 1, 3
Let b(a) be the third derivative of a**6/72 + 37*a**5/180 + 7*a**4/36 + 4*a**2 - 8*a. Let b(c) = 0. What is c?
-7, -2/5, 0
Let x(d) be the third derivative of 26*d**2 - 1/135*d**5 + 0*d + 0*d**3 + 0 - 1/9*d**4. What is p in x(p) = 0?
-6, 0
Let j be 3 - (-2 - -6) - (-7)/4. Let r = -1/4 + j. Let -1 - 5/2*h + h**3 - r*h**2 = 0. What is h?
-1, -1/2, 2
Let s(d) = 13*d**4 - 17*d**3 + 8*d**2 + 2*d + 2. Let z(p) = 27*p**4 - 34*p**3 + 17*p**2 + 5*p + 5. Let t(v) = 15*s(v) - 6*z(v). Factor t(w).
3*w**2*(w - 1)*(11*w - 6)
Suppose 0 = -2*b + 17 + 7. Let x be (b/15)/(4/10). Determine t so that -t**4 - x*t**3 + 7*t**2 - 15*t**2 + 7*t**2 = 0.
-1, 0
Let f(a) be the third derivative of -a**6/480 + a**5/240 + a**4/6 + 5*a**3/6 + 22*a**2 - 6. Factor f(c).
-(c - 5)*(c + 2)**2/4
Let s(b) be the third derivative of 0*b - 5/12*b**4 + 0 + 5/6*b**3 + 5*b**2 - 5/672*b**8 + 5/48*b**6 + 1/168*b**7 - 5/48*b**5. Suppose s(p) = 0. What is p?
-2, -1, 1/2, 1, 2
Let y(q) = 3*q - 60. Let c be y(21). Let g(o) be the first derivative of 0*o**2 - 2/3*o**c - 1/4*o**4 + 0*o - 5. Suppose g(j) = 0. What is j?
-2, 0
Factor 7/5*i**2 - 1/5*i**3 - 11/5*i + 1.
-(i - 5)*(i - 1)**2/5
Let b(h) = h**2 - 3*h - 1. Let l(q) = -5*q**2 - 9*q - 37. Let a(m) = -6*b(m) - 2*l(m). Suppose a(s) = 0. Calculate s.
-5, -4
Let d(c) = c**2 - 43*c + 403. Let t(p) = p - 1. Let l(v) = 5*d(v) + 15*t(v). Suppose l(o) = 0. Calculate o.
20
Let g(x) be the third derivative of 0*x**4 + 0*x - 1/160*x**6 + 0*x**3 + 1/120*x**5 + 1/840*x**7 + 0 + 18*x**2. Determine s, given that g(s) = 0.
0, 1, 2
Let x(j) be the second derivative of j**5/30 - 7*j**3/3 + 20*j**2/3 + 20*j - 1. Factor x(b).
2*(b - 4)*(b - 1)*(b + 5)/3
Let b(n) be the third derivative of -5*n**8/336 + 11*n**7/42 - 17*n**6/12 - 2*n**5/3 + 100*n**4/3 - 320*n**3/3 - 5*n**2 - 16. Factor b(f).
-5*(f - 4)**3*(f - 1)*(f + 2)
Factor -3/4*u**2 + 291/4*u - 72.
-3*(u - 96)*(u - 1)/4
Let a(k) = -8*k**2 + 9*k + 8. Let h = -86 - -80. Let i(f) = 2*f**2 - f. Let z(y) = h*i(y) - 2*a(y). Factor z(u).
4*(u - 4)*(u + 1)
Let j(o) = -o**3 - 4*o**2 - 3*o + 3. Let y be j(-3). Suppose 7*v**4 + 8*v**2 + 30*v - 3*v**2 + 7*v**4 - 9*v**4 - 20*v**y = 0. Calculate v.
-1, 0, 2, 3
Let r = -6749395/36 + 187471. Let m = -94/9 - r. Find b such that 3/4*b**3 + 1/2*b - m*b**2 + 0 + 7/4*b**4 - 5/4*b**5 = 0.
-1, 0, 2/5, 1
Factor 18 - 254807*q**2 + 6 + 254791*q**2 + 20*q.
-4*(q - 2)*(4*q + 3)
Let r(h) be the second derivative of h**4/6 + 13*h**3 + 38*h**2 - 190*h. Solve r(i) = 0.
-38, -1
Let h(o) be the first derivative of -o**4/8 - 7*o**3/6 - 4*o**2 - 6*o + 14. Factor h(l).
-(l + 2)**2*(l + 3)/2
Let x(f) = 17*f**2 - f. Let m be x(1). Suppose 16 = -o + m. Factor 1/4*t**2 + o + 0*t.
t**2/4
Let b(k) be the second derivative of -k**4/16 - 9*k**3/8 - 3*k**2 - 96*k. Solve b(u) = 0.
-8, -1
Suppose -6*y**4 - 617*y**3 + 635*y**3 + 3*y**4 = 0. What is y?
0, 6
Suppose -2*o + 0*q - q + 23 = 0, -4*q - 40 = -3*o. Suppose 0 = -4*b + 5*i - 8*i + 2, -3*i - o = -3*b. Solve -1/2*y**b - 1/4*y + 0 - 1/4*y**3 = 0.
-1, 0
Let o(d) be the second derivative of -d**7/105 + 7*d**6/75 - 8*d**5/25 + 2*d**4/5 - 5*d + 13. Factor o(f).
-2*f**2*(f - 3)*(f - 2)**2/5
Suppose 25*g = 22*g + 21. Suppose 0 = c + 5*f + 7, 4*c = -c - 4*f + g. Determine p so that 8/3*p + 1/3*p**c - 7/3*p**2 + 16/3 = 0.
-1, 4
Let s be (2505/(-225) - -15) + (-2)/(-15). Let r(h) be the second derivative of -1/4*h**2 + 1/24*h**s - 2*h + 0*h**3 + 0. Factor r(m).
(m - 1)*(m + 1)/2
Let r(z) = z**2 - 8*z - 5460. Let x be r(-70). Solve x - 1/2*d**2 - 2*d = 0.
-4, 0
Let b be ((-15)/(-200)*10)/((-3)/(-8)). Factor 0 - 1/5*q + 2/5*q*