 2*u = 3*u + 10, -4*x - 8 = 4*u. Let b(g) be the third derivative of -1/20*g**5 - 3/8*g**4 + 2*g**3 - 8*g**2 + 0*g + x. What is l in b(l) = 0?
-4, 1
Suppose -64 = -37*f + 36*f. Suppose 66*w - 4 = f*w. Factor 2/9*p**3 + 0*p**w - 4/9 - 2/3*p.
2*(p - 2)*(p + 1)**2/9
Let b be (7/14)/((-2)/(-24)). Suppose 0*v**2 + 8 + 9*v**2 + 12*v - b*v**2 + v**2 = 0. What is v?
-2, -1
Let s(n) be the second derivative of -n**4/4 + 7*n**3 - 36*n**2 + 2*n - 9. Solve s(w) = 0.
2, 12
Let u(y) be the first derivative of 21/2*y**5 + 3 - 6*y**2 - 5/2*y**6 + 14*y**3 - 69/4*y**4 - 3*y. Let w(k) be the first derivative of u(k). Factor w(i).
-3*(i - 1)**2*(5*i - 2)**2
Factor -13*r**2 + 24*r**2 - 50*r - 9*r**2 + 20547 + 686*r + 30015.
2*(r + 159)**2
Let r = -21 + 40. What is f in r*f - 23*f - 3 + f**2 + 7 = 0?
2
Let a(w) be the third derivative of 13*w**5/210 - 25*w**4/84 - 2*w**3/21 - 501*w**2. Factor a(s).
2*(s - 2)*(13*s + 1)/7
Let p be ((-2)/(-12)*58)/(2/3). Let i = -14 + p. Factor -1/2*r + 0 - i*r**2.
-r*(r + 1)/2
Solve -4*x**2 + 25 - 1 + 3*x**3 + 34*x**2 + 51*x = 0.
-8, -1
Let a = -16 + 24. Let g(x) = 7*x**3 - 23*x**2 + 31*x - 12. Let q(w) = 20*w**3 - 68*w**2 + 92*w - 36. Let l(o) = a*g(o) - 3*q(o). Suppose l(n) = 0. What is n?
1, 3
Let g(h) = 2*h**3 + 2*h**2 - 16*h + 5. Let r be g(6). Let u = r + -2885/7. Factor -2/7*i**4 - u*i**3 + 0*i**2 + 0 + 8/7*i.
-2*i*(i - 1)*(i + 2)**2/7
Let v(z) = -4*z**2 - 44*z. Let h = -87 - -50. Let f = h - -21. Let c(g) = -g**2 - 9*g. Let t(j) = f*c(j) + 3*v(j). Factor t(q).
4*q*(q + 3)
Let f(g) be the first derivative of 9*g**2 - 9/2*g**4 + 23*g**3 - 24*g - 23. Factor f(m).
-3*(m - 4)*(2*m - 1)*(3*m + 2)
Determine q so that 26*q**5 - 56 + 70*q**2 + 66*q**2 + 8*q**4 - 48*q**3 + 38*q**5 - 88*q**4 + 36*q - 52*q**5 = 0.
-1, 2/3, 1, 7
Let z = 38 + -17. Let h be 9/(-2)*z/(-63). Factor 0 + 1/2*w**2 - 3/2*w**3 - 1/2*w**5 + h*w**4 + 0*w.
-w**2*(w - 1)**3/2
Let b(t) = -15*t**2 + 330*t - 895. Let j(d) be the first derivative of 2*d**3/3 - 47*d**2/2 + 128*d - 8. Let o(n) = -3*b(n) - 20*j(n). Factor o(q).
5*(q - 5)**2
Let g(a) be the second derivative of -a**6/60 + a**5/30 - 4*a**2 - a. Let l(f) be the first derivative of g(f). Factor l(r).
-2*r**2*(r - 1)
Let g be 27 + -23 - (1 - 0). Let o = -1/85 + 853/255. Factor 2*x + o*x**2 - 6 + 2/3*x**g.
2*(x - 1)*(x + 3)**2/3
Let d(r) = -r**3 + 11*r**2 + 27*r - 8. Let k be d(13). Solve 0*z**3 - 1/8*z**k + 1/4*z**2 + 1/8*z - 1/4*z**4 + 0 = 0.
-1, 0, 1
Let f(v) be the third derivative of -v**5/210 + 37*v**4/84 - 34*v**3/7 - 216*v**2 - 1. Determine g, given that f(g) = 0.
3, 34
Let i = 14 + -11. Suppose 9 = -0*x + i*x. Solve -x*o**2 - 51 + 25 + 26 = 0 for o.
0
Let o = 3130/7 + -442. Determine q, given that -8/7*q - o*q**2 + 0 - 4*q**3 = 0.
-1, -2/7, 0
Let h be -2*(-2)/(-18) - (-784)/126. Factor -5*z + 10*z + h*z**2 + 4 - 14 - z**2.
5*(z - 1)*(z + 2)
Let t(f) = -f**4 + f**3 + f**2 + f - 1. Let q(j) = -4*j**4 + 13*j**3 - 6*j**2 + 3*j - 3. Let l(p) = -5*q(p) + 15*t(p). Suppose l(m) = 0. Calculate m.
0, 1, 9
Let k = 20 - 10. Let j = k - 6. Solve 6*w**3 + 0*w**5 + 0*w - 7*w - 3*w**5 + j*w = 0 for w.
-1, 0, 1
Let m = 8/127 + 436/1143. Let h = 301/1395 - -1/155. Solve m*u - 2/3*u**2 + 0 + h*u**3 = 0 for u.
0, 1, 2
Suppose -1936/9*q + 220/3*q**2 + 2/9*q**4 - 2662/9 - 64/9*q**3 = 0. What is q?
-1, 11
Let m = -13285 - -13287. Factor 0 - 28/5*z**m - 14/5*z**3 - 2/5*z**4 - 16/5*z.
-2*z*(z + 1)*(z + 2)*(z + 4)/5
Let r = -25 + 31. Let q(k) be the second derivative of 1/6*k**3 - 1/20*k**5 + 3*k + 0 - k**2 - 1/30*k**r + 1/4*k**4. Factor q(u).
-(u - 1)**2*(u + 1)*(u + 2)
Find x such that -156/7*x - 16/7*x**2 + 40/7 = 0.
-10, 1/4
Let y(x) be the third derivative of x**6/600 - x**5/75 - x**4/10 + 75*x**2. Solve y(o) = 0 for o.
-2, 0, 6
Solve 75*s**3 + 19*s + 5*s**4 + 36*s**2 + 99*s**2 + 46*s = 0.
-13, -1, 0
Let q = 15404/7 + -2200. Solve -9/7*u**2 - 5/7*u + q = 0 for u.
-1, 4/9
Suppose -3*n - 4*q + 59 - 61 = 0, 2*q = 4*n - 12. Let v(c) be the second derivative of 0*c**n + 0 - 1/30*c**4 + 0*c**3 - 6*c. Factor v(o).
-2*o**2/5
Let w be 5/(-15) + 19/3. Factor q**3 - 6*q**2 - 19*q + w + 2*q**3 + 16*q.
3*(q - 2)*(q - 1)*(q + 1)
Solve -48*k**5 - 2*k**2 - 123*k**3 + 2*k**2 + 144*k**3 - 3*k**2 - 24*k**4 = 0.
-1, 0, 1/4
Suppose 0 = 2*l + 3*l - 25. Factor 4*v**3 + v**5 + 0*v**3 + 2 - 6*v**4 - 6*v + 4*v**2 + v**l.
2*(v - 1)**4*(v + 1)
Suppose 6 + 6 = 4*d. Let z(j) = -5*j**3 - 8*j**2 - j - 9 + 3 + 0*j**2. Let k(n) = 4*n**3 + 7*n**2 + 2*n + 5. Let s(b) = d*z(b) + 4*k(b). Factor s(o).
(o + 1)**2*(o + 2)
Find h such that -3*h + 3/5 + 12/5*h**2 = 0.
1/4, 1
Let m(k) be the second derivative of -k**7/21 - k**6/3 + 31*k**5/10 - 43*k**4/6 + 6*k**3 + 3*k - 7. Let m(r) = 0. What is r?
-9, 0, 1, 2
Let q be (-119)/34*(-104)/28. Let n(w) be the first derivative of -4/5*w**5 + 0*w**4 + 4/3*w**3 - 1/3*w**6 + q + w**2 + 0*w. Determine v, given that n(v) = 0.
-1, 0, 1
Let h(l) be the first derivative of l**3/4 - 15*l**2/4 - 3. Factor h(a).
3*a*(a - 10)/4
Let n(p) be the third derivative of -p**8/112 + 8*p**7/35 + p**6/20 - 132*p**5/5 - 1089*p**4/8 - 720*p**2 + 2. Suppose n(y) = 0. What is y?
-3, 0, 11
Solve -66/7*s**2 + 72/7 - 64/7*s = 0 for s.
-18/11, 2/3
Let p(i) = 7 - 3*i + 10*i**3 + 6*i + 13*i**2 + 4*i. Let w(h) = 3*h**3 + 4*h**2 + 2*h + 2. Let c(u) = 6*p(u) - 21*w(u). Factor c(v).
-3*v**2*(v + 2)
Solve 0 - 2/7*a + 2/7*a**2 = 0 for a.
0, 1
Let x(b) be the second derivative of -b**5/50 + b**4/5 - 4*b**3/5 + 8*b**2/5 + b - 28. Find h, given that x(h) = 0.
2
Let s(x) be the third derivative of x**5/15 + 7*x**4/3 + 16*x**3 - 5*x**2 + 13. Factor s(v).
4*(v + 2)*(v + 12)
Factor 2/5*q + 0 + 2/5*q**3 - 4/5*q**2.
2*q*(q - 1)**2/5
Let 2/9*m**3 + 4/3*m + 23/9*m**2 - 4 - 1/9*m**4 = 0. What is m?
-3, -2, 1, 6
Suppose 15*r - 2*r = -416. Let s(b) = -111*b**3 + 12*b**2 + 11*b - 3. Let y(g) = -1220*g**3 + 132*g**2 + 120*g - 32. Let v(t) = r*s(t) + 3*y(t). Factor v(c).
-4*c*(3*c - 1)*(9*c + 2)
Determine k, given that -5*k**4 + 39*k**3 - 9*k**2 - 360 + 36*k**3 + 580*k - 103*k**2 + 246*k**2 - 464*k**2 = 0.
2, 9
Let s(c) = -11*c**2 + 58*c + 109. Let z(k) = -7*k**2 + 39*k + 71. Let d(w) = -5*s(w) + 8*z(w). Factor d(o).
-(o - 23)*(o + 1)
Let s(p) = -120*p**3 + 540*p**2 + 845*p + 55. Let h(l) = -13*l**3 + 60*l**2 + 94*l + 6. Let u(t) = 55*h(t) - 6*s(t). Factor u(r).
5*r*(r + 2)*(r + 10)
Let i be 4/6*(694 - 25). Let d = i - 2222/5. What is b in -4/5*b**2 + 12/5*b - d = 0?
1, 2
Let p(b) be the second derivative of -b**5/40 + 11*b**4/36 + 17*b**3/36 - 2*b**2/3 - 18*b. Factor p(t).
-(t - 8)*(t + 1)*(3*t - 1)/6
Let o(z) = 3*z**4 + z**3 + z**2 - 1. Let w(t) = -11*t**4 - 9*t**3 + 2*t**2 + 4*t - 4. Let j(y) = 4*o(y) + w(y). Let j(u) = 0. What is u?
-1, 2
Let p = 747/31 + -1094/93. Suppose 17/3*m**4 - p*m**3 - m**5 + 13*m**2 + 4/3 - 20/3*m = 0. What is m?
2/3, 1, 2
Let d(j) = 7*j**3 + 3*j**2 - 5*j - 10. Let n(u) = 3*u**3 + 2*u**2 - 2*u - 4. Let m(q) = -2*d(q) + 5*n(q). Suppose m(i) = 0. Calculate i.
-4, 0
Let l(p) be the second derivative of p**4/126 - 23*p**3/63 - 179*p. Suppose l(w) = 0. What is w?
0, 23
Let z(s) = -s**2 - 7*s - 6. Let a be z(-5). Let k(g) be the first derivative of 3/4*g**4 - g**3 - a + 1/2*g**2 - 1/5*g**5 + 0*g. Find p, given that k(p) = 0.
0, 1
Let y be ((-6)/10 - 48/15) + -4 + 9. Factor -3/5*f**2 + 9/5 + y*f.
-3*(f - 3)*(f + 1)/5
Let v = 149 + -90. Let s = 299/5 - v. Find h such that -s - h**2 + 1/5*h**3 + 8/5*h = 0.
1, 2
Find f, given that 173 - 139 - 175 - 109 + 10*f**2 - 125*f + 5*f**3 = 0.
-5, -2, 5
Let o(k) be the third derivative of -k**6/12 - 17*k**5/12 - 35*k**4/24 + 20*k**3/3 - 226*k**2. Suppose o(s) = 0. What is s?
-8, -1, 1/2
Let a = 81 + -691/9. Let c = 313/72 - a. Factor c*u**2 + 1/2*u + 3/8.
(u + 1)*(u + 3)/8
Let i(o) be the second derivative of o**5/5 - o**4/6 - 8*o**3/3 - 5*o**2 - 2*o. What is d in i(d) = 0?
-1, 5/2
Let c(w) be the second derivative of -w**6/1080 + w**5/90 - w**4/18 - 5*w**3 + 3*w. Let z(o) be the second derivative of c(o). Solve z(b) = 0 for b.
2
Let o(u) = u**3 + 2*u**2 - 5*u - 3. Let n be o(-3). Suppose -g = n*g. Find a, given that 0*a**2 + g*a**3 - a**2 + 4*a**3 + 3*a**4 - 1 - a**2 - 4*a = 0.
-1, -1/3, 1
Let 102 - 56 - 5*w**2 - 30*w - 86 = 0. What is w?
-4, -2
Let r = -3794 - -49358/13. Find f, given that 2/13*f**4 - 54/13 + 