5)**2/4
Let w(d) be the first derivative of 20*d**3/51 - 37*d**2/17 + 42*d/17 + 399. Suppose w(t) = 0. What is t?
7/10, 3
Let 2/7*r**4 + 36/7*r**3 + 216/7*r**2 + 0 + 432/7*r = 0. Calculate r.
-6, 0
Let g(m) be the third derivative of -1/12*m**4 - 1/42*m**7 + 33*m**2 - 1/336*m**8 - 7/60*m**5 - 3/40*m**6 + 0 + 0*m**3 + 0*m. Factor g(r).
-r*(r + 1)**3*(r + 2)
Let p(q) be the first derivative of -q**3 + 207*q**2/2 + 1848*q - 547. Factor p(n).
-3*(n - 77)*(n + 8)
Let u(c) be the first derivative of -1/3*c**3 + 30*c + 1/2*c**2 - 277. Let u(n) = 0. Calculate n.
-5, 6
Suppose -u - 5 = -7. Let v(s) = 6*s**u - 8*s**2 + 37 - 16*s - s**2. Let m(j) = -2*j**2 - 16*j + 36. Let t(b) = 5*m(b) - 4*v(b). Find h, given that t(h) = 0.
4
Determine v, given that -2/7*v**2 + 572/7 - 282/7*v = 0.
-143, 2
Factor -16*f**3 - 2/3*f**4 + 32 + 2/3*f**5 - 80/3*f**2 + 32/3*f.
2*(f - 6)*(f - 1)*(f + 2)**3/3
Let q(r) = 4*r**2 + 5*r - 14. Let b be q(5). Suppose -3*i - b = -117. Factor u - 3*u**2 - 9*u - u**i.
-4*u*(u + 2)
Let p be ((-3)/(-5))/(63/210). What is a in 15646*a**2 - 108*a + 29*a + 33*a - 82*a - 15650*a**p = 0?
-32, 0
Let o(u) = -u**3 - 8*u**2 - 12*u + 5. Let t be o(-6). Suppose 115*c**2 - t*c**5 + 75*c**3 + 140*c + 5*c**4 - 72*c - 18*c = 0. What is c?
-2, -1, 0, 5
Let f(d) be the first derivative of 1/35*d**5 + 100/7*d + 1/2*d**4 + 10*d**2 + 39 + 23/7*d**3. Find n such that f(n) = 0.
-5, -2
Suppose -3*i - 35 = -2*k, -11*k - 2*i + 46 = -8*k. Find x, given that -137*x**4 - 5*x**2 - k*x**3 - 11*x**2 + 133*x**4 = 0.
-2, 0
Let o(w) = -w**2 - 3*w - 1. Let q be o(-3). Let g be q + ((-30)/(-36) - 2/(-12)). Determine h, given that 3*h**2 - 21*h + 10 + g + 16*h - 8*h**2 = 0.
-2, 1
Suppose 23*v**4 - 6*v**5 + 280*v**3 - 1824*v**2 - 271*v**4 + 9*v**5 + v**5 + 556*v**4 = 0. What is v?
-76, -3, 0, 2
Let x(q) = -q**4 - 7*q**3 + 4*q**2 + q. Let r(t) be the third derivative of t**6/15 - t**5/15 + 65*t**2. Let p(v) = 3*r(v) + 4*x(v). Solve p(c) = 0.
-1, 0, 1
Let x(u) = -u**2 + u - 1. Let m be 1*((-4)/8 - 6/12). Let d(b) = 4*b**2 + 10*b + 3. Let l(i) = m*d(i) - 3*x(i). Let l(a) = 0. What is a?
-13, 0
Let i be 2 + (-2 + 3 - 0). Let 16*k**3 + 10*k**i - 16*k**2 - 24*k**3 + 24*k = 0. Calculate k.
0, 2, 6
Let o be 164/13 + 56 + (-4284)/63. What is p in -o + 0*p + 0*p**3 + 10/13*p**2 - 2/13*p**4 = 0?
-2, -1, 1, 2
Let l be ((225/(-80))/9)/((-2)/8728). Let u = l - 1357. Factor u + 12*p**2 - 18*p.
3*(4*p - 3)**2/4
Let r(y) be the second derivative of 16/5*y**4 + 3/5*y**3 + 0*y**2 + 2*y - 32/25*y**6 + 11/35*y**7 - 66 - 21/25*y**5. What is g in r(g) = 0?
-1, -1/11, 0, 1, 3
Suppose 0 = -0*k - 4*k + 12. Find v such that 10*v**4 - 1013 + 2026 - 12*v**k - 2*v**5 - 1013 = 0.
0, 2, 3
Let r be 6/(-108)*-138 + (-4)/6. Let m be r + (270/50)/(-1). Factor -4/5*j - m + 4/5*j**2.
4*(j - 2)*(j + 1)/5
Suppose 6*a + 3 - 27 = 0. Let m(u) be the second derivative of 0 - 3/28*u**a - 3/14*u**2 - 2/7*u**3 - 10*u. Let m(v) = 0. Calculate v.
-1, -1/3
Let q(g) = 2*g**3 - 24*g**2 + 92*g - 68. Let v(x) = -4*x**3 + 48*x**2 - 179*x + 135. Let s(h) = -7*q(h) - 4*v(h). Determine w so that s(w) = 0.
2, 8
Let a(h) = -6*h**4 + 34*h**3 + 64*h**2 + 4*h + 8. Let k(m) = -13*m**4 + 69*m**3 + 127*m**2 + 9*m + 18. Let r(o) = 9*a(o) - 4*k(o). Factor r(c).
-2*c**2*(c - 17)*(c + 2)
Suppose 0 = -o + 31 + 49. Let d be (3/20 - 1) + o/64. Factor 0 + d*h**3 - 6/5*h**2 - 8/5*h.
2*h*(h - 4)*(h + 1)/5
Let c(v) be the third derivative of -11*v**6/30 + 28*v**5 - 161*v**4/2 + 148*v**3/3 + v**2 + 6*v - 33. Factor c(o).
-4*(o - 37)*(o - 1)*(11*o - 2)
Find r such that -3*r**3 + 33*r**2 + 102 + 27*r**2 - 959*r + 800*r = 0.
1, 2, 17
Suppose 49*c + 27 = 2*f + 46*c, -2*f + 30 = -2*c. Factor -r + 7 - 18*r**2 - 6*r**2 - 17*r - 3*r**4 + 20 + f*r**3.
-3*(r - 3)**2*(r - 1)*(r + 1)
Suppose -15*j + 7*j = 32. Let y = j - -6. What is r in -90*r + 405 + r**2 + 6*r**2 - 6*r**y + 4*r**2 = 0?
9
What is k in 4*k**4 + 2/3*k**5 - 32/3*k**2 - 28/3 + 22*k - 20/3*k**3 = 0?
-7, -2, 1
Let y(c) = c**2 - 177*c - 1434. Let k(r) = r**2 - 532*r - 4304. Let d(w) = -3*k(w) + 8*y(w). Factor d(v).
5*(v + 12)*(v + 24)
Let c(d) be the third derivative of d**8/4032 + d**7/144 + d**5/10 - d**3/3 - 20*d**2 - 3*d. Let p(y) be the third derivative of c(y). Factor p(s).
5*s*(s + 7)
Suppose 6814 - 6702 = 56*v. Factor 7/6*a + 0 - a**v - 1/6*a**3.
-a*(a - 1)*(a + 7)/6
Let p(f) be the third derivative of 3*f**6/5 + 43*f**5/5 + 2449*f**4/48 + 961*f**3/6 + 6607*f**2. Factor p(g).
(g + 2)*(12*g + 31)**2/2
Let j(m) be the second derivative of m**4/24 + m**3/4 - 65*m**2/2 + 439*m. Factor j(l).
(l - 10)*(l + 13)/2
Let t(b) be the first derivative of -4*b**6/39 - 22*b**5/65 + 35*b**4/26 + 80*b**3/39 - 76*b**2/13 + 32*b/13 - 95. Find z, given that t(z) = 0.
-4, -2, 1/4, 1, 2
Suppose -4*k - 17*z + 26*z + 134 = 0, -3*k = -3*z - 48. What is w in 81/5 + 16/5*w**3 + 46/5*w**k + 1/5*w**4 - 144/5*w = 0?
-9, 1
Let k(q) = -104*q**2 - 9660*q - 1666350. Let i(t) = 29*t**2 + 2760*t + 476100. Let p(c) = -36*i(c) - 10*k(c). Factor p(m).
-4*(m + 345)**2
Let t(o) be the second derivative of 37/33*o**3 - 45 + 36/11*o**2 + 1/66*o**4 - o. Find k such that t(k) = 0.
-36, -1
Let g(r) be the first derivative of -19*r**6 - 232*r**5/5 - 2*r**4 + 76*r**3 + 61*r**2 + 4*r + 1891. Suppose g(x) = 0. Calculate x.
-1, -2/57, 1
Suppose -6*b = -b + 3*u + 5, 24 = -b + 4*u. Let q be 3/b*-2*96/72. What is t in -5/2*t**q - 1 + 7/2*t = 0?
2/5, 1
Let w(f) = -f**3 - 70*f**2 - 367*f + 1091. Let b be w(-64). Find h such that 8/3*h**2 + 0 + 0*h + 10/3*h**b + 2/3*h**4 = 0.
-4, -1, 0
Suppose -289/2*m**2 - 221/4*m**3 + 0*m + 8*m**4 - 1/4*m**5 + 0 = 0. Calculate m.
-2, 0, 17
Let h = -642043/165690 - -2793/526. Let d = 58/35 - h. Factor 10/9*o + 0 - 4/3*o**2 + d*o**3.
2*o*(o - 5)*(o - 1)/9
Let q be 2/(52/65) - 1/2. Solve -o - 88*o**q + 2*o**4 - 5*o**3 + 84*o**2 - 4*o**4 = 0 for o.
-1, -1/2, 0
Let r(k) = -9*k**4 + 365*k**3 - 218*k**2 - 768*k - 348. Let u(i) = 18*i**4 - 728*i**3 + 435*i**2 + 1537*i + 687. Let x(v) = -7*r(v) - 4*u(v). Factor x(q).
-(q - 39)*(q - 2)*(3*q + 2)**2
Let j(q) = 3*q**2 + 2*q - 3. Suppose 4*l - 10 = -3*v, 3*v = -3*l + 8 + 1. Let a be j(l). What is c in -1/6*c**4 + 0*c + 0 + 2/3*c**5 + 1/6*c**a - 2/3*c**3 = 0?
-1, 0, 1/4, 1
Let u(g) be the first derivative of 2*g**3/27 + 35*g**2/9 + 3. Factor u(p).
2*p*(p + 35)/9
Let l(p) = 5*p**2 + 15*p + 5. Let k be l(-3). Factor -k*m**5 - 18*m + 18*m + 2*m**5 + 6*m**4.
-3*m**4*(m - 2)
Factor 1006*n**4 - 33*n**2 - 25*n**2 - 2002*n**4 - 24 - 20*n**3 - 64*n + 994*n**4.
-2*(n + 1)**2*(n + 2)*(n + 6)
Let s = 5622/107 + -16652/321. Factor 10/3*n**2 + 8/3 - s*n**3 - 16/3*n.
-2*(n - 2)**2*(n - 1)/3
Let f(j) be the first derivative of 2/5*j**2 - 36 + 0*j + 2/15*j**3. Solve f(v) = 0 for v.
-2, 0
Let z be ((-10)/4 - -2)*(-1 - 63). Solve h**4 + 668*h**5 - 16*h - 664*h**5 - 5*h**3 + 7*h**4 - 7*h**3 - z*h**2 = 0.
-2, -1, 0, 2
Factor -36480*i - 17364*i**4 - 14121 - 9767 - 17666*i**2 + 5456 + 17362*i**4 + 380*i**3.
-2*(i - 96)**2*(i + 1)**2
Let l = 840922 + -2522762/3. Let 0 + 2/3*d**4 + 0*d**3 + l*d - 2*d**2 = 0. What is d?
-2, 0, 1
Let a be 0*(6/21)/(4/7). Suppose -3*k + 4*f = -4*k - 2, a = 3*k - 2*f - 50. Factor m**3 - 1 - 11*m**2 + 1 + k*m**2.
m**2*(m + 3)
Let h be 5/(-115)*23/(-5). Find r, given that 6/5*r**4 + h*r**5 + 0 - 36/5*r - 24/5*r**2 + r**3 = 0.
-3, -2, 0, 2
Let s(l) be the third derivative of 3*l**8/28 - 17*l**7/14 + 23*l**6/8 + 15*l**5/4 - 127*l**4/8 + 5*l**3 - 12*l**2 - 5. Determine k so that s(k) = 0.
-1, 1/12, 1, 2, 5
Suppose -7 + 27 = 10*g. Solve -36 - 1628*r - 6*r**g + 1668*r + 2*r**2 = 0.
1, 9
Let g(x) be the first derivative of 5*x**4/24 - 65*x**3/18 - 125*x**2/12 + 1625*x/6 - 169. Factor g(z).
5*(z - 13)*(z - 5)*(z + 5)/6
Let h(z) be the first derivative of -z**3/3 + 19*z**2/2 - 31*z - 16. Let q be h(17). Suppose -6*d**3 - 7*d**4 + 3*d**q + 4*d**4 = 0. Calculate d.
-1, 0
Let p(v) = -80*v**2 + 146*v - 329. Let l(s) = 37*s**2 - 72*s + 165. Let x(g) = 13*l(g) + 6*p(g). Factor x(q).
(q - 57)*(q - 3)
What is u in 70*u**2 - 858 - 981*u + 121*u + 72*u**2 - 144*u**2 = 0?
-429, -1
Let d(o) be the first derivative of -o**3/4 - 33*o**2/8 + 63*o/2 + 2923. Find r such that d(r) = 0.
-14, 3
Let q be 342/81 + (-4)/18. Suppose -q*o = -114 + 94. Solve -12*u**3 + 8*u + 25*u**2 - 3*u**3 + 17*u - 20 - 