 d(l) be the third derivative of 6*l**2 + 0 + 0*l + 0*l**3 + 0*l**4 + 1/150*l**5. Find p, given that d(p) = 0.
0
Suppose -1867 = -4*p + 4*x + 14897, 5*x + 12563 = 3*p. Solve -4220*i**2 + p*i**2 - 27*i**3 + 0*i**4 - 3*i**4 = 0 for i.
-8, -1, 0
Let f(q) be the third derivative of 0 + 1/3*q**5 + 0*q**3 + 1/6*q**6 + 5/24*q**4 - 10*q**2 + 0*q. Factor f(x).
5*x*(2*x + 1)**2
Factor -12/7*v + 2/7*v**2 + 0.
2*v*(v - 6)/7
Let p(a) be the second derivative of 0 + 1/90*a**5 + 0*a**2 + 24*a + 1/54*a**4 + 0*a**3. Suppose p(x) = 0. Calculate x.
-1, 0
Suppose -132 = 12*g - 0. Let r(q) = 2*q**3 + 22*q**2 - 3*q - 31. Let f be r(g). Factor -2/3*d**2 - f*d - 4/3.
-2*(d + 1)*(d + 2)/3
Let g(p) be the first derivative of -5*p**3/12 - 7*p**2/8 + 3*p/2 + 106. Solve g(q) = 0.
-2, 3/5
Suppose -9450 = -13*i + 6*i. Determine t, given that -7 - i*t + 5*t**4 + 1350*t - 25*t**2 + 27 = 0.
-2, -1, 1, 2
Factor 59794*c + 35258*c - 1068*c**2 + 3*c**3 - 2819876 + c**3.
4*(c - 89)**3
Let o be 6/42*112/80. What is p in 0*p + 0 + 4/5*p**4 - 3/5*p**3 - o*p**2 = 0?
-1/4, 0, 1
Let c(o) be the first derivative of o**6/15 + 18*o**5/25 + 11*o**4/5 + 4*o**3/5 - 23*o**2/5 - 6*o + 822. Suppose c(w) = 0. Calculate w.
-5, -3, -1, 1
Let x be (-2)/(-6) + 42/9. Suppose 6 + 9 = x*q. Suppose 2/3*y**2 + 0 + 0*y - 2/3*y**q = 0. Calculate y.
0, 1
Let b be 53/13 + 23/(-299). Solve 4*z - 8/3 + 2/3*z**2 - 7/3*z**3 + 1/3*z**5 + 0*z**b = 0 for z.
-2, 1, 2
Let d(i) be the third derivative of i**5/120 - i**4/12 + i**3/4 + 4*i**2 + 10*i. Find z, given that d(z) = 0.
1, 3
Let m(n) = -118*n**2 - 496*n + 134. Let g(s) = -40*s**2 - 164*s + 44. Let h(c) = 17*g(c) - 6*m(c). Factor h(f).
4*(f + 7)*(7*f - 2)
Let a(g) = 4*g**2 - 3. Let w be a(-2). Suppose -3*y - 1 + w = 0. Find l such that -108 - 8*l**3 - 4*l**y + 108 = 0.
-2, 0
Let o be 12/(-32)*(-6)/81*2. Let v(l) be the third derivative of 1/90*l**6 + 0*l + 0 + 0*l**5 - o*l**3 - 7*l**2 - 1/24*l**4. Factor v(f).
(f - 1)*(2*f + 1)**2/3
Let u = 2725 + -8171/3. Factor 2/3*z**2 + u*z + 2/3.
2*(z + 1)**2/3
Let s(r) = -3*r**2 + 5*r + 4. Suppose 4*a = -10 + 18. Let j(z) = -4 - 14*z + 8*z**a + 3 - 6 - 4. Let o(i) = -4*j(i) - 11*s(i). Determine t, given that o(t) = 0.
-1, 0
Let f(n) = 3*n**2 + 107*n + 73. Let a be f(-35). Let o(x) be the second derivative of 0*x**2 - 2/3*x**a + 1/6*x**4 + 0 - 3*x. Suppose o(p) = 0. Calculate p.
0, 2
Let o(k) be the third derivative of 0 + 1/50*k**5 + 0*k + 1/20*k**4 - 2/5*k**3 + 32*k**2. Determine j so that o(j) = 0.
-2, 1
Suppose 12 = 4*q - 0*q. Let c be (176/(-55))/2 + 2. Find r such that 0 + c*r**2 - 2/5*r - 2/5*r**4 + 2/5*r**q = 0.
-1, 0, 1
Let m(f) be the third derivative of f**8/1848 - 13*f**6/660 + 8*f**5/165 + f**4/11 - 16*f**3/33 + f**2 - 115. Find j such that m(j) = 0.
-4, -1, 1, 2
Let v(f) be the third derivative of -f**7/6300 + f**5/300 + f**4/4 - 9*f**2. Let r(q) be the second derivative of v(q). Factor r(h).
-2*(h - 1)*(h + 1)/5
Let x(j) = 12*j - 31. Let y be x(3). Suppose 4*d = -3*t + 11, 0*t - y*t = -4*d + 3. What is g in 1/8 + 1/4*g**d - 3/8*g = 0?
1/2, 1
Let t(i) = -3*i**2 + 8*i - 8. Let m(k) = k**2 - 3*k + 3. Let n be (-34)/4 - (1 + (-3)/2). Let d(w) = n*m(w) - 3*t(w). Factor d(a).
a**2
Factor 2/11*r**3 + 0 - 18/11*r**2 + 0*r.
2*r**2*(r - 9)/11
Let s be (12/(-3))/(6*(-2)/4). Factor 16*t**2 + 0 - 32/3*t - 8*t**3 + s*t**4.
4*t*(t - 2)**3/3
Let x(m) be the second derivative of 0 + 3/80*m**5 + 5/16*m**4 + 0*m**2 + 1/2*m**3 - 3*m. What is l in x(l) = 0?
-4, -1, 0
Let x(j) be the first derivative of 3/2*j**2 + 0*j + 0*j**3 + 1/30*j**5 + 1/6*j**4 - 5. Let u(k) be the second derivative of x(k). Factor u(l).
2*l*(l + 2)
Let r = -3879 - -7761/2. Suppose -3/4*m**5 + 3/2*m**3 - 3/4 - 3/4*m - 3/4*m**4 + r*m**2 = 0. What is m?
-1, 1
Suppose 4*r - 5*g = 2, 0 = r - 5*g + 12 - 5. Suppose r*h = 6*h - 6. Let 143 - 3*y**h - 143 + 6*y = 0. Calculate y.
0, 2
Let r(a) = -6*a - 20. Let h be r(-5). Suppose 1 = -3*s + h. What is l in -2 + 7*l + 17/4*l**s - 3/4*l**4 - 17/2*l**2 = 0?
2/3, 1, 2
Let b(l) = l**3 - l**2 - 1. Let j(p) = -4*p**3 + 98*p**2 + 192*p + 78. Let w(i) = 14*b(i) + j(i). Factor w(c).
2*(c + 4)**2*(5*c + 2)
Let q(d) = -25*d**4 + 95*d**3 + 745*d**2 - 5145*d. Let m(k) = 17*k**4 - 63*k**3 - 497*k**2 + 3430*k. Let g(w) = 10*m(w) + 7*q(w). Factor g(s).
-5*s*(s - 7)**2*(s + 7)
Let z = -5110 + 5110. Factor g - 5/2*g**4 + 9/2*g**3 + 1/2*g**5 - 7/2*g**2 + z.
g*(g - 2)*(g - 1)**3/2
Suppose -u - 9*u + 20 = 0. Let o(b) be the first derivative of -1/2*b**3 + u - 1/2*b**2 - 1/8*b**4 + 0*b. Let o(p) = 0. What is p?
-2, -1, 0
Let v(r) be the first derivative of 3*r**4/16 + 3*r**3/4 + 9*r**2/8 + 3*r/4 - 127. Let v(u) = 0. Calculate u.
-1
Let g(y) = -3 + 5 - 8 - 3 - 2*y. Let v be g(-7). Factor v - 4*s + 5*s**2 + 8*s + 6*s.
5*(s + 1)**2
Let l(g) be the third derivative of -g**6/160 + 79*g**5/80 - 1599*g**4/32 + 1521*g**3/8 - 41*g**2 + 2*g. Suppose l(c) = 0. What is c?
1, 39
Let a(r) be the third derivative of -r**7/630 - r**6/45 + 5*r**4/8 - 6*r**2. Let x(q) be the second derivative of a(q). Factor x(k).
-4*k*(k + 4)
Let p(g) be the second derivative of -1/6*g**2 + 1/18*g**3 + 0 + 1/18*g**4 + 1/126*g**7 - 1/30*g**5 - 1/90*g**6 - 9*g. Factor p(x).
(x - 1)**3*(x + 1)**2/3
Let p(i) be the third derivative of -3/4*i**3 + 0 + 0*i - 1/8*i**5 - 7/16*i**4 - 1/80*i**6 - 24*i**2. Let p(d) = 0. Calculate d.
-3, -1
Let u(x) = -x**4 + 47*x**3 + 29*x**2 - 173*x - 15. Let k(v) = -v**4 + 71*v**3 + 44*v**2 - 260*v - 24. Let h(w) = -5*k(w) + 8*u(w). Factor h(a).
-3*a*(a - 7)*(a - 2)*(a + 2)
Let s(u) be the second derivative of u**4/42 + 2*u**3/21 - 15*u**2/7 - 204*u. Let s(g) = 0. Calculate g.
-5, 3
Let l = 24 + -22. Suppose -4*z = -2*s - 16, -s - 6 = s - l*z. Suppose -2 - 4*x**s + 8*x**2 - 2*x**2 = 0. What is x?
-1, 1
Suppose 36 = -0*r + 4*r - 4*d, 46 = 4*r + d. Let g = -10 + r. Solve -1 - g + 3 - q**2 = 0 for q.
-1, 1
Let q(u) be the third derivative of u**6/40 - 3*u**5/20 + u**4/4 + 9*u**2 - 6. Determine j so that q(j) = 0.
0, 1, 2
Let z = -12 - -19. Factor -2 - 12*h + 4*h**2 + 4 - h**2 + z*h**2.
2*(h - 1)*(5*h - 1)
Let l(c) be the second derivative of -c**7/189 + 2*c**6/135 + 8*c + 4. Factor l(j).
-2*j**4*(j - 2)/9
Let x(p) be the second derivative of 4/5*p**5 - 4/3*p**4 + 36*p**2 - 10*p**3 + 0 - 46*p. Suppose x(a) = 0. Calculate a.
-2, 3/2
Let h(r) = -6*r**3 - 30*r**2 - 140*r - 214. Let a(d) = -2*d**3 + 2*d + 1. Let q(g) = -2*a(g) + h(g). What is f in q(f) = 0?
-6, -3
Factor -19*s**3 + 798*s - 882 - 277/2*s**2 - 1/2*s**4.
-(s - 2)**2*(s + 21)**2/2
Let k(w) be the third derivative of w**6/240 - w**4/4 - 4*w**3/3 + w**2 - 5*w. Factor k(i).
(i - 4)*(i + 2)**2/2
Factor 0 - 2/7*i**5 + 4/7*i**3 + 0*i + 2/7*i**4 + 0*i**2.
-2*i**3*(i - 2)*(i + 1)/7
Factor -66/5*n**2 - 32/5*n**4 + 0 - 144/5*n**3 - 8/5*n.
-2*n*(n + 4)*(4*n + 1)**2/5
Let n = -2054 - -6166/3. Solve 8/3*g**2 + 8/3*g**3 - n - 4/3*g**5 - 4/3*g - 4/3*g**4 = 0.
-1, 1
Let 1221/2*i**2 + 18*i**4 + 0 + 363/2*i + 204*i**3 = 0. What is i?
-11/2, -1/3, 0
Determine u so that -5/4*u**5 + 0 - 57/4*u**3 - 9/2*u**2 + 0*u - 8*u**4 = 0.
-3, -2/5, 0
Let y(a) = -a**2 - 7*a - 9. Let q be y(-3). Factor -q*g**3 + 6 + 5*g**2 + g**2 + 10*g + g**3 - 4*g**2.
-2*(g - 3)*(g + 1)**2
Let t(b) be the third derivative of b**6/1140 + b**5/570 - b**4/57 - 4*b**3/57 + 52*b**2 - 1. Factor t(s).
2*(s - 2)*(s + 1)*(s + 2)/19
Let c(n) be the second derivative of n**4/144 + n**3/36 - n**2/8 - 94*n. Solve c(m) = 0 for m.
-3, 1
Factor 40401/8 + 1/8*c**2 + 201/4*c.
(c + 201)**2/8
Let b(r) be the first derivative of -3/2*r - 9 + 1/8*r**2 + 1/12*r**3. Solve b(d) = 0.
-3, 2
Let j(z) = 2*z**3 + 15*z**2 + 30*z + 17. Let t(d) = -d**3 - d**2 - d - 1. Let w(s) = -2*j(s) - 6*t(s). Determine b, given that w(b) = 0.
-1, 14
Determine n so that 3/5*n**3 - 229/5*n**2 + 76/5*n + 0 = 0.
0, 1/3, 76
Let m = -42 + 46. Factor 14*g - 100*g**2 + 9*g**4 - 17*g**4 + 26*g - 7*g**m + 70*g**3.
-5*g*(g - 2)**2*(3*g - 2)
Let n be (-11)/((-66)/160)*(-5)/(-75). Let n - 4/9*y**2 + 2/9*y**5 + 8/3*y + 0*y**4 - 14/9*y**3 = 0. What is y?
-2, -1, 2
Let w(b) be the first derivative of 3*b - 8. Let f(l) = l**2 + 4. Let j(m) = -3*f(m) + 4*w(m). Suppose j(c) = 0. What is c?
0
Let h(a) be the first derivative of a**6/120 + a**5/30 + a**4/24 + 8*a**2 - 7. Let q(k) be the second derivative o