 1)*(d + 1)
Let h(d) be the third derivative of 0*d**3 - 1/84*d**4 + 8*d**2 - 1/35*d**5 + 0*d - 3/140*d**6 + 0. Suppose h(s) = 0. Calculate s.
-1/3, 0
Let a = 21 - 19. Factor -18*l**3 - 4*l**5 + 28*l**a + 20*l**4 - 8*l - 3*l**3 - 8*l**3 - 7*l**3.
-4*l*(l - 2)*(l - 1)**3
Let o(x) = x**4 + 1. Let m be (36/21)/(0 + 2/7). Let i(l) = l**5 + 7*l**4 - l**3 - l**2 + 6. Let n(s) = m*o(s) - i(s). Find a such that n(a) = 0.
-1, 0, 1
Let k(f) = 35*f**3 - 55*f**2 - 40*f. Let l(i) = -2*i**3 - i**2 - i. Let j(o) = k(o) + 10*l(o). Factor j(r).
5*r*(r - 5)*(3*r + 2)
Suppose 47 - 59 = -3*h. Let d(x) be the second derivative of 1/252*x**7 + 1/12*x**2 - 5*x + 1/36*x**h - 1/12*x**3 + 1/60*x**5 - 1/60*x**6 + 0. Factor d(t).
(t - 1)**4*(t + 1)/6
Let c(t) be the third derivative of -3/70*t**7 + 1/56*t**8 + 1/20*t**5 + 0*t**4 + 0*t + 0*t**6 + 0*t**3 - 45*t**2 + 0. What is x in c(x) = 0?
-1/2, 0, 1
Let y(b) be the first derivative of b**3/7 + 93*b**2/14 - 96*b/7 - 167. Solve y(w) = 0 for w.
-32, 1
Let u = -11248 - -56243/5. Factor 9/5*a - u*a**2 + 12/5.
-3*(a - 4)*(a + 1)/5
Let j(c) be the first derivative of c**4/8 + 3*c**3/4 - 17*c**2/8 + 3*c/2 - 260. Solve j(f) = 0.
-6, 1/2, 1
Let i(j) be the third derivative of 0*j + 1/12*j**6 + 15*j**2 + 0 + 0*j**5 + 5/336*j**8 + 0*j**4 + 0*j**3 + 1/14*j**7. Solve i(r) = 0 for r.
-2, -1, 0
Solve -10/3*i**2 - 176/3*i + 2/3*i**3 - 416/3 = 0.
-4, 13
Let z(y) = -8*y**2 - 8*y - 5. Let c(g) = 44*g**2 + 44*g + 28. Let q(v) = 2*v + 11. Let u be q(-8). Let t(s) = u*c(s) - 28*z(s). Find r such that t(r) = 0.
-1, 0
Let s(v) be the second derivative of v**6/600 - v**5/75 + v**4/30 - 5*v**2 + 3*v. Let a(x) be the first derivative of s(x). Solve a(j) = 0.
0, 2
Suppose -17 = -12*a - 185. Let y(o) = -2*o - 24. Let k be y(a). Factor -27*v**k - 13/3*v**2 - 42*v**3 + 28/3*v - 4/3.
-(v + 1)**2*(9*v - 2)**2/3
Suppose -2*r + 8 = -2*k - 4*r, -5*k = -r + 50. Let j(z) = 2*z + 20. Let g be j(k). Factor -2/9*t**g + 0 + 4/9*t.
-2*t*(t - 2)/9
Let h(j) = -2*j**5 + 6*j**4 - 9*j**3 - 5*j**2 - 5*j. Let o(n) = -n**5 + 3*n**4 - 5*n**3 - 3*n**2 - 3*n. Let v(r) = 3*h(r) - 5*o(r). Let v(i) = 0. Calculate i.
0, 1, 2
Let z(f) be the first derivative of -10 + 0*f - 6*f**5 + 65/4*f**4 + 10*f**2 + 5/6*f**6 - 20*f**3. Factor z(q).
5*q*(q - 2)**2*(q - 1)**2
Let c(y) = -y**3 + 22*y**2 + 8. Let q be c(22). Find r, given that 3*r**3 - q*r**2 + r**3 + 4*r - 5*r - 15*r + 32 = 0.
-2, 2
Suppose -s = 0, -6 = -5*z + 2*z - 3*s. Factor -20*a + a**3 - 17*a**z + a**2 + 3*a**3.
4*a*(a - 5)*(a + 1)
Suppose 0 = -5*i + 20 + 25. Suppose -i*s**4 + 4*s**5 - s**5 + 15*s**4 + 3*s**3 = 0. What is s?
-1, 0
Let j = -2239/16 - -140. Let u(t) be the first derivative of 1/20*t**5 + 0*t - 1/12*t**3 - 1/8*t**2 + j*t**4 - 5. Factor u(w).
w*(w - 1)*(w + 1)**2/4
Let t(s) = 72*s + 2954. Let a be t(-41). Find p such that -2/3*p**a + 2/3*p**3 + 2/3*p**4 - 2/3*p + 0 = 0.
-1, 0, 1
Let v(z) be the first derivative of -z**7/2940 - z**6/630 + z**5/420 + z**4/42 - 11*z**3/3 - 14. Let k(a) be the third derivative of v(a). Factor k(c).
-2*(c - 1)*(c + 1)*(c + 2)/7
Let b = -1769 + 1769. Solve 2/9*u**5 + 0*u + b - 4/9*u**4 - 2/9*u**3 + 4/9*u**2 = 0.
-1, 0, 1, 2
Let c(f) be the third derivative of -f**6/72 + f**5/6 - 5*f**4/8 - 8*f**3/3 + 16*f**2. Let i(l) be the first derivative of c(l). Let i(k) = 0. What is k?
1, 3
Let l(q) be the third derivative of -2*q**3 - 10*q**2 + 0 - 7/2*q**4 - 69/20*q**5 - 7/4*q**6 - 5/14*q**7 + 0*q. Let l(m) = 0. Calculate m.
-1, -2/5
Let b(n) = 6*n - 76. Let d be b(13). Let y(k) be the third derivative of 4*k**d + 0 + 1/56*k**4 + 0*k + 1/21*k**3 + 1/420*k**5. Solve y(v) = 0.
-2, -1
Let b(x) = x**3 + 3*x**2 - x + 1. Let r(i) = -2*i**3 - 8*i**2 + 4*i - 4. Let n(f) = 21*b(f) + 6*r(f). Suppose n(p) = 0. What is p?
-1, 1/3
Factor -10*w**3 - 4*w + 8*w**3 + 16*w**2 - 5*w**3.
-w*(w - 2)*(7*w - 2)
Let h(i) be the second derivative of -2*i**6/15 + i**5 - 3*i**4 + 14*i**3/3 - 4*i**2 - 74*i. Factor h(t).
-4*(t - 2)*(t - 1)**3
What is s in -9*s**2 + s**4 - 8*s - 26*s**4 - 14*s**2 - 36*s**3 + 5*s**4 - 4*s**5 - 5*s**2 = 0?
-2, -1, 0
Suppose -2*k - 1080 = -8*k. Let u = 180 - k. Find v, given that -3/4*v**2 + u - 1/2*v + 1/2*v**3 + 3/4*v**4 = 0.
-1, -2/3, 0, 1
Let g be 52/4 - (-2 - -13). Solve -6*k**g + 4*k**3 + 9/4*k - 1/4 = 0 for k.
1/4, 1
Let v(x) be the first derivative of -3*x**4/4 - 5*x**3 + 33*x**2 - 48*x + 61. Determine c, given that v(c) = 0.
-8, 1, 2
Let h(k) be the second derivative of 3*k**5/20 - 27*k**4/4 - 57*k**3/2 - 87*k**2/2 + 812*k. Find t, given that h(t) = 0.
-1, 29
Let a be (5/(-20))/((-2)/420). Let k = a + -52. Factor 0 - 3/2*o + k*o**2.
o*(o - 3)/2
Suppose 0 = -10*q - 20*q + 90. Let p(t) be the second derivative of 5*t + 4*t**2 + 0 + 1/6*t**4 + 4/3*t**q. What is f in p(f) = 0?
-2
Let a(d) be the third derivative of -d**5/100 + d**3/10 - 160*d**2. Factor a(f).
-3*(f - 1)*(f + 1)/5
Let x(h) be the third derivative of 3*h**2 + 0*h**3 - 6 - 2/135*h**7 + 1/27*h**4 - 2/135*h**5 + 0*h - 19/540*h**6 - 1/504*h**8. Find f such that x(f) = 0.
-2, -1, 0, 1/3
Let -27823*y**3 - 35*y - 44*y**2 - 28 + 27831*y**3 - 45*y = 0. What is y?
-1, -1/2, 7
Let v(m) be the second derivative of 1/9*m**4 + 0 - 8/9*m**3 - 11*m + 2*m**2. Factor v(r).
4*(r - 3)*(r - 1)/3
Let s(b) be the second derivative of -b**4/18 - 5*b**3/12 + b**2/3 - 2*b + 380. Factor s(n).
-(n + 4)*(4*n - 1)/6
Suppose -6*l + 3*l = -9. Determine z so that -2*z**l + 5*z**3 + 3*z**4 + 0*z**4 + 0*z**4 = 0.
-1, 0
Suppose 3*i = 2*v + 104 - 363, -2*i + v = 173. Let c = 89 + i. Factor 0*f**c + 0 + 1/2*f**3 - 1/2*f.
f*(f - 1)*(f + 1)/2
Let m(v) = -3*v. Let j be m(-2). Suppose 0 = -5*a - 5*f - 5, -5*a - 1 = -5*f - j. Factor a*z**2 + 2 + 6*z**2 - 3 - 5*z**2.
(z - 1)*(z + 1)
Let l(a) = 1 + a**3 + a - 91*a**2 - a**4 + 91*a**2. Let o(g) = 3*g**4 - 8*g**3 - 4*g - 5. Let q(h) = 5*l(h) + o(h). Factor q(x).
-x*(x + 1)**2*(2*x - 1)
Let i(n) be the third derivative of -1/100*n**6 + 0 + 1/560*n**8 - 1/350*n**7 + 0*n - 5*n**2 + 1/40*n**4 - 1/10*n**3 + 1/50*n**5. Solve i(m) = 0 for m.
-1, 1
What is g in 12*g**4 - 8*g**3 + 18*g + 1 - 36*g**2 + 10*g**3 + 0*g**4 - 5 + 8 = 0?
-2, -1/6, 1
Let p(n) be the first derivative of 0*n**3 - 1/15*n**6 + 0*n + 8 - 1/5*n**2 + 1/5*n**4 + 0*n**5. Factor p(i).
-2*i*(i - 1)**2*(i + 1)**2/5
Let k(b) be the third derivative of b**8/1680 - b**6/60 - b**5/15 - 3*b**4/4 + 37*b**2. Let a(y) be the second derivative of k(y). Determine v so that a(v) = 0.
-1, 2
Suppose -4*y = 2*i - 14, 3*i = -0*i - 3. Let d(u) be the first derivative of -4*u - u**y + 2*u**2 + 4/3*u**3 - 2. Factor d(l).
-4*(l - 1)**2*(l + 1)
Let j(w) be the third derivative of w**7/72 - 5*w**6/24 + w**5/3 + w**4/8 - 5*w**2. Let h(f) be the second derivative of j(f). Let h(t) = 0. Calculate t.
2/7, 4
Suppose 5*m = -3*q + 465, 4*m - 379 = -0*q - q. Factor -m*g**2 - 8*g**2 - 8 - 172*g + 28*g**3 - 32.
4*(g - 5)*(g + 1)*(7*g + 2)
Solve 3/4*d + 0 - 3/8*d**4 - 3/4*d**3 + 3/8*d**2 = 0.
-2, -1, 0, 1
Suppose -3*o + 2*u = 7*u - 7, -3 = -3*o - 3*u. Let k be (-9)/((-3)/o) - (-20)/6. Find v such that 2/3 + k*v**2 + v = 0.
-2, -1
Let z = 43292 + -217168/5. Let q = z + 142. Suppose 0*t + 0 - 3/5*t**4 - q*t**3 + 1/5*t**2 = 0. What is t?
-1, 0, 1/3
Suppose -2*d + 147 - 139 = q, -2*d + 2*q = 4. Determine z so that 15/7*z - 3/7*z**d - 12/7 = 0.
1, 4
Let h(x) be the first derivative of -x**3/27 - 8*x**2/9 - 64*x/9 + 88. Suppose h(p) = 0. What is p?
-8
Factor 50/3*i + 1/3*i**5 - 7/3*i**4 - i**3 + 0 + 55/3*i**2.
i*(i - 5)**2*(i + 1)*(i + 2)/3
Let z(c) be the second derivative of 3/4*c**3 + 0 + 1/8*c**4 - 3*c - 3*c**2. Factor z(x).
3*(x - 1)*(x + 4)/2
Suppose 5*g - h = -30 + 74, 3*h = 3. Suppose 31*i - 6*i - 4*i**2 - 1 - i**2 - 10*i**3 - g = 0. What is i?
-2, 1/2, 1
Let g(a) = -a**3 + 12*a**2 + 3*a - 4. Let k be g(-4). Factor -58*d**3 + 30*d**3 + k*d - 200 - 42*d**2 + 30*d**3.
2*(d - 10)**2*(d - 1)
Factor 48/5*m + 0 + 4/5*m**2.
4*m*(m + 12)/5
Let g(x) be the third derivative of 13*x**5/15 - 25*x**4/6 - 4*x**3/3 - 23*x**2. Suppose g(d) = 0. What is d?
-1/13, 2
Factor 0 + 0*l - 2/3*l**2 + 2/3*l**4 + 0*l**3.
2*l**2*(l - 1)*(l + 1)/3
Solve 137180*s**2 - 8*s**5 - 25*s**4 + 215*s**4 + 4952198 - 7220*s**3 + 6*s**5 - 1303210*s = 0.
19
Let h = -3082/5 + 618. Suppose -w**2 - 4/5 - h*w - 1/5*w**3 = 0. Calcul