- 19*c**3.
4*c**2*(c + 1)**3
Let s(k) be the first derivative of -1024*k**3 + 32*k**2 - k/3 + 168. Suppose s(x) = 0. What is x?
1/96
Suppose -3*h = -2*h + 2. Let p be 168/18*(-3)/h. Suppose -p*m**2 + 2*m**2 + 6*m - 3*m**2 = 0. What is m?
0, 2/5
Factor -1936 + 125*j**2 - 129*j**2 + 21*j + 155*j.
-4*(j - 22)**2
Determine q, given that 74*q - 2*q**3 + 6*q**3 + 45*q**2 + 120 - 9*q**3 + 96*q = 0.
-2, -1, 12
Let r = 24/1301 + 31056/9107. Factor -r*i - 12/7*i**2 - 16/7 - 2/7*i**3.
-2*(i + 2)**3/7
Let p(j) = -j**3 + 4*j**2 - j - 2. Let n be p(3). Let q be (n - 2) + 4/2. Determine t, given that t**q - 2*t**4 - 3*t**5 + 0*t**4 - 2*t**4 = 0.
-1, 0
Let g(y) be the first derivative of 0*y + 3/2*y**4 + 4/5*y**5 - 1/3*y**6 + 8 - 8/3*y**3 - 4*y**2. Solve g(s) = 0 for s.
-1, 0, 2
Let v = 26 + -24. Suppose -11 = -3*g - 0*h + h, 5*g - 33 = -v*h. Factor -3*w**3 + 0*w**2 + g*w**2 + 2*w**2 - w**2.
-3*w**2*(w - 2)
Let s(g) be the second derivative of -11*g - 1/4*g**2 - 1/12*g**4 + 1/80*g**5 + 5/24*g**3 + 0. Solve s(n) = 0 for n.
1, 2
Determine p, given that 276*p + 7*p**2 - p**2 + 4677 - 2*p**2 + 1671 - p**2 = 0.
-46
Let o(v) be the first derivative of v**6/18 - v**5/3 + 40*v**3/9 - 40*v**2/3 + 16*v + 95. Factor o(d).
(d - 2)**4*(d + 3)/3
Let j(n) be the third derivative of n**9/13608 - n**8/3780 + n**6/810 - n**5/540 - n**3/3 + 14*n**2. Let p(c) be the first derivative of j(c). Factor p(w).
2*w*(w - 1)**3*(w + 1)/9
Let v(p) be the first derivative of -4 - 5/3*p**3 - 5/2*p**4 - p**5 + 0*p**2 + 0*p. Find h such that v(h) = 0.
-1, 0
Suppose 40 = w - 6*w. Let z = 12 + w. Factor -4*f + 11*f**3 + 2*f**z + 1 - 3 - 7*f**3.
2*(f - 1)*(f + 1)**3
Let h(k) = -k**2 + 16*k + 82. Let c be h(-4). Let f(a) be the first derivative of -16*a**c - 7*a**4 + 76/3*a**3 - 16*a + 4. Find m such that f(m) = 0.
-2/7, 1, 2
Let c(h) be the second derivative of -11*h + 0 + 0*h**2 + 7/96*h**4 - 1/24*h**3. Let c(o) = 0. Calculate o.
0, 2/7
Suppose 34*r = 135*r - 505. Factor -1/2*b**3 + 0*b**2 + 0 - 1/2*b**r + 0*b + b**4.
-b**3*(b - 1)**2/2
Let q be ((-70)/42)/((-45)/54). Solve -30/7*m**4 + 2*m**q - 18/7*m**5 + 0 + 4/7*m - 2/7*m**3 = 0 for m.
-1, -1/3, 0, 2/3
Factor 5/2*h**4 + 0*h + 0 - 15*h**3 + 25/2*h**2.
5*h**2*(h - 5)*(h - 1)/2
Factor -1/7*c**4 + 0 - 4/7*c**3 + 16/7*c**2 + 64/7*c.
-c*(c - 4)*(c + 4)**2/7
Suppose -8*x - 42 + 58 = 0. Let u(g) be the second derivative of 7*g + 0*g**4 - g**3 + 3/2*g**x - 1/10*g**6 + 3/10*g**5 + 0. Factor u(l).
-3*(l - 1)**3*(l + 1)
Suppose 14*d - 11*d = -6. Let v be 1*(d - (-3 + 1)). Factor v - 2/5*b**2 - 3/5*b + 1/5*b**3.
b*(b - 3)*(b + 1)/5
Find y, given that -8 - 2/5*y**4 + 4*y**3 + 88/5*y - 66/5*y**2 = 0.
1, 2, 5
Let u(w) = -w**2 + 414*w - 409. Let o(k) = -5*k**2 + 1655*k - 1635. Let c(h) = -4*o(h) + 15*u(h). Solve c(p) = 0.
1, 81
Let y(r) be the first derivative of r**4/4 - 10*r**3 - 15*r**2 - 25*r + 56. Let d be y(31). Solve -26/9*q + 14/9*q**4 + d*q**2 + 4/9 - 46/9*q**3 = 0.
2/7, 1
Suppose 4 = 2*u, -u + 734 - 728 = 2*f. Suppose -3/7*z**4 + 0*z**f + 3/7*z**5 + 0*z - 6/7*z**3 + 0 = 0. What is z?
-1, 0, 2
Let y(p) = -152*p - 299. Let s be y(-2). Find w, given that s*w + 5/2 + 5/2*w**2 = 0.
-1
Let t(u) be the second derivative of u**5/80 + 5*u**4/48 + u**3/6 - 7*u - 1. Factor t(v).
v*(v + 1)*(v + 4)/4
Let q(g) be the first derivative of -g**6/21 + 2*g**5/35 + g**4/14 - 2*g**3/21 - 389. Determine z, given that q(z) = 0.
-1, 0, 1
Let q(j) be the third derivative of -j**7/105 + 13*j**6/60 - 17*j**5/10 + 67*j**4/12 - 28*j**3/3 - 115*j**2. Factor q(h).
-2*(h - 7)*(h - 4)*(h - 1)**2
Let j be (-14)/77 - (-46)/11. Let i be 280/(-196) + ((-144)/(-28))/3. Determine q, given that 0*q**3 - i*q**5 + 2/7*q - 4/7*q**2 + 4/7*q**j + 0 = 0.
-1, 0, 1
Let k(c) be the third derivative of c**5/20 - 11*c**4/24 + 17*c**3/6 - 2*c**2 + 14*c. Let h be k(2). Solve -3/2*s**2 - 4 + h*s = 0.
2/3, 4
Let t(z) be the second derivative of -z**6/75 + 9*z**5/50 - 3*z**4/5 - 218*z. Let t(h) = 0. Calculate h.
0, 3, 6
Let n be 35/14 + 1/2. Let x be (-2)/6 - (-21)/9. Solve 6*j**x + 3*j**n - 2 - 3 - 3 - j**3 = 0.
-2, 1
Suppose -10 = -3*g + 4*s, 5*g = -3*s + 7*s + 14. Factor 4*x**3 - x**2 + 3*x**2 + 4*x**2 + x**g - 2*x.
x*(x + 2)*(4*x - 1)
Let b = -16 + 27. Let l be b + -1 - 24/(-8). Determine c, given that -l*c**2 + 24*c**3 + 4*c + c**3 - 7*c**2 = 0.
0, 2/5
Let l(w) be the third derivative of w**8/504 + w**7/945 - w**6/30 + w**5/15 - w**4/108 - w**3/9 - 64*w**2. Find j such that l(j) = 0.
-3, -1/3, 1
Let x(n) be the second derivative of -19/14*n**4 - 13/35*n**6 + 67/70*n**5 + 0 + 8/7*n**3 - 13*n + 3/49*n**7 - 4/7*n**2. Factor x(p).
2*(p - 1)**3*(3*p - 2)**2/7
Let f(d) be the third derivative of -d**7/70 - d**6/40 + d**5/5 + d**4/2 - 2*d**2 + 1. Solve f(m) = 0 for m.
-2, -1, 0, 2
Let j(u) be the second derivative of 0 + 0*u**4 + 1/45*u**6 - 1/30*u**5 - 11*u + 0*u**2 + 0*u**3. What is g in j(g) = 0?
0, 1
Let p(f) = 4*f**3 + 13*f**2 + 5*f. Let j(a) = 3*a**3 + 12*a**2 + 4*a. Suppose 4*m = 3*d, -5*d - 4*m + 28 = -d. Let u(h) = d*p(h) - 5*j(h). Factor u(t).
t**2*(t - 8)
Let x(z) be the third derivative of z**7/5040 + z**6/180 + z**5/20 - 17*z**3/3 + 17*z**2. Let t(g) be the first derivative of x(g). Factor t(q).
q*(q + 6)**2/6
Solve -j + 0*j**2 - 20*j**2 - 22*j**2 - j + 3*j**3 - j + 42 = 0.
-1, 1, 14
Let p(w) be the first derivative of 0*w**3 + 1/15*w**6 + 0*w + 2/25*w**5 + 0*w**2 + 0*w**4 - 10. Factor p(m).
2*m**4*(m + 1)/5
Let f = -40 - -44. Suppose -3*x = f*r - 8*x - 11, 15 = 5*r - 5*x. Factor -1/3*y**r + 0*y**3 + 1/6*y**5 + 1/3*y**2 + 0 - 1/6*y.
y*(y - 1)**3*(y + 1)/6
Suppose -m = m - 2. Let l be m/((-5)/(-2) - 2). Let 2*g**l + g**3 - g**3 + 3*g**3 - 5*g**3 = 0. Calculate g.
0, 1
Let a(h) be the third derivative of h**7/1365 + h**6/390 - h**4/78 - h**3/39 + 2*h**2 + 2. Find g such that a(g) = 0.
-1, 1
Let f(h) be the third derivative of h**6/300 + h**5/75 + h**4/60 - 14*h**2 + h. Let f(z) = 0. Calculate z.
-1, 0
Let l = 15514 - 15511. Let -4/7 - 165/7*i**2 - 121/7*i**l - 48/7*i = 0. Calculate i.
-1, -2/11
Let o(j) be the second derivative of j**4/18 + 2*j**3/3 - 16*j**2/3 - 4*j + 14. Solve o(q) = 0.
-8, 2
Let g = 42 + -24. Suppose 0 = 3*h + 12 - g. Factor v**2 + 0*v**h + 3*v - 6 + 2*v**2.
3*(v - 1)*(v + 2)
Factor -3 + 6 + 12 - 25*w**2 + 223*w + 3.
-(w - 9)*(25*w + 2)
Let i(v) = 5*v**2 + 29*v + 128. Let j(x) = 11*x**2 + 57*x + 256. Let s(o) = -14*i(o) + 6*j(o). Find d such that s(d) = 0.
-8
Let j(t) be the second derivative of -t**6/120 + 21*t**5/80 - 19*t**4/16 + 55*t**3/24 - 9*t**2/4 + 2*t + 16. Factor j(g).
-(g - 18)*(g - 1)**3/4
Let i(v) = -v**3 + v**2 + v - 1. Let d be i(2). Let p be d/(6/16*-2). Factor -m**3 - m**4 + 7 - 7 - 2*m**3 + p*m.
-m*(m - 1)*(m + 2)**2
Let g(a) be the first derivative of -2*a**3/11 - 18*a**2/11 + 42*a/11 + 316. Let g(c) = 0. What is c?
-7, 1
Let r be 4/14 - (-4)/((-56)/(-486)). Let 91*g + r*g**2 + 435 + 59*g - 395 = 0. Calculate g.
-4, -2/7
Let g(h) be the first derivative of -9*h**5/5 - 7*h**4/4 + 11*h**3/3 + 7*h**2/2 - 2*h - 237. Suppose g(x) = 0. What is x?
-1, 2/9, 1
Let s(f) be the second derivative of f**6/900 - f**4/60 - 5*f**3/2 + 16*f. Let z(a) be the second derivative of s(a). What is h in z(h) = 0?
-1, 1
Suppose -3*d = -u, u - 7 = -0*u - 4*d. Suppose -155*m**u - 6*m**2 - 2*m**2 + 156*m**3 + 16*m = 0. What is m?
0, 4
Suppose -s = 2*g - 5, 5*g - 10 = -2*s + 3. Suppose 63 = j - 3*d, -g*d - 2*d = 2*j - 137. Let 2*u**3 + 33 + 8 - 12*u + 13 + 18*u**2 + j*u = 0. Calculate u.
-3
Factor 0*n**3 + 3*n**4 - 178*n**5 - 21*n**3 - 39*n**2 - 18*n + 181*n**5.
3*n*(n - 3)*(n + 1)**2*(n + 2)
Let o(d) be the first derivative of 14*d**3/33 + 30*d**2/11 + 16*d/11 - 181. Determine h, given that o(h) = 0.
-4, -2/7
Let s(x) = -x**2 + 2*x + 3. Let t(m) = -m + 1. Let h(c) = 3*c - 1. Let u(r) = -h(r) - 2*t(r). Let n(z) = -s(z) - 5*u(z). Factor n(g).
(g + 1)*(g + 2)
Factor 39*u**4 - 13*u**2 + 12*u - 19*u**4 - u**3 - 11*u**3 - 7*u**2.
4*u*(u - 1)*(u + 1)*(5*u - 3)
Let m(y) = -108*y**3 - 944*y**2 - 4596*y - 3664. Let a(q) = -10*q**3 - 86*q**2 - 418*q - 333. Let k(i) = 32*a(i) - 3*m(i). Factor k(b).
4*(b + 1)*(b + 7)*(b + 12)
Suppose 0 = -20*l - 11*l. Let f(x) be the second derivative of -2/25*x**5 + l*x**4 + 2/25*x**6 + 2/21*x**7 + 0*x**3 + 0 + 2*x + 0*x**2. Solve f(j) = 0 for j.
-1, 0, 2/5