ive of -h**7/105 + h**6/20 - h**4/3 + 13*h**2/2 + 3*h. Let r(s) be the first derivative of a(s). Find u, given that r(u) = 0.
-1, 0, 2
Factor 7*z - 13 - 1/4*z**2.
-(z - 26)*(z - 2)/4
Let 11*z**3 + 19*z**3 - 41*z**3 - 126 - 75*z + 12*z**3 - 8*z**2 = 0. What is z?
-3, 14
Let m(f) be the second derivative of 0 + 5/6*f**3 - 1/6*f**6 + 3/4*f**5 + 0*f**2 - 15*f - 5/4*f**4. Factor m(y).
-5*y*(y - 1)**3
Suppose 5*g**4 - 105*g**2 - g**4 + 52*g**3 - 11*g**2 + 60*g + 0*g**4 = 0. What is g?
-15, 0, 1
Let w(p) be the third derivative of 0*p + 1/12*p**4 + 12*p**2 + 0*p**3 + 1/210*p**7 + 1/20*p**5 + 0 + 1/112*p**8 - 3/40*p**6. Factor w(s).
s*(s - 1)**2*(s + 2)*(3*s + 1)
Let z = -119 - -306. Let h = z - 181. Factor 15 + 3/5*b**2 - h*b.
3*(b - 5)**2/5
Suppose 7*i + 32 = 15*i. Suppose 0*z + 4*w = 5*z - 19, -i*z - 3*w = -9. What is r in -18*r**z - 8/5*r + 10*r**4 + 0 + 48/5*r**2 = 0?
0, 2/5, 1
Factor -315*g**3 + 30*g**2 - 34*g - 2*g**4 + 12 + 620*g**3 - 311*g**3.
-2*(g - 1)**3*(g + 6)
Let q(h) = h**2 - h + 1. Let v(w) = -10*w**2 + 85*w + 230. Let k(x) = -15*q(x) - v(x). Factor k(b).
-5*(b + 7)**2
Let x(s) be the second derivative of 4/3*s**4 + 15*s + 0 + 22/3*s**3 - 6*s**2. Factor x(g).
4*(g + 3)*(4*g - 1)
Solve -152/5*a + 8/5 + 722/5*a**2 = 0 for a.
2/19
Let h(u) be the second derivative of u**5/20 - 121*u**4/12 - 245*u**3/6 - 123*u**2/2 - 42*u - 1. What is j in h(j) = 0?
-1, 123
Let y = 29 + -28. Solve -3*p**5 - 1 + y + 9*p**3 + 6*p**2 = 0 for p.
-1, 0, 2
Let o(m) be the third derivative of m**5/120 + 59*m**4/48 - 222*m**2. Factor o(w).
w*(w + 59)/2
Find l such that 24 + 1/6*l**3 - 70/3*l + 16/3*l**2 = 0.
-36, 2
Let w be 6/1*(-4)/(-36)*69. Let c = -44 + w. Factor 0 + 4/9*d - 2/9*d**c.
-2*d*(d - 2)/9
Let w(u) be the second derivative of 0*u**2 + 0 + 0*u**3 + 1/30*u**6 + 1/6*u**4 + 14*u - 3/20*u**5. Suppose w(m) = 0. What is m?
0, 1, 2
Let p(c) be the second derivative of 2*c**7/315 - c**5/45 + 7*c**2/2 - 10*c. Let t(r) be the first derivative of p(r). Suppose t(n) = 0. What is n?
-1, 0, 1
Suppose -16 - 52*l**2 - 170/3*l**3 - 50/9*l**4 + 632/9*l = 0. Calculate l.
-9, -2, 2/5
Let k(m) = 10*m**3 + m - 1. Let y be k(1). Let p be ((-9)/(-12))/(3/12). Find h, given that 0*h**2 - y*h**p - 5*h**2 + h**3 - 3*h - 4*h**2 - 3*h**4 = 0.
-1, 0
Let p(n) be the second derivative of -n**6/225 - n**5/30 + 7*n**4/30 - 23*n**3/45 + 8*n**2/15 - 118*n. Factor p(r).
-2*(r - 1)**3*(r + 8)/15
Let m(l) be the first derivative of 7 - 16/7*l + 4/21*l**3 + 0*l**2. Suppose m(c) = 0. Calculate c.
-2, 2
Let s(a) = -a**3 + 6*a**2 + 6*a - 9. Let m be s(6). Factor 6*k - 12*k - 5*k - 7*k + m*k**2 + 3.
3*(3*k - 1)**2
Let n = 129 + -47. Let l = n + -80. Factor 0 - 2/3*y**l + 1/3*y**5 + 0*y - 4/3*y**4 + 5/3*y**3.
y**2*(y - 2)*(y - 1)**2/3
Let l(y) be the first derivative of 15*y**5 + 305*y**4/4 + 395*y**3/3 + 175*y**2/2 + 10*y + 227. Determine h, given that l(h) = 0.
-2, -1, -1/15
Let c(l) = 28*l**3 + 25*l**2 - 9*l. Let p(a) = -6 + 2*a + 7 + 51*a**2 + 55*a**3 - 20*a. Let o(h) = 15*c(h) - 6*p(h). Factor o(y).
3*(y + 1)*(5*y - 2)*(6*y + 1)
Let s(c) be the third derivative of c**7/840 + c**6/48 + c**5/10 + c**4/4 - 2*c**2. Let n(k) be the second derivative of s(k). Factor n(l).
3*(l + 1)*(l + 4)
Let i(k) be the second derivative of -k**5/10 + 7*k**4/3 - 64*k**3/3 + 96*k**2 - 2*k + 35. Find v such that i(v) = 0.
4, 6
Suppose 0 = 2*u + 4*h + 200 - 188, 4*u + 2*h = 0. Find q such that 2/5 - 3/5*q - 2/5*q**u = 0.
-2, 1/2
Let f(u) be the first derivative of -16 + 10/11*u**4 + 8/33*u**3 + 0*u**2 + 10/11*u**5 + 0*u. Factor f(s).
2*s**2*(5*s + 2)**2/11
Suppose 4*l - q + 7 = 11, -4*l = q - 12. Let n(p) = -p**3 + p**2 + p + 4. Let o be n(0). Determine j so that l*j**2 + 2*j**2 + 1 - 6*j**2 + j**o = 0.
-1, 1
Let t = 1249/276 - -13/92. Let n(j) be the first derivative of -t*j**3 + 5/2*j**4 - 5 + 2*j**2 + 0*j. Factor n(p).
2*p*(p - 1)*(5*p - 2)
Suppose -8 + 0 = -2*f. Suppose 11 - 3 = f*v. Determine x so that 2*x**4 - 1/2*x - 3*x**3 + v*x**2 - 1/2*x**5 + 0 = 0.
0, 1
Let h(d) be the second derivative of d**6/72 - 5*d**5/12 + 125*d**4/24 + 5*d**3/3 + 6*d. Let n(r) be the second derivative of h(r). Solve n(o) = 0 for o.
5
Let s = 49/276 - 1/92. Let q(l) be the first derivative of 0*l - 5 - 1/3*l**3 + 1/4*l**4 + 0*l**2 + 1/5*l**5 - s*l**6. Factor q(b).
-b**2*(b - 1)**2*(b + 1)
Suppose 14*v - 57 = 503. Factor 24 + 29*f + 4*f**2 + v*f - 49*f.
4*(f + 2)*(f + 3)
Let o = 353 - 58. Let a = o - 291. Determine f so that 0*f - 3/4*f**5 + 3/4*f**3 + 0*f**2 + 0*f**a + 0 = 0.
-1, 0, 1
Let t(a) = -a**3 + 136*a**2 - 268*a + 2. Let r be t(134). Find s, given that 9*s + 3/2*s**3 + 15/2*s**r + 0 = 0.
-3, -2, 0
Let h(v) be the second derivative of v**4/9 - 6*v**2 + 37*v - 1. Suppose h(a) = 0. What is a?
-3, 3
Find i, given that 6*i**3 - 3*i**5 - 3*i - 3/2*i**2 + 3/4 + 3/4*i**4 = 0.
-1, 1/4, 1
Find x such that -32*x**2 - 8*x**5 + 11*x**5 + 15*x - 8*x**3 + 12*x**4 + 20*x**2 - 10*x**3 = 0.
-5, -1, 0, 1
Suppose -4*r = 10*b - 9*b - 15, 0 = b - 3*r + 6. Let s(g) be the first derivative of -27*g + 8*g**b + 9/2*g**4 + 3/5*g**5 + 5 - 9*g**2. Factor s(u).
3*(u - 1)*(u + 1)*(u + 3)**2
Let h(u) be the second derivative of 11*u**9/75600 - u**8/16800 + u**4/2 + 3*u**2/2 + 9*u. Let k(a) be the third derivative of h(a). Factor k(c).
c**3*(11*c - 2)/5
Let w(l) be the first derivative of -l**4 + 8*l**3/3 + 10*l**2 - 24*l - 53. Find b such that w(b) = 0.
-2, 1, 3
Let 0 - 1/6*i**4 + 0*i**2 - 1/2*i**3 + 2/3*i = 0. Calculate i.
-2, 0, 1
Suppose 0 = -96*j + 97*j. Determine i so that 5/2*i - 5/2*i**3 + j*i**2 + 5/4 - 5/4*i**4 = 0.
-1, 1
Let c = -6 + 12. Solve 0 - c*i + 3/2*i**2 = 0.
0, 4
Let u(o) be the third derivative of o**6/60 - 7*o**5/2 + 901*o**4/4 + 2809*o**3/3 + 2*o**2 + 128. Factor u(l).
2*(l - 53)**2*(l + 1)
Suppose 97*d = 131*d. Factor 0*o - 1/2*o**2 + d - 1/2*o**3.
-o**2*(o + 1)/2
Factor -6 + 6*x**2 + 8*x**2 - 15*x**2 + 4*x**3 + 0*x**2 - 11*x.
(x - 2)*(x + 1)*(4*x + 3)
Let l(r) be the second derivative of r**9/3024 - r**8/1344 - r**7/252 + 17*r**4/12 + 30*r. Let i(x) be the third derivative of l(x). Let i(m) = 0. Calculate m.
-1, 0, 2
Let q = 76 - 76. Let m(r) be the second derivative of q - 1/24*r**3 + r + 1/80*r**5 + 0*r**2 - 1/120*r**6 + 1/48*r**4. Factor m(s).
-s*(s - 1)**2*(s + 1)/4
Let q(a) = 3*a. Let t be q(-7). Let r be ((-2)/(-5))/(t/(-35)). Factor -1/2 - r*y - 1/6*y**2.
-(y + 1)*(y + 3)/6
Suppose 2*r + 50 = 3*c, -3*c - r = -c - 31. Let -c*u + 37*u + 20*u**2 - 23*u = 0. Calculate u.
0, 1/10
Let m(w) be the second derivative of w**6/210 - w**5/70 - w**4/28 + 2*w**3/21 + 2*w**2/7 + 32*w - 2. Factor m(z).
(z - 2)**2*(z + 1)**2/7
Factor -2/3*n**3 + 0 + 4/9*n + 2/9*n**2.
-2*n*(n - 1)*(3*n + 2)/9
Suppose 6*t - 3*t - 5 = a, 0 = 3*t + 4*a + 20. Let -8*m + 2*m**2 + 0*m**2 + t*m + 0*m**2 = 0. Calculate m.
0, 4
Let j = 14/23 + 270/161. Let s = 1307/56 + -141/8. Find r such that j*r - s*r**2 + 0 + 36/7*r**3 - 2*r**4 + 2/7*r**5 = 0.
0, 1, 2
Let x be 1*-269 - (3 + -2). Let l be 2 + 1 - x/3. Factor 19*j**3 + 12*j**4 + 4*j**2 - l*j + 89*j + j**3.
4*j*(j + 1)**2*(3*j - 1)
Let a(r) be the first derivative of 10/3*r + 11/3*r**2 + 14/9*r**3 + 1/6*r**4 - 16. Solve a(d) = 0 for d.
-5, -1
Let y(i) be the second derivative of -3*i**5/20 + 137*i**4/4 - 4623*i**3/2 - 14283*i**2/2 + 236*i - 1. Factor y(f).
-3*(f - 69)**2*(f + 1)
Let j(d) be the second derivative of d**4/3 - 14*d**3/3 - 36*d**2 - d - 91. Let j(u) = 0. What is u?
-2, 9
Let w be 1*5*(-10)/(-50). Suppose -6*u - w = -19. Determine x so that u*x - 3/2*x**2 - 3/2 = 0.
1
Let q(h) be the second derivative of -h**6/15 + 24*h**5/5 - 96*h**4 - 509*h. Determine g, given that q(g) = 0.
0, 24
Suppose 6*n = n + 210. Let i = 42 - n. Solve i*p**3 - 1/8*p**5 + 0 + 0*p**2 + 0*p + 1/8*p**4 = 0.
0, 1
Let a = -2/1677 - -569/8385. Let v(b) be the third derivative of -4/3*b**4 + a*b**5 + 32/3*b**3 + 0*b - 4*b**2 + 0. Find m such that v(m) = 0.
4
Let l = -813 + 1629/2. Let o(q) be the first derivative of 3*q - 9 + 1/4*q**3 + l*q**2. Factor o(y).
3*(y + 2)**2/4
Let q(f) be the third derivative of f**8/6720 - f**7/840 - f**6/80 + 7*f**5/60 + 2*f**2. Let u(p) be the third derivative of q(p). What is c in u(c) = 0?
-1, 3
Let x be ((-8)/(-24))/((-2)/(-18)). Factor -15*t**2 + 17*t + 8*t - t - 5 - 7 + x*t**3.
3*(t - 2)**2*(t - 