*3. Suppose a(p) = 0. Calculate p.
-1, 1
Let d(x) be the second derivative of -24*x - 1/14*x**7 + 1/4*x**4 + 3/20*x**5 - 1/10*x**6 + 0*x**3 + 0 + 0*x**2. Suppose d(l) = 0. Calculate l.
-1, 0, 1
Let k(z) = z**3 - 2*z**2 + z + 1. Let p(a) = -12*a**3 - 63*a**2 + 162*a - 98. Let x(i) = 44*k(i) + 4*p(i). Factor x(q).
-4*(q - 1)**2*(q + 87)
Let y be (-3)/18 + (-64570)/(-60). Let r = y + -13964/13. Suppose 2/13 - r*q + 72/13*q**2 = 0. What is q?
1/6
Let x = -25 - -28. Suppose -6*f**2 + 2*f**x + 15*f - 5*f**3 - 18*f = 0. What is f?
-1, 0
Let i(k) be the third derivative of 4*k**2 + 9 + 0*k**3 + 0*k - 1/84*k**4 + 1/210*k**5. Find p, given that i(p) = 0.
0, 1
Let n(q) be the third derivative of q**8/40320 - q**7/840 + 11*q**6/1440 + 7*q**5/20 - 7*q**2. Let s(j) be the third derivative of n(j). Factor s(t).
(t - 11)*(t - 1)/2
Let l(k) be the second derivative of -2/3*k**3 + 0*k**2 + 13*k - 6/5*k**5 - 2/21*k**7 + 4/3*k**4 + 8/15*k**6 + 0. Factor l(r).
-4*r*(r - 1)**4
Let r = -703 + 707. Let i(d) be the second derivative of 8*d + 0 - 1/5*d**5 + 1/6*d**r + 1/15*d**6 + 0*d**2 + 0*d**3. Factor i(f).
2*f**2*(f - 1)**2
Determine h, given that 0 - 5/4*h**2 + 3/2*h**3 - 1/4*h = 0.
-1/6, 0, 1
Let z be ((36/126)/(24/21))/((-1)/(-12)). Solve 2/5*l**2 + 1/5*l**4 + 0*l + 3/5*l**z + 0 = 0.
-2, -1, 0
Let z(h) be the first derivative of -4*h**3/3 + 6*h**2 + 40*h - 49. Factor z(t).
-4*(t - 5)*(t + 2)
Let u(t) be the first derivative of 3*t**5/25 - 23*t**4/20 + 11*t**3/3 - 33*t**2/10 - 18*t/5 + 364. Factor u(r).
(r - 3)**2*(r - 2)*(3*r + 1)/5
Let i(q) be the third derivative of 5*q**8/1344 + q**7/168 - q**6/48 - q**5/24 + 5*q**4/96 + 5*q**3/24 - 26*q**2 + q. Determine s, given that i(s) = 0.
-1, 1
Let n(f) be the third derivative of -f**10/37800 + f**9/4320 - f**8/1260 + f**7/840 + f**5/4 - 32*f**2. Let a(g) be the third derivative of n(g). Factor a(m).
-2*m*(m - 1)**2*(2*m - 3)
Let u(j) = 4*j**4 + 12*j**3 - 14*j**2 - 44*j - 24. Let l(v) = -10*v + 10*v + 129*v**2 - 130*v**2. Let p(m) = 2*l(m) - u(m). Suppose p(o) = 0. What is o?
-3, -1, 2
Suppose -25*a - 40 = -35*a. Let s(n) be the second derivative of -1/16*n**a + 0 - 7/24*n**3 - 1/4*n**2 + 2*n. Determine x so that s(x) = 0.
-2, -1/3
Let b be ((-1)/3)/(9/(-81)). Solve b*y**3 + 2*y - 10*y + 8*y = 0 for y.
0
Let j be (-1)/(-22)*-3*(119/21 - 7). Factor -20/11*d + 0 + j*d**2.
2*d*(d - 10)/11
Let t(c) be the first derivative of -6*c**7/7 + 6*c**6/5 - 2*c**5/5 - 34*c - 35. Let a(n) be the first derivative of t(n). What is v in a(v) = 0?
0, 1/3, 2/3
Let y be 4/(-28) + 72/112 + 0. Let t(z) be the third derivative of 13/60*z**5 - 3*z**2 - 1/20*z**6 + 1/210*z**7 + 2/3*z**3 + 0 + 0*z - y*z**4. Factor t(g).
(g - 2)**2*(g - 1)**2
Find k, given that -6*k**3 + 12*k**5 - 5*k**5 - 4*k - 10*k**2 + 0*k**4 - 5*k**5 + 2*k**4 = 0.
-1, 0, 2
Let s be ((-36)/(-8))/((-3)/12). Let b(u) = u**3 + 19*u**2 + 17*u - 16. Let a be b(s). Let 6/7*d + 2/7*d**a + 0 = 0. Calculate d.
-3, 0
Let o(h) be the second derivative of h**7/147 + 8*h**6/35 - h**5/35 - 8*h**4/7 + h**3/21 + 24*h**2/7 + 47*h + 1. Determine y so that o(y) = 0.
-24, -1, 1
Find i such that -13*i + 3*i - 1420*i**2 + 1415*i**2 = 0.
-2, 0
Factor 0 + 24/7*w**4 + 4*w**2 + 54/7*w**3 + 0*w - 2/7*w**5.
-2*w**2*(w - 14)*(w + 1)**2/7
Let c(b) be the first derivative of 3/10*b**5 + 5/2*b**2 + 0*b - b**4 + 4/3*b**3 - 4. Let v(j) be the second derivative of c(j). Determine p so that v(p) = 0.
2/3
Let o be (0 - -1) + 7/(-14). Let r = -227 + 229. Factor -1/4*l**r + o*l + 0.
-l*(l - 2)/4
Let d = 99 - 96. Let h(v) = v**2 - 5*v - 3. Let a be h(6). Let -6*s + 4 - 1/2*s**a + d*s**2 = 0. What is s?
2
Factor -30/11*o**2 + 30/11 - 2/11*o**3 + 2/11*o.
-2*(o - 1)*(o + 1)*(o + 15)/11
Let f(p) be the second derivative of p**4/18 - 13*p**3/3 + 74*p**2/3 + 19*p - 1. Factor f(k).
2*(k - 37)*(k - 2)/3
Let b = -10645/8 - -1331. Factor b*d**2 - 9/8 - 3/4*d.
3*(d - 3)*(d + 1)/8
Let k be 40/48*(-96)/(-30). Factor -4/3*n**2 + 2/3*n**5 - 4/3 - 10/3*n + k*n**3 + 8/3*n**4.
2*(n - 1)*(n + 1)**3*(n + 2)/3
Suppose 4*j + 30 = 5*p + 10, 20 = -5*j + 5*p. Let u(k) = -k**3 + 2*k**2 + 2*k + 3. Let t be u(j). Factor 1/2*y**t + 1 + 5/2*y + 2*y**2.
(y + 1)**2*(y + 2)/2
Let j = -10/97 - -127/291. Let s(l) = l + 8. Let h be s(-5). Factor 1/3*m**h - j*m**4 - 1/3*m + 1/3*m**2 + 0.
-m*(m - 1)**2*(m + 1)/3
Let g(w) be the third derivative of -w**5/12 + 10*w**4/3 + 85*w**3/6 + 29*w**2 + 2*w. Find a, given that g(a) = 0.
-1, 17
Let i = 329 - 2957/9. Let f(t) be the first derivative of 1/3*t**2 - 5 + i*t + 2/27*t**3. What is d in f(d) = 0?
-2, -1
Let t(h) = 15*h**3 - 28*h**2 + 4*h - 8. Let j(f) = -f**2 - f - 2. Let u be j(2). Let k(i) = 5*i**3 - 9*i**2 + i - 3. Let d(c) = u*k(c) + 3*t(c). Factor d(g).
g*(g - 2)*(5*g - 2)
Let i be ((-21)/(-9) - 3)*(-24)/118. Let u = i - -298/413. Solve -33/7*y**4 + 12/7*y**5 + 0*y + 15/7*y**3 + u*y**2 + 0 = 0.
-1/4, 0, 1, 2
Let d(y) = -22*y**3 + 238*y**2 - 426*y + 218. Let r(o) = -8*o**3 + 80*o**2 - 142*o + 73. Let v(h) = 3*d(h) - 8*r(h). Factor v(a).
-2*(a - 35)*(a - 1)**2
Find l such that -237/2*l**3 - 483/2*l**2 + 3/2*l**4 + 0 - 243/2*l = 0.
-1, 0, 81
Let l = 2 + 0. Factor l*j**5 - 2*j**4 + 4*j**2 + 4*j**4 - 2*j - 6*j**4.
2*j*(j - 1)**3*(j + 1)
Let r(o) = 15*o**3 + o**2 + 2. Let j be r(-2). Let s = -42 - j. Factor -9*g**3 - 52*g**3 - 37*g + 10*g + 13*g**3 - 3 - s*g**2.
-3*(g + 1)*(4*g + 1)**2
Suppose 3*j - 2*s = 2*j - 10, -4*j = -2*s + 4. Let -1/8*b**j - 3/8 - 1/2*b = 0. Calculate b.
-3, -1
Let t(z) be the second derivative of -z**6/55 - 18*z**5/55 - 21*z**4/22 - 10*z**3/11 - 493*z. Factor t(k).
-6*k*(k + 1)**2*(k + 10)/11
Let x be 17/6 - (-2)/12. Suppose -6*c + c - 20 = -5*z, -z - x*c = 4. Let 1/2*b - z*b**2 - b**5 + 7/4*b**4 + 1/2*b**3 + 1/4 = 0. What is b?
-1, -1/4, 1
Suppose 4*h + 3*z - 90 = 0, 3*h - 89 = -z - 24. Determine o, given that -48*o**4 + 12*o**3 + h*o**5 - 46*o + 46*o + 0*o**3 = 0.
0, 2/7, 2
Let g(t) = -t**3 - 5*t**2 - 8*t - 11. Let l be g(-4). Factor 26*o - 14 + 4*o - l*o**2 - 13 + 2.
-5*(o - 5)*(o - 1)
Let p(f) be the third derivative of f**7/630 - f**6/120 - 4*f**5/45 - f**4/6 + 2*f**2 + 7*f. Suppose p(r) = 0. What is r?
-2, -1, 0, 6
Let r(f) be the third derivative of f**9/20160 + f**8/1120 + 3*f**7/560 + f**6/60 - f**5/6 - 3*f**2. Let s(q) be the third derivative of r(q). Factor s(t).
3*(t + 1)**2*(t + 4)
Suppose -21*v = -30*v + 36. Suppose 28*d**3 + 6*d + 4*d**4 + d**v + 6*d**2 - 6*d**3 + 17*d**2 = 0. What is d?
-3, -1, -2/5, 0
Suppose 6 = r + 4. Suppose j = 2*v + 4, -r*j + 7*j + 2*v = 8. Determine p so that 4/5 + 2/5*p**j - 6/5*p = 0.
1, 2
Let z(d) be the second derivative of d**7/14 + d**6/10 - 3*d**5/20 - d**4/4 + 2*d + 255. Let z(k) = 0. What is k?
-1, 0, 1
Let n(y) be the third derivative of -y**7/735 - 2*y**6/105 - 17*y**5/210 - 5*y**4/42 + 293*y**2. What is g in n(g) = 0?
-5, -2, -1, 0
Let y be -1 - ((-782)/260 + 1 + 1). Let o(t) be the second derivative of 1/13*t**4 + 8/13*t**2 - 6*t + y*t**5 + 4/13*t**3 + 0. Factor o(d).
2*(d + 2)**3/13
Let x(b) be the third derivative of 4*b**5/105 - b**4/42 - 411*b**2. Factor x(c).
4*c*(4*c - 1)/7
Let o be (2/(-8))/(5/(-40)). Suppose 3*q + 2*q + 11 = 2*d, -o*d - 2*q = -18. Factor -6 - 10*k + 2 + d*k + 2*k**2.
2*(k - 2)*(k + 1)
Let z(r) be the second derivative of r**6/60 + r**5/10 - 5*r**4/12 - 7*r**3/3 - 15*r**2/4 + 4*r + 2. Determine q so that z(q) = 0.
-5, -1, 3
Suppose 4*a - 3*g - 3 = -0, -g - 12 = -5*a. Suppose a*u + 2*o = 2, -5 - 7 = -u + 5*o. What is z in 0*z**3 - z**4 - z**5 - 3*z**3 + u*z**3 - z**4 = 0?
-1, 0
Let x(r) be the first derivative of -r**6/900 - r**5/75 - r**4/20 - 5*r**3 + 2. Let y(b) be the third derivative of x(b). Find t such that y(t) = 0.
-3, -1
Let k(u) be the second derivative of u**7/336 + 23*u**6/80 + 1587*u**5/160 + 12167*u**4/96 - 3*u - 102. Let k(c) = 0. Calculate c.
-23, 0
Let r(c) be the second derivative of -23*c**5/90 - c**4/27 + c + 82. Factor r(t).
-2*t**2*(23*t + 2)/9
Determine k so that -106*k**4 + 118*k**3 + 4*k**5 - 69*k**4 - 70*k**4 - 20 + 207*k**4 - 158*k**2 + 94*k = 0.
1/2, 1, 2, 5
Let h = 8 + -3. Suppose -2*t - 15 = -h*t. What is n in 28*n**4 - 8*n**3 - 5*n**2 + 0*n**2 + n**2 - 16*n**t = 0?
-1/4, 0, 1
Let a(j) be the third derivative of 0 - 1/120*j**5 + 0*j**4 + 1/840*j**7 + 0*j**3 + 0*j - 1/480*j**6