 = -4*l + 70. Suppose 0 = 3*h - 2 - l. Factor 15/2*i + 3 + h*i**2 + 3/2*i**3.
3*(i + 1)**2*(i + 2)/2
Let g(d) be the first derivative of -d**4/6 - d**3/3 - 17*d + 28. Let r(b) be the first derivative of g(b). Factor r(k).
-2*k*(k + 1)
Let w = 2959 - 26629/9. Determine i so that 2/9*i + w*i**2 - 4/9 = 0.
-2, 1
Let s(y) be the third derivative of 5*y**6/42 - 4*y**5/21 - 19*y**4/168 - y**3/42 - 59*y**2. Determine o, given that s(o) = 0.
-1/10, 1
Suppose 3*k = k - 2*t - 16, 0 = -2*k + 4*t - 16. Let c = k + 10. Factor -c + 5 + 25*d + 75*d**2 + 5*d.
3*(5*d + 1)**2
Suppose 122*p - 30*p + 2*p**3 + 24*p**2 - 20*p = 0. Calculate p.
-6, 0
What is k in -5/4*k**3 - 45/4*k + 15/2*k**2 + 0 = 0?
0, 3
Suppose -4*r + 4*g + 36 = 0, -4*r - r + 4*g + 40 = 0. Suppose -11*i**5 + r*i**2 - 4*i**2 + 8*i**3 + 8*i**4 + 13*i**5 = 0. Calculate i.
-2, 0
Let t(m) be the third derivative of -m**5/360 - m**4/18 - 7*m**3/36 + 3*m**2 + 15. Determine l so that t(l) = 0.
-7, -1
Suppose 0*a - 3*a + q + 13 = 0, -20 = -4*a + 2*q. Factor -b**2 - 5 - 6*b**2 + 9*b**2 + a.
2*(b - 1)*(b + 1)
Let k be 60/(-120)*9/(-6). Factor -3/4*b**3 + 3/2 + k*b - 3/2*b**2.
-3*(b - 1)*(b + 1)*(b + 2)/4
Find g such that 48/7*g + 3/7*g**3 - 36/7 - 3*g**2 = 0.
2, 3
Let i(u) be the first derivative of -u**4/4 - 5*u**3/3 + 3*u**2 - 21. Let i(k) = 0. What is k?
-6, 0, 1
Suppose 126/5*n**3 + 57/5*n**4 - 3/5*n**5 - 123/5*n + 6/5*n**2 - 63/5 = 0. Calculate n.
-1, 1, 21
Factor -1/2*r**4 - 1/6*r**2 - 1/2*r**3 + 0 + 0*r - 1/6*r**5.
-r**2*(r + 1)**3/6
Let m(z) = -5*z**3 - 160*z**2 - 195*z - 40. Let k(p) = p**3 + 23*p**2 + 28*p + 6. Let i(b) = 20*k(b) + 3*m(b). Determine t so that i(t) = 0.
-1, 0, 5
Suppose 0 = 7*j + j + 2*j. Let p(f) be the third derivative of -f**2 - 1/40*f**5 + 0*f - 1/32*f**4 - 1/70*f**7 + 7/160*f**6 + 0*f**3 + j. What is w in p(w) = 0?
-1/4, 0, 1
Let x(z) be the third derivative of 0*z**3 + 17*z**2 + 0 + 1/105*z**5 + 0*z - 1/28*z**4 - 1/1260*z**6. What is c in x(c) = 0?
0, 3
Let w(f) be the first derivative of f**5/30 + 67*f**4/24 + 385*f**3/6 + 363*f**2/4 - 504. Let w(i) = 0. Calculate i.
-33, -1, 0
Let v(p) = 4*p - 6. Let m be 0 + -2*(-4 + 3). Let s be v(m). Factor -2*u + 2/3 - 2/3*u**3 + s*u**2.
-2*(u - 1)**3/3
Suppose 5*f - 8*f + 3 = 0. Suppose -q = -l + 6, -2*l - f = 5*q + 1. Factor 2/3*h**2 - 2/9*h**l + 0 + 0*h**3 - 4/9*h.
-2*h*(h - 1)**2*(h + 2)/9
Let d(n) be the second derivative of -n**4/21 + 10*n**3/21 - 8*n**2/7 - 140*n + 2. Factor d(p).
-4*(p - 4)*(p - 1)/7
Factor 8/17 + 10/17*t**3 + 28/17*t**2 + 26/17*t.
2*(t + 1)**2*(5*t + 4)/17
Let l(h) be the third derivative of -1/60*h**5 + 0 + 0*h + 1/210*h**7 + 0*h**3 + 12*h**2 + 1/40*h**6 - 1/168*h**8 - 1/24*h**4. Determine b so that l(b) = 0.
-1, -1/2, 0, 1
Suppose 284*p - 274*p = 0. Factor p + 4/5*k**3 - 8/5*k**2 - 16/5*k + 2/5*k**4.
2*k*(k - 2)*(k + 2)**2/5
Suppose 6*s = 5*s - 5*t + 104, -2*s + t + 241 = 0. Let w = s + -117. Find b such that 0*b**3 - 1/2*b**5 - b**4 + 1/2*b + 0 + b**w = 0.
-1, 0, 1
Let k(p) = -2*p + 1. Let w be k(5). Let r(x) = x**3 + 10*x**2 + 9*x + 3. Let z be r(w). Find n such that -4*n + 6*n + 4*n - z + 0*n**2 - 3*n**2 = 0.
1
Let z(y) be the first derivative of 22 + 24/7*y + 4/7*y**3 + 22/7*y**2. Factor z(g).
4*(g + 3)*(3*g + 2)/7
Let f(s) = 5*s**2 + 177*s - 193. Let a(b) = -b**2 - 35*b + 38. Let o(x) = 22*a(x) + 4*f(x). Solve o(g) = 0 for g.
-32, 1
Let f = -2131 + 2131. Factor 2/3*l**3 + 0 + 2/3*l**4 - 2/3*l**5 - 2/3*l**2 + f*l.
-2*l**2*(l - 1)**2*(l + 1)/3
Let w be 228 - 233 - (-19)/2. Determine r, given that -1/2*r**3 + w*r**2 + 8 - 12*r = 0.
1, 4
Determine t, given that -98/19 - 402/19*t**2 - 492/19*t - 8/19*t**3 = 0.
-49, -1, -1/4
Let o be (-36)/(-112) - (-4)/80*-5. Let k(l) be the first derivative of 4/7*l - 3/7*l**2 + o*l**4 + 0*l**3 + 3. Let k(q) = 0. What is q?
-2, 1
Let o(s) be the third derivative of -s**6/180 - s**5/180 + 5*s**4/72 - s**3/9 + 84*s**2. Factor o(l).
-(l - 1)*(l + 2)*(2*l - 1)/3
Let q(n) be the second derivative of n**6/6 + 3*n**5 + 75*n**4/4 + 125*n**3/3 - 95*n. Let q(g) = 0. What is g?
-5, -2, 0
Let f(n) = n**2 + n - 14. Let o be f(-5). Let c(y) = -y + 10. Let k be c(o). Factor -1/3*z**k + z**2 + 0 + 2/3*z + 0*z**3.
-z*(z - 2)*(z + 1)**2/3
Let k = -410 - -412. Factor 0*w - 2/19*w**k + 0.
-2*w**2/19
Let l(n) = n**3 + n + 1. Let f(d) = 3*d**3 - 5*d**2 - 22*d + 18. Let c(z) = f(z) + 2*l(z). Factor c(r).
5*(r - 2)*(r - 1)*(r + 2)
Let k(y) = 10*y**5 + 58*y**4 + 34*y**3 - 206*y**2 - 284*y - 90. Let f(u) = 3*u**4 - u**3 - u**2 + u. Let h(d) = -f(d) + k(d). Let h(m) = 0. Calculate m.
-3, -1, -1/2, 2
Let g be (240422/(-5920))/7 - (-2 + -2). Let b = -1/592 - g. Factor 9/5*q**4 + b*q**3 + 3/5*q**2 + 0*q + 0 + 3/5*q**5.
3*q**2*(q + 1)**3/5
Let d = -15155 - -15158. Find k, given that 0*k - 7/3*k**4 + 4/3*k**5 + 1/3*k**2 + 2/3*k**d + 0 = 0.
-1/4, 0, 1
Factor 0*n - 2/5*n**5 + 34/5*n**3 - 14/5*n**4 + 0 - 18/5*n**2.
-2*n**2*(n - 1)**2*(n + 9)/5
Let w(i) be the first derivative of 55 + 0*i**2 + 3*i**4 + 0*i**5 + 8/3*i**3 + 0*i - 2/3*i**6. Factor w(a).
-4*a**2*(a - 2)*(a + 1)**2
Suppose 2*b + 22*b = 0. Let h(y) be the second derivative of 1/12*y**4 + b*y**3 + 0 - 1/2*y**2 - 3*y. Factor h(r).
(r - 1)*(r + 1)
Let -116*a**2 + 22*a**3 + 110*a**3 - 24 - 220*a**2 + 164*a + 64*a**3 = 0. Calculate a.
2/7, 3/7, 1
Solve -37*v**4 - 8*v**3 - 8*v**4 - 45 + 5*v - 4*v**3 + 2*v**3 + 90*v**2 + 5*v**5 = 0.
-1, 1, 9
Let l(h) = 1 + 2 + 2 - h + 5. Let c be l(10). Factor 10*a - 13*a**2 + 0*a + 48*a**2 + 15*a**3 + c*a.
5*a*(a + 2)*(3*a + 1)
Let q(s) = -s**5 - s**3 + s**2 + s - 1. Let p(w) = 20*w**5 - 15*w**4 + 20*w**3 - 10*w**2 - 15*w + 25. Let g(o) = -p(o) - 25*q(o). Find c, given that g(c) = 0.
-2, -1, 0, 1
Factor -213/8*v - 23/8*v**3 - 139/8*v**2 - 9/8.
-(v + 3)**2*(23*v + 1)/8
Suppose 16641/2 + 1/2*c**2 - 129*c = 0. Calculate c.
129
Let w(a) = 2*a**3 - a**2 + 1. Let l(g) = 5*g**4 - 145*g**3 - 515*g**2 - 20*g + 685. Let n(q) = -l(q) + 5*w(q). Factor n(j).
-5*(j - 34)*(j - 1)*(j + 2)**2
Factor 26662*r**2 - r**3 - 5*r + 4*r**4 - 26678*r**2 + 18*r**3.
r*(r - 1)*(r + 5)*(4*r + 1)
Let u(m) be the second derivative of m**7/420 + m**6/720 - m**5/60 - m**4/48 - 9*m**3/2 + 30*m. Let p(s) be the second derivative of u(s). Factor p(i).
(i - 1)*(i + 1)*(4*i + 1)/2
Suppose -106*a + 4 - 4 = -573*a. Factor a - 5/4*n + 0*n**2 + 5/4*n**3.
5*n*(n - 1)*(n + 1)/4
Let p(c) be the first derivative of -5*c**4/16 + 2*c**3/3 + c**2/2 - 62. Determine x so that p(x) = 0.
-2/5, 0, 2
Suppose 35 - 11 = 6*n. Suppose 5*s - n*s = 3*z + 10, 3*z = 4*s - 22. Factor 0 + 4/3*v**s + 0*v**2 + 4/3*v**3 + 0*v.
4*v**3*(v + 1)/3
Let a(x) be the third derivative of 0 + 0*x**3 + 0*x - 1/270*x**5 + 1/540*x**6 - 8*x**2 - 1/54*x**4. Factor a(z).
2*z*(z - 2)*(z + 1)/9
Let u(h) be the first derivative of 9 + 0*h + 1/5*h**3 - 1/25*h**5 - 1/5*h**2 + 0*h**4. What is o in u(o) = 0?
-2, 0, 1
Let v(c) be the second derivative of c**5/15 - 2*c**4/3 + 8*c**3/3 + 11*c**2 + 18*c. Let f(t) be the first derivative of v(t). Factor f(u).
4*(u - 2)**2
Let w(o) = -o**2 + 6*o + 44. Let f be w(10). Find z, given that 18 + 14 + 51*z**2 - 11*z**2 + f*z**3 + 68*z = 0.
-8, -1
Solve 85*x**3 + 18 + 3*x**4 - 24*x**3 - 33*x + 6*x**3 - 15*x**4 - 6*x**2 - 3*x**5 - 31*x**3 = 0 for x.
-6, -1, 1
Let a(w) be the third derivative of -w**7/210 + 4*w**6/15 - 26*w**5/5 + 112*w**4/3 - 392*w**3/3 + 541*w**2. Factor a(v).
-(v - 14)**2*(v - 2)**2
What is o in 57/4*o**2 - 3/4*o**5 - 21/4*o**4 + 0 - 21/2*o + 9/4*o**3 = 0?
-7, -2, 0, 1
Let w = 10610/11 - 961. Let z = 189/44 - w. Factor 3/4*x**3 + 0 - 3/4*x - 3/4*x**4 + z*x**2.
-3*x*(x - 1)**2*(x + 1)/4
Let h(s) = 5*s + 75. Let m be h(-14). Let n(o) be the second derivative of 0 - o**2 + 5/18*o**3 - 3*o - 1/20*o**m + 2/9*o**4. Determine v so that n(v) = 0.
-1, 2/3, 3
Suppose 47 = 3*t - 4*f, 0*f - 16 = t + 5*f. Let 10*k**2 + t*k**2 - 16*k**2 = 0. What is k?
0
Factor -102/5*m + 0 + 3/5*m**3 - 99/5*m**2.
3*m*(m - 34)*(m + 1)/5
Let w(v) be the third derivative of v**5/75 - 6*v**3/5 - 5*v**2 + 6. Factor w(d).
4*(d - 3)*(d + 3)/5
Let z(j) be the second derivative of -j**7/70 - 4*j**6/25 - 12*j**5/25 - 121*j. Factor z(m).
-3*m**3*(m + 4)**2/5
Let g(f) be the third derivative of f**5/570 - f**4/114 - f**3/19 + 7*f**2 + 11. Factor g(h).
2*(h - 3)*(h + 1)/19
Solve -2/3*t**2 + 6*