- 1/4*i**p - 10*i + 0*i**2 + 1/12*i**4 + 1/6*i**3 + 1/10*i**6. Factor o(q).
q*(q - 1)**2*(3*q + 1)
Suppose -2*w - 4*t + 46 = -3*w, -5*w - 5*t = 230. Let v = 48 + w. Factor -1/5 + 1/5*x**v + 0*x.
(x - 1)*(x + 1)/5
Let o(j) = -3*j**3 + 881 - 24*j - 24*j**2 - 904 + 4*j**3. Let d be o(25). Factor -2/5*a**3 + 0*a + 2/5*a**d + 0.
-2*a**2*(a - 1)/5
Let r be (-12)/7*4/((-640)/45). Let t = -5/14 + r. Determine o so that t*o**2 + 0 + 0*o = 0.
0
Let l be ((-56)/35)/(11/(-22)). Solve 1/5*j**3 + 24/5*j - l - 9/5*j**2 = 0.
1, 4
Let r(f) be the first derivative of f**4/16 - 2*f**3/3 + 7*f**2/8 + 53. Factor r(u).
u*(u - 7)*(u - 1)/4
Let m = 86 - 81. Factor 31 - m + 5*v**2 - 16 - 15*v.
5*(v - 2)*(v - 1)
Factor 558/5*d + 6/5*d**3 + 756/5 + 24*d**2.
6*(d + 3)**2*(d + 14)/5
Let a(i) be the second derivative of i**5/4 - 17*i**4/12 + i**3 + 325*i. Find k, given that a(k) = 0.
0, 2/5, 3
Let u(z) be the third derivative of 0*z**3 + 1/70*z**7 + 1/20*z**6 + 0*z + 0 - 4*z**2 + 0*z**5 + 0*z**4. Factor u(q).
3*q**3*(q + 2)
Let v be (-37)/444*(0 + -10). Let x(m) be the first derivative of v*m**2 + 5 + 1/9*m**3 - 1/5*m**5 - 5/12*m**4 + 2/3*m. Determine r so that x(r) = 0.
-1, -2/3, 1
Let g(t) be the second derivative of t**6/120 + 37*t**5/80 + 179*t**4/24 + 21*t**3/2 - 81*t**2 + 711*t. Suppose g(m) = 0. What is m?
-18, -2, 1
Suppose -14 = 10*c - 64. Let j(a) be the third derivative of 0*a**3 - 1/480*a**6 + 0 + 0*a + 2*a**2 + 1/80*a**c - 1/48*a**4. Suppose j(t) = 0. Calculate t.
0, 1, 2
Factor -4/3*n**2 + 1/9*n**3 - 16*n - 320/9.
(n - 20)*(n + 4)**2/9
Let y(t) be the third derivative of -3 + 0*t**3 + 0*t + 1/525*t**7 + 1/20*t**4 + 1/60*t**6 + 8*t**2 + 7/150*t**5. Factor y(x).
2*x*(x + 1)**2*(x + 3)/5
Suppose 0 = -3*l + 12 + 6. Let b(d) be the third derivative of 0*d**3 + 1/180*d**l + 1/36*d**4 + 0 + 0*d + 1/45*d**5 + 7*d**2. Factor b(u).
2*u*(u + 1)**2/3
Let x(n) = -n**2 - 12*n + 21. Let y(t) = t**2 + 24*t - 41. Suppose -14 - 1 = 3*h. Let z(g) = h*x(g) - 3*y(g). Factor z(r).
2*(r - 3)**2
Suppose 146*n - 151*n = 1335. Let b = n + 3477/13. Determine l so that -8/13 + 14/13*l**2 + 0*l - b*l**3 = 0.
-2/3, 1, 2
Let d = 19 - 16. Let 11*q**3 - 6*q**2 + 61*q**4 + 4*q**d - 27*q**4 - 13*q**4 = 0. Calculate q.
-1, 0, 2/7
Let i(f) be the first derivative of -5/4*f**4 - 5*f + 5/3*f**3 + 5/2*f**2 + 3. Factor i(z).
-5*(z - 1)**2*(z + 1)
Let a(i) be the first derivative of 1/25*i**5 + 0*i - 1/5*i**2 + 16 - 1/3*i**3 + 1/30*i**6 - 3/20*i**4. Find h such that a(h) = 0.
-1, 0, 2
Let d(p) be the second derivative of 1/90*p**6 - 10/9*p**3 - 7/60*p**5 + 4/3*p**2 + 1/2*p**4 + 7*p + 0. Solve d(r) = 0 for r.
1, 2
Suppose 5*h - z - 22 = 0, -15*h = -18*h - z + 18. Factor -7/4*d**3 - h*d + 1 + 23/4*d**2.
-(d - 2)*(d - 1)*(7*d - 2)/4
Let d(t) be the second derivative of -t**8/3136 + t**7/735 - t**6/1680 - t**5/140 + 4*t**4/3 + 15*t. Let k(c) be the third derivative of d(c). Factor k(w).
-3*(w - 1)**2*(5*w + 2)/7
Let t(y) be the first derivative of -y**6/60 + 7*y**5/50 - 11*y**4/40 + y**3/6 - 368. Solve t(h) = 0 for h.
0, 1, 5
Let r = 141 + -1268/9. Let l(c) be the first derivative of 2/15*c**5 - 1/3*c + 1/36*c**6 + 4 - r*c**3 - 5/12*c**2 + 1/6*c**4. Factor l(f).
(f - 1)*(f + 1)**3*(f + 2)/6
Let a be (3 - (-7 + 1280/130))*16. Factor 2/13*y**2 + 16/13*y + a.
2*(y + 4)**2/13
Let g(l) = -2*l**3 + 20*l**2 - 43*l + 10. Let v be g(7). Let 2/3*x - 4/3 + 2*x**2 - 2/3*x**v - 2/3*x**4 = 0. What is x?
-2, -1, 1
Let u(b) = -b**2 - 171*b - 4754. Let l be u(-35). Solve -9/2 - l*r**2 + 3/4*r**3 + 39/4*r = 0 for r.
1, 6
Let l be -3 + (-2 - -6) - -3. Factor -l*o + o**4 - 9*o**3 + 4*o + 10*o**3.
o**3*(o + 1)
Let g = 5 - 33/7. Suppose -8/7*t - g*t**2 - 8/7 = 0. Calculate t.
-2
Solve 1/6*g**3 + 578/3 + 544/3*g - 67/6*g**2 = 0 for g.
-1, 34
Let l be (24/30)/(36/15 - 2). Solve 18 + k**3 - 6 + 2*k**3 - 4*k**l - 5*k**2 = 0 for k.
-1, 2
Let g(o) be the first derivative of o**4/6 + 80*o**3/3 + 1200*o**2 - 561. Factor g(b).
2*b*(b + 60)**2/3
Let f(v) be the third derivative of v**7/2940 + v**6/1260 - v**5/210 + v**3 + 11*v**2. Let j(a) be the first derivative of f(a). Suppose j(k) = 0. Calculate k.
-2, 0, 1
Factor -142*y + 60*y + 82*y - 5*y**3 - 10*y**2.
-5*y**2*(y + 2)
Let r(c) be the first derivative of -3*c**4 + 141*c**3/2 - 891*c**2/2 - 729*c/2 - 444. Factor r(p).
-3*(p - 9)**2*(8*p + 3)/2
Let t(j) be the second derivative of -j**6/210 + 3*j**5/20 - 10*j**4/7 + 50*j**3/21 + 123*j. Factor t(f).
-f*(f - 10)**2*(f - 1)/7
Let d = -10550 + 10552. Determine x so that 3/5*x + 0 - 3/5*x**3 - 1/5*x**d + 1/5*x**4 = 0.
-1, 0, 1, 3
Let c(t) = 9*t**2 + 48*t + 84. Let w(q) = -17*q**2 - 96*q - 168. Let y(i) = 11*c(i) + 6*w(i). Factor y(p).
-3*(p + 2)*(p + 14)
Let h(l) be the third derivative of l**5/15 - l**4/6 + 31*l**2 - l. Factor h(p).
4*p*(p - 1)
Let x be (-2 - -2)/(-5) + -10. Let l be 2/((-35)/x + -3). Determine m, given that -l*m**2 + 0 + 9*m**2 + 10*m + 5 = 0.
-1
Let m(y) = 3*y**2. Let x be m(0). Let h(p) be the first derivative of 8 + 0*p**2 - 1/3*p**3 + x*p. Let h(t) = 0. Calculate t.
0
Let t(r) be the third derivative of -r**7/210 - r**6/24 - r**5/15 + 254*r**2. Factor t(d).
-d**2*(d + 1)*(d + 4)
Let t(r) be the second derivative of 1/24*r**6 + 0 + 1/6*r**5 + 0*r**3 + 5/24*r**4 + 9/2*r**2 + 6*r. Let v(w) be the first derivative of t(w). Factor v(n).
5*n*(n + 1)**2
Suppose -4*l - 2*b + 35 - 19 = 0, -b + 12 = 4*l. Factor -16/3*r + 4/3*r**l - 1/9*r**3 + 64/9.
-(r - 4)**3/9
Let r(w) = -w**2 - 1. Let t(k) = -6*k**3 + 102*k**2 - 416*k + 132. Let m(p) = 4*r(p) + t(p). Let m(b) = 0. Calculate b.
1/3, 8
Let g(d) = -13*d**3 + 25*d**2 + 2*d. Let r(o) = -3*o**3 + 6*o**2 + o. Let f(c) = 2*g(c) - 9*r(c). Solve f(a) = 0 for a.
-1, 0, 5
What is m in 0 + 0*m + 8/13*m**2 - 18/13*m**3 + 4/13*m**4 = 0?
0, 1/2, 4
Let x be 0/(144/(-75) - 12/150). Find s such that s**5 + 3/4*s**2 - 5/4*s**3 + 1/4*s + x - 3/4*s**4 = 0.
-1, -1/4, 0, 1
Let l(o) = -o**5 + o**4 - o**2 - 1. Let w(c) = -4*c**5 + 14*c**4 - 46*c**2 - 30*c - 2. Let b(q) = 4*l(q) - 2*w(q). Factor b(p).
4*p*(p - 5)*(p - 3)*(p + 1)**2
Let k(w) be the first derivative of -3*w**5/5 - 3*w**4/4 + 3*w**3 + 3*w**2/2 - 6*w - 165. Factor k(n).
-3*(n - 1)**2*(n + 1)*(n + 2)
Let v(u) be the second derivative of u**7/315 + u**6/90 - u**5/30 - u**4/9 + 4*u**3/9 - 4*u**2 + 16*u. Let a(x) be the first derivative of v(x). Factor a(i).
2*(i - 1)**2*(i + 2)**2/3
Suppose 2*l + 10 = -4*p, 3*p - 25 = 3*l + 2*l. Suppose -2*y + p*y + 4*i + 8 = 0, -4 = 5*y + 2*i. Factor 6/7*s**2 + y*s - 2/7*s**3 + 0.
-2*s**2*(s - 3)/7
Let u = 1/51 - -13/204. Let r(k) be the first derivative of 0*k + u*k**3 + 4 + 0*k**2. Let r(w) = 0. What is w?
0
Let b(s) = 3*s**3 - 52*s**2 + 127*s - 125. Let v(n) = 3*n**3 - 50*n**2 + 128*n - 124. Let p(q) = -4*b(q) + 5*v(q). Find y, given that p(y) = 0.
2, 10
Determine x, given that 0 + 9/7*x - 15/7*x**2 + 3/7*x**3 + 3/7*x**4 = 0.
-3, 0, 1
Factor -3/2*i**2 - 3*i**3 + 3/2*i**4 + 0 + 3*i.
3*i*(i - 2)*(i - 1)*(i + 1)/2
Factor -280 - 148*n**2 + 142 - 5*n + 138 + 76*n**4 + 80*n**3 - 3*n.
4*n*(n - 1)*(n + 2)*(19*n + 1)
Let x = -127 + 127. Let h(v) be the second derivative of 6/5*v**5 - 1/4*v**4 - v**3 + x - 1/2*v**6 + 0*v**2 - v. What is k in h(k) = 0?
-2/5, 0, 1
Let r(z) = -323*z + 7109. Let v be r(22). Suppose -4*m + m = 3*w - 12, 0 = -3*m - 3. Solve -9/5*p**v - 2/5*p**4 + 0*p**2 + 4/5*p + 3/5*p**w + 0 = 0.
-1, 0, 2/3, 2
Suppose 3*u = u - 4. Let s be (-1)/u + 377/(-130) - -3. Solve -s*b**2 - 3/5*b + 0 = 0.
-1, 0
Let p(d) be the first derivative of 2/15*d**3 + 3/20*d**4 + 0*d**2 + 0*d - 9. Factor p(o).
o**2*(3*o + 2)/5
Find u such that -40*u + 32*u + 10 - 20*u**2 - 54 - 56*u = 0.
-11/5, -1
Let 4/3*h**2 + 0 - 28*h = 0. Calculate h.
0, 21
Suppose 3*w + 3 - 2112 = 0. Let t be (-4)/(-14) + w/259. Factor -4/9*r**2 + 4/9 + 2/9*r - 2/9*r**t.
-2*(r - 1)*(r + 1)*(r + 2)/9
Let c(i) be the third derivative of 1/60*i**5 - 1/336*i**8 + 1/120*i**6 + 17*i**2 - 1/210*i**7 + 0 + 0*i + 0*i**4 + 0*i**3. Determine p, given that c(p) = 0.
-1, 0, 1
Suppose 2*t - 2*k + 10 = 0, 2*k - 7*k = -3*t - 29. Factor -4/7*b**t + 0 - 24/7*b.
-4*b*(b + 6)/7
Let -4/7 - 1/7*u**2 + 5/7*u = 0. Calculate u.
1, 4
Let n(i) be the second derivative of -i**9/945 + 3*i**8/560 - i**7/105 + i**6/180 - 5*i**4/12 - 19*i. Let g(f) be the third derivative o