5/60 + 7*d**2/2 + 23. Let m(w) be the second derivative of l(w). Factor m(o).
o**2*(2*o - 1)*(3*o + 2)/2
Let f(r) = -r**2 - r + 2. Let p be f(0). Factor 3 + 3*h**p + 3 + 7 - 7 - 9*h.
3*(h - 2)*(h - 1)
Suppose 7*j + 4 = 9*j. Suppose 3*n = j*n + 2. Solve -h**4 + 10*h**n + 6*h**4 + 109*h**3 - 124*h**3 = 0.
0, 1, 2
Let f = -24 - -27. Find t such that f*t**3 - 4*t**2 - t**3 + 0*t**3 = 0.
0, 2
Let w = 21/389 + 2639/1556. Factor 7/4*i**2 - w*i**4 + 1/2*i - 1/2*i**3 + 0.
-i*(i - 1)*(i + 1)*(7*i + 2)/4
Let j(p) = 17*p**5 - 23*p**4 + 33*p**3 - 9*p**2 - 9. Let i(b) = 4*b**5 - 6*b**4 + 8*b**3 - 2*b**2 - 2. Let w(k) = 18*i(k) - 4*j(k). Factor w(g).
4*g**3*(g - 3)*(g - 1)
Suppose -73*k = -62*k - 55. Let z(h) be the first derivative of -6*h**4 - 1/3*h**3 + 3*h - 6 + 8/3*h**6 + k*h**2 - 4/5*h**5. Suppose z(g) = 0. What is g?
-3/4, -1/2, 1
Let t(s) be the third derivative of -s**5/30 - 11*s**4/12 - 10*s**3/3 + 174*s**2 - 1. Factor t(i).
-2*(i + 1)*(i + 10)
Let w be -2 + ((-1064)/308 - (2 + -8)). Determine g so that 0 + 1/11*g**5 + w*g**3 + 4/11*g**2 + 4/11*g**4 + 1/11*g = 0.
-1, 0
Let t be (-6)/((-54)/(-20) - 3). Let x be 8/t - 18/(-5). Factor 2*c**3 - c**2 + x*c - c**3 - c**2 - 3*c.
c*(c - 1)**2
Let h = -315 - -316. Let g be h*5 + (-143)/33. Determine k so that 2/3*k**3 + 0 + g*k - 4/3*k**2 = 0.
0, 1
Let y(t) be the first derivative of -5/3*t**3 + 0*t + 26 + 5/2*t**2. Determine s, given that y(s) = 0.
0, 1
Let q(o) be the first derivative of -14*o**3/75 + 134*o**2/25 - 38*o/25 - 80. Factor q(p).
-2*(p - 19)*(7*p - 1)/25
Let h(c) = -45*c + 99*c - 57*c. Let a = -2 + 0. Let t(y) = -y**2 - 7*y. Let k(r) = a*t(r) + 5*h(r). Determine j, given that k(j) = 0.
0, 1/2
Suppose 2*w - 5*f + 2*f = 18, f = -5*w + 62. Find d, given that 22*d**4 - 19*d**4 - 12*d**3 + 6*d**2 + w*d - 10 + 1 = 0.
-1, 1, 3
Factor 150/7 - 24/7*t**2 - 3/7*t**3 - 15/7*t.
-3*(t - 2)*(t + 5)**2/7
Factor -5/7*m**3 + 1/7*m**4 - 6/7*m**2 + 0*m + 0.
m**2*(m - 6)*(m + 1)/7
Let m be (-3 - (5 + 0))*(-3)/4. Let j be -2 - (m + -2 + -3)*-2. Factor 0 - 2*i**5 + 32/7*i**4 - 22/7*i**3 + 4/7*i**2 + j*i.
-2*i**2*(i - 1)**2*(7*i - 2)/7
Let y be 2/((-1)/(6/(-4))). Suppose 3*m - 4*k = -y*k + 1, 3*m = -5*k - 5. Factor -1/2*j**2 + m*j + 1/2.
-(j - 1)*(j + 1)/2
Let w be -2*(6 + 60/(-8)). Let i(o) = o**3 - o**2 - 7*o + 5. Let r be i(w). Factor 0 + 1/8*a**3 + 0*a + 0*a**r + 1/8*a**4.
a**3*(a + 1)/8
Let n = 6057/176 - 371/11. Let c(g) be the second derivative of 3/5*g**5 + 1/4*g**3 + 5*g + 0*g**2 + 7/40*g**6 + n*g**4 + 0. Find i such that c(i) = 0.
-1, -2/7, 0
Let f = -7 + 9. Suppose -4*p + 14 = d, 3*d + f*p = 7*d - 2. Solve -2 - 1 + 15*h**d - 18*h**2 + 6*h = 0.
1
Let o(x) be the second derivative of -x**5/4 - 75*x**4/4 - 1125*x**3/2 - 16875*x**2/2 + 30*x + 1. Factor o(a).
-5*(a + 15)**3
Let j(m) be the first derivative of -3*m**4/32 + 5*m**3/8 + 3*m**2/16 - 15*m/8 - 52. Determine b so that j(b) = 0.
-1, 1, 5
What is c in 0 + 114/5*c**2 + 3/5*c**5 + 9*c + 6*c**4 + 96/5*c**3 = 0?
-5, -3, -1, 0
Let v(k) be the second derivative of -k**7/126 + k**6/18 - k**5/60 - 13*k**4/36 + k**3/9 + 4*k**2/3 + 173*k - 1. Suppose v(t) = 0. What is t?
-1, 1, 2, 4
Let y(s) = 4*s**2 + 13*s + 25. Let r(m) = 5*m**2 + 18 - 11 + 14*m + 18. Let t(o) = 3*r(o) - 4*y(o). Find l, given that t(l) = 0.
-5
Suppose 3*n = 7*n. Factor -68*o + 0 + 66*o + n + o**2.
o*(o - 2)
Let p(k) be the first derivative of -k**9/6048 - k**8/3360 + k**7/840 + 8*k**3 + 7. Let q(f) be the third derivative of p(f). Solve q(m) = 0 for m.
-2, 0, 1
Let c(g) be the second derivative of -g**5/4 + 145*g**4/12 + 25*g**3 + 166*g. Suppose c(o) = 0. What is o?
-1, 0, 30
Let z = 8278 + -16547/2. Suppose -z*u + 6*u**2 - 27 + 3/2*u**3 = 0. What is u?
-3, 2
Factor -1/6*s**4 - 17*s**2 - 128/3*s - 17/6*s**3 - 112/3.
-(s + 2)*(s + 4)**2*(s + 7)/6
Let l(s) be the first derivative of 0*s**2 + 11 + 0*s - 5/3*s**3. Solve l(y) = 0.
0
Let j(p) be the third derivative of p**7/210 + p**6/10 - p**5/60 - p**4/2 + 177*p**2 + 1. Factor j(t).
t*(t - 1)*(t + 1)*(t + 12)
Determine c, given that -5/3*c + 11/3*c**2 + 1/3*c**4 - 7/3*c**3 + 0 = 0.
0, 1, 5
Let y be (0/1 + -3)/(-1). Factor 0*h**2 + 10 - 6*h**2 - 3*h - 21 + 3*h**y + 17.
3*(h - 2)*(h - 1)*(h + 1)
Let c(k) be the first derivative of -13*k**4/3 - 148*k**3/9 - 40*k**2/3 + 16*k/3 + 23. Find p, given that c(p) = 0.
-2, -1, 2/13
Determine l so that 92081*l**4 - 92075*l**4 + 6*l**3 - 48*l + 3*l**5 - 51*l**3 - 96*l**2 = 0.
-4, -1, 0, 4
Let q(v) = -4*v + 21. Let p be q(6). Let s be (-9)/(-6)*-1*p/9. Determine l so that -1/2*l**4 + 0*l + s*l**2 - 1/2*l**5 + 0 + 1/2*l**3 = 0.
-1, 0, 1
Let t(z) be the third derivative of z**5/40 - 15*z**4/16 - 4*z**3 - 65*z**2. Factor t(k).
3*(k - 16)*(k + 1)/2
Find w, given that -6/11*w**4 + 0*w + 14/11*w**2 - 8/11 - 2/11*w**3 + 2/11*w**5 = 0.
-1, 1, 2
Let n be 240/270*((-6)/15 - 22/(-40)). Factor 0 + 2/15*v**2 - n*v.
2*v*(v - 1)/15
Let j(o) be the second derivative of 0 - 1/2*o**5 + 20/3*o**3 - 65/12*o**4 - 28*o + 10*o**2 + 1/2*o**6. Determine n, given that j(n) = 0.
-2, -1/3, 1, 2
Let j(l) = -8*l**3 + 282*l**2 - 5409*l + 34298. Let r(h) = 55*h**3 - 1975*h**2 + 37865*h - 240085. Let w(v) = 20*j(v) + 3*r(v). Factor w(a).
5*(a - 19)**3
Suppose 16 - 11*h**2 + 4*h**4 + 1/2*h**5 - 16*h + 13/2*h**3 = 0. What is h?
-4, -2, 1
Let r = -9 - -11. Factor 0*d**4 + 3*d**2 - 15*d**2 + 10*d**r - 2*d**3 + 2*d**4 + 2*d**5.
2*d**2*(d - 1)*(d + 1)**2
Let k be 4 - ((-17)/(-4) - 11/44). Factor 1/2*i**3 + 0 + 0*i**2 + 5/4*i**4 + k*i.
i**3*(5*i + 2)/4
What is l in 0 - 17/3*l**2 - 4/3*l**3 - 4/3*l = 0?
-4, -1/4, 0
Let s be (-26)/6 - 9/(-27). Let v(p) = -2*p**3 - 9*p**2 - 6*p - 3. Let m be v(s). Let 3*q**3 + 2*q + q**2 - m*q**3 - 5*q**2 + 4 = 0. What is q?
-2, -1, 1
Let a be 60/25 + (3 - 7*(-50)/(-70)). Factor -2/5*k**3 + a*k + 2/5 - 2/5*k**2.
-2*(k - 1)*(k + 1)**2/5
Let s = 733 - 731. Let x(g) be the second derivative of 0*g**2 + 0 - 2*g**4 - 21/20*g**5 + 1/2*g**6 - s*g + 2*g**3. Find u, given that x(u) = 0.
-1, 0, 2/5, 2
Let l(q) = -3*q + 4. Let r(x) = x**2 + 4*x. Let w be r(0). Let u be l(w). Factor 3/2*v - 6*v**u + 9*v**3 - 6*v**2 + 0 + 3/2*v**5.
3*v*(v - 1)**4/2
Let j(d) be the first derivative of -d**3/3 + 15*d**2/2 + 2*d + 5. Let b be j(15). Factor -b + 0 - 2*a**2 - 2*a**3 - 6*a - 4*a**2.
-2*(a + 1)**3
Let s**2 + 369*s - 289*s - 267 + 72 - 4*s**2 - 2*s**2 = 0. What is s?
3, 13
Let b(k) be the third derivative of -k**6/600 + 7*k**5/150 + k**4/120 - 7*k**3/15 + 134*k**2 - 2. Solve b(x) = 0.
-1, 1, 14
Let f be (-1097)/(-12) + 4/(-6). Let k = 91 - f. Factor -1/4*d**4 + k*d**3 + 0*d + 0 + 0*d**2.
-d**3*(d - 1)/4
Let r be 4*(12/16 - 2). Let n(l) = -3*l**3 + 2*l**2 + 8*l + 8. Let j(d) = -3*d**3 + 3*d**2 + 9*d + 9. Let x(t) = r*j(t) + 6*n(t). Factor x(k).
-3*(k - 1)*(k + 1)**2
Let k(j) be the first derivative of -j**4/38 - 2*j**3/57 + 5*j**2/19 - 6*j/19 + 112. Factor k(w).
-2*(w - 1)**2*(w + 3)/19
Suppose 4*o - 11 + 3 = 0. Factor -4/5*q + 0 - 2/5*q**3 + 6/5*q**o.
-2*q*(q - 2)*(q - 1)/5
Let n(h) be the second derivative of -h**7/14 - h**6/2 - 6*h**5/5 - h**4 + 252*h. Let n(w) = 0. What is w?
-2, -1, 0
Determine y so that 18/7 - 1/7*y**2 - 17/7*y = 0.
-18, 1
Let o(d) be the third derivative of d**7/6720 - d**6/480 + d**5/120 + 7*d**3/2 - 28*d**2. Let i(l) be the first derivative of o(l). Factor i(w).
w*(w - 4)*(w - 2)/8
Let s = -2001 + 2006. Factor 0 + 16/11*d**4 + 4/11*d**2 + 6/11*d**s + 0*d + 14/11*d**3.
2*d**2*(d + 1)**2*(3*d + 2)/11
Suppose q = 2*v + 2, -2*q + 8*v + 4 = 10*v. Determine i so that -1/6*i**4 + 0 + 1/2*i**3 - 1/6*i**5 - 1/3*i + 1/6*i**q = 0.
-2, -1, 0, 1
Let r = 23 - 20. Suppose 7*o = r*o. Factor 3*j + o*j + 2*j**3 - 3*j + j**4.
j**3*(j + 2)
Suppose 3*r - 5*a + 29 = 0, 4*a = -4*r - r - 73. Let q = r + 28. Factor -f - 2*f + q*f**3 - 12*f**3.
3*f*(f - 1)*(f + 1)
Let k(i) = 89*i + 356. Let d be k(-4). Solve 25/6*n**2 + d - 5/3*n**4 - 5/3*n - 5/6*n**3 = 0.
-2, 0, 1/2, 1
Determine a, given that -27/2 + 63/4*a - 6*a**2 + 3/4*a**3 = 0.
2, 3
Let o(c) be the first derivative of -c**6/15 + 56*c**5/25 - 122*c**4/5 + 448*c**3/5 - 576*c**2/5 - 2. Find j, given that o(j) = 0.
0, 2, 12
Let r(l) = -7*l**2 - 2*l - 9. Let p(g) = 20*g**2 + 7*g + 26. Let q(t) = -6*p(t) - 17*r(t). Let v be q(-7). Factor n**3 + 1/2*n**2 + 0*n + 0 + 1/2*n**v.
n**2*(n + 1)**2