
1, 2
Let z(v) be the first derivative of -2/105*v**5 + 0*v - 6 + 2/63*v**3 + 0*v**2 + 0*v**4. Factor z(i).
-2*i**2*(i - 1)*(i + 1)/21
Factor -9*o**2 + 12*o**3 - 6*o - 13*o**3 - 2*o**3.
-3*o*(o + 1)*(o + 2)
Let i(z) be the first derivative of z**6/3 + 6*z**5/5 - 27*z**4/2 - 18*z**3 + 162*z**2 + 247. Factor i(v).
2*v*(v - 3)**2*(v + 3)*(v + 6)
Suppose 0 = -r + 5*r - 8. Suppose b - 2 = -5*s, -5*b + 51 = r*s + 18. Let 3*q**4 + 0*q - 10*q**2 + b*q**2 + 6*q - 6*q**3 = 0. Calculate q.
-1, 0, 1, 2
What is a in 64/3*a**3 - 4/3*a**5 - 8/3*a**2 + 8/3*a**4 + 0 - 20*a = 0?
-3, -1, 0, 1, 5
Let x(f) = 5*f**2 - 125*f - 114. Let n be x(26). Factor 32/7 - n*o + 14*o**2.
2*(7*o - 4)**2/7
Suppose 5*f - 3*w = 13, -4 = 2*w - 2. Factor -24*o**4 - 18*o - 23*o**3 + 79*o**3 - 43*o**2 - 21*o**f + 4*o**5 + 54*o - 8.
4*(o - 2)*(o - 1)**4
Let o = -744 + 747. Let c(i) be the second derivative of -8*i + 1/60*i**4 - 1/10*i**2 + 0*i**o + 0. Factor c(q).
(q - 1)*(q + 1)/5
Let g = 14 - 11. Suppose -4*b - 2 + 8 = -o, 0 = -g*o + 4*b - 2. Factor 6*v - o + 2 + 3*v**2 - 3*v.
3*v*(v + 1)
Let g = 248 - 493/2. Let s(i) be the first derivative of -5/3*i**3 + g*i**2 - 3 + 2*i. Suppose s(f) = 0. What is f?
-2/5, 1
Let r(b) be the second derivative of b**7/14 + 6*b**6/5 + 33*b**5/20 - 6*b - 17. Factor r(i).
3*i**3*(i + 1)*(i + 11)
Find g such that 4/3*g**5 + 0*g + 2/3*g**2 + 11/3*g**3 + 13/3*g**4 + 0 = 0.
-2, -1, -1/4, 0
Factor -2/9*s**3 + 10/9*s + 8/9*s**2 + 0.
-2*s*(s - 5)*(s + 1)/9
Let q = 20 - 19. Let p(a) = 2*a**2 + 1. Let y(w) be the second derivative of w**4/12 + 14*w. Let i(j) = q*p(j) - 3*y(j). Factor i(l).
-(l - 1)*(l + 1)
Suppose 7*f + 50 = 260. Let f*a + 34*a + a**4 - 62*a - 7*a**2 + 4*a**3 + 3*a**4 = 0. Calculate a.
-2, 0, 1/2
Let s(x) be the third derivative of -x**8/560 - 2*x**7/175 + 2*x**6/25 + 11*x**5/50 - 3*x**4/8 - 9*x**3/5 + 23*x**2 - 5*x. Find u, given that s(u) = 0.
-6, -1, 1, 3
Determine c so that -39/2 - 1/2*c**3 - 9/2*c**2 + 49/2*c = 0.
-13, 1, 3
Suppose 6*w - 6 = 3*w. Factor -6*p**4 - 13*p**2 + 4*p + 5*p**w + 13*p**3 - 4*p**2 + 4*p**5 - 3*p**5.
p*(p - 2)**2*(p - 1)**2
Let r be 3/((-1)/2*-2). Factor 2 + 0 + 5*u + 3 - 5*u**2 + 0 - 5*u**r.
-5*(u - 1)*(u + 1)**2
Let o(u) be the first derivative of 12 - 64/5*u - 10/3*u**6 - 104/5*u**4 + 32/3*u**3 - 84/5*u**5 + 96/5*u**2. Determine h so that o(h) = 0.
-2, -1, 2/5
Let o = -379/4 + 95. Let m(d) be the first derivative of 1/24*d**6 + 9/16*d**4 + 1/4*d**5 - 3 + o*d**2 + 7/12*d**3 + 0*d. Suppose m(y) = 0. What is y?
-2, -1, 0
Let a(j) = j**2 - 6*j + 15. Let i be a(5). Let -11*c - 3*c**2 - 9 - i*c + 9*c = 0. Calculate c.
-3, -1
Let y(s) = s**3 - 2*s**2 + 5*s - 9. Let n be y(2). Factor -20*i**4 + 5 - 6 - 8*i**3 + n.
-4*i**3*(5*i + 2)
Let v = -32 - -48. Let x be -15 + v + 6/(-14). Find l, given that x*l**2 + 2/7*l + 2/7*l**3 + 0 = 0.
-1, 0
Let m be 0 + (198/(-11))/(-9). Let -1/3*i**m - 1/3*i**4 + 2/3 - i + i**3 = 0. What is i?
-1, 1, 2
Let n be 12/(-258) + 5340/3870. What is b in -n*b**3 + 0 + 1/3*b**4 - 2/3*b + 5/3*b**2 = 0?
0, 1, 2
Let w(v) be the third derivative of -1/12*v**6 - 3*v**2 - 3/32*v**4 + 0*v + 0 + 0*v**3 - 2/105*v**7 - 11/80*v**5. Factor w(y).
-y*(y + 1)*(4*y + 3)**2/4
Determine u, given that 8/9*u**2 + 8/3*u - 2*u**3 + 2/9*u**5 + 0 + 0*u**4 = 0.
-3, -1, 0, 2
Solve 4/3*s - 32*s**2 + 32 - 4/3*s**3 = 0.
-24, -1, 1
Let v(k) be the third derivative of -k**6/540 - 4*k**5/135 - 5*k**4/27 - 16*k**3/27 - 15*k**2. Factor v(f).
-2*(f + 2)**2*(f + 4)/9
Factor -2/7*x**2 + 0 + 8/7*x.
-2*x*(x - 4)/7
Let d(t) = -t**2 + 10*t - 16. Let y be d(7). Suppose -10 = -3*m - 2*m, f - 10 = -y*m. Factor -4*v**2 + 2*v - 2 - 4*v**3 + 3*v - 2*v**5 + f*v**5 + 6*v**4 + v.
-2*(v - 1)**4*(v + 1)
Let r(b) be the third derivative of -1/72*b**4 - 1/315*b**7 + 0*b**3 + 11*b**2 + 1/90*b**5 + 1/1008*b**8 + 0*b**6 + 0*b + 0. Solve r(o) = 0 for o.
-1, 0, 1
Suppose -17 = -4*s - 1. Let -12*l**5 - 6*l**3 + 9*l**5 - 9*l**s + 9*l**2 - 9*l**2 = 0. Calculate l.
-2, -1, 0
Let l = -28 - -32. Find d, given that 35*d + 7 + 6 + 5*d**2 + l + 13 = 0.
-6, -1
Let x be 0*((-4)/10)/(-2 + 56/20). Factor x + 0*r**4 + 15/2*r**3 - 5/2*r**5 + 0*r + 5*r**2.
-5*r**2*(r - 2)*(r + 1)**2/2
Let a(b) be the third derivative of -b**7/420 + 7*b**6/480 - b**5/60 - b**4/24 + 5*b**2 + 39*b. Suppose a(c) = 0. Calculate c.
-1/2, 0, 2
Let q(s) = s**2 - 73*s + 1276. Let h be q(29). Factor 0 - k + h*k**2 + 1/4*k**3.
k*(k - 2)*(k + 2)/4
Let b(m) be the first derivative of 2*m**3/3 + 35*m**2 + 68*m - 119. Find x such that b(x) = 0.
-34, -1
Let g(c) be the first derivative of 3*c**5/5 + 3*c**4/2 + c**3 - 50. Factor g(u).
3*u**2*(u + 1)**2
Let b(c) be the first derivative of -1/12*c**4 - 1/9*c**3 + 8 + 1/6*c**2 + 1/3*c. Factor b(f).
-(f - 1)*(f + 1)**2/3
Let x be 0*((-60)/(-6))/10. What is t in 4/7*t + x + 2/7*t**2 = 0?
-2, 0
Let c = 911 - 907. Find k, given that -8/7*k**c + 0 - 36/7*k**3 - 12/7*k - 40/7*k**2 = 0.
-3, -1, -1/2, 0
Let -23/5*g**2 + 6*g**3 + 0 + 9/5*g**4 + 4/5*g = 0. What is g?
-4, 0, 1/3
Let p(u) be the first derivative of -2*u**3/27 + 13*u**2/9 + 28*u/9 + 622. Factor p(k).
-2*(k - 14)*(k + 1)/9
Let t(q) be the first derivative of q**6/21 - 2*q**5/5 + 8*q**4/7 - 16*q**3/21 - 16*q**2/7 + 32*q/7 - 156. Factor t(k).
2*(k - 2)**4*(k + 1)/7
Let n(a) be the third derivative of -13*a**2 + 1/48*a**4 + 0*a + 0*a**3 + 1/240*a**5 + 0. Find h, given that n(h) = 0.
-2, 0
Solve 861*g**4 + 841*g**4 + 120*g**3 - 1730*g**4 + 24*g - 116*g**2 = 0 for g.
0, 2/7, 1, 3
Let n(u) = -u**2 + u - 1. Let b(t) = t**2 - t + 1. Let d(x) = -3*b(x) - 2*n(x). Let g = -3 - -4. Let r(h) = 6*h - 2. Let j(o) = g*r(o) - 2*d(o). Factor j(s).
2*s*(s + 2)
Let i(w) be the first derivative of w**6/140 + 2*w**5/35 + w**4/7 + 5*w**2/2 - 21. Let o(r) be the second derivative of i(r). Factor o(l).
6*l*(l + 2)**2/7
Let l = 5315 - 611231/115. Let p = l - -478/345. Factor 40/3*t - 100/3 - p*t**2.
-4*(t - 5)**2/3
Let i(c) be the first derivative of c**6/2160 - c**5/144 + c**4/36 + 7*c**3/3 + 8. Let l(j) be the third derivative of i(j). What is d in l(d) = 0?
1, 4
Let g = -414 - -2098/5. Factor 0 - 4/5*s**2 + g*s.
-4*s*(s - 7)/5
Let z(i) be the second derivative of 3/35*i**5 + 1/21*i**3 - 2/21*i**4 + 0*i**2 + 0 + 3*i + 1/147*i**7 - 4/105*i**6. Find u, given that z(u) = 0.
0, 1
Let x(r) be the third derivative of -r**6/180 + r**5/15 - r**4/4 + 4*r**3/9 - 42*r**2. Factor x(g).
-2*(g - 4)*(g - 1)**2/3
Factor 0 - 2/5*u - 4/5*u**3 + u**2 + 1/5*u**4.
u*(u - 2)*(u - 1)**2/5
Factor -b**5 - 10*b + 4*b + 12*b**4 + 3*b**3 - 9*b**4 - 7*b**2.
-b*(b - 3)*(b - 2)*(b + 1)**2
Let z(c) be the first derivative of -2*c**3/3 - 14*c**2 - 98*c - 47. Factor z(u).
-2*(u + 7)**2
Let u = -34 - -36. Suppose -c + 10 = 2*g + 2*g, 12 = 5*g + c. Factor -o**2 - 2*o**g + 5*o**u + 6*o - 9 - 3*o**2.
-(o - 3)**2
Let t = 2/1147 + 30959/5735. What is q in 21/5*q**5 - 3*q**3 - t*q**2 + 27/5*q**4 - 6/5*q + 0 = 0?
-1, -2/7, 0, 1
Let d be (-19 + 18)/((10/(-4))/5). Let z(j) be the first derivative of 1/5*j**3 + 0*j - 3 - 3/10*j**d. Factor z(c).
3*c*(c - 1)/5
Let q be 36/33*1529/2085. Factor -q*b + 0 - 4/5*b**2.
-4*b*(b + 1)/5
Let v(l) be the second derivative of l**5/35 - l**4/7 - l - 24. Suppose v(q) = 0. What is q?
0, 3
Let t(s) be the third derivative of -s**8/5880 - s**7/980 - s**6/420 - s**5/420 + 4*s**3/3 - 5*s**2. Let l(f) be the first derivative of t(f). Factor l(u).
-2*u*(u + 1)**3/7
Let a(g) = -g**3 - 3*g**2 - 4*g - 8. Let h be a(-3). Suppose h*r - 4 = 0, -3*r + r = -t. Factor 2/15*o**3 - 2/15*o**t + 0 - 2/15*o + 2/15*o**4.
2*o*(o - 1)*(o + 1)**2/15
Let p be 178/178 + 3*4/6. Let a(l) be the first derivative of 0*l + 0*l**4 + 0*l**2 - 7 + 2/21*l**p - 2/35*l**5. Find j, given that a(j) = 0.
-1, 0, 1
Let i(r) = 2*r**3 + 35*r**2 + 117*r + 4. Let b be i(-13). Suppose -64/13*k + 48/13*k**2 - 16/13*k**3 + 2/13*k**b + 32/13 = 0. What is k?
2
Let w be 15 + ((-15)/2 - 7). Let m be 3 + -1 - (-5 - -5). Determine a so that -1/4*a**m + w*a + 0 = 0.
0, 2
Let a be 12/(-114) + -2 + 5540/2090. Factor 6/11*o**2 - 6/11*o**3 + 0 + a*o - 6/11*o**4.
-6*o*(o - 1)*(o + 1)**2/11
Let u(o) be the first derivative of -5*o**7/14 - o**6/3 + o**5 + 5*o**4/6 - 5*o**3/6 + 7*o + 3. Let z(w) be the first derivative of u(w). What is g in z(g) = 0?
-1, 0, 1/3, 1
Let k(t) be the second derivative of 