
Let h(n) be the first derivative of n**8/224 - n**7/120 + n**6/240 + 7*n**2 + 10. Let m(f) be the second derivative of h(f). Factor m(x).
x**3*(2*x - 1)*(3*x - 2)/4
Let b(j) be the first derivative of -2*j**5/45 - j**4/6 + 10*j**3/27 + j**2/3 - 8*j/9 - 21. Find y, given that b(y) = 0.
-4, -1, 1
Let j(s) be the first derivative of 3*s**5/5 + 33*s**4/4 + 33*s**3 + 111*s**2/2 + 42*s - 352. Factor j(p).
3*(p + 1)**2*(p + 2)*(p + 7)
Solve -12/5 - 2*x - 2/5*x**2 = 0.
-3, -2
Let a(h) be the first derivative of -2/5*h**4 + 2/15*h**3 + 13 - 2/5*h + 4/5*h**2. Solve a(i) = 0 for i.
-1, 1/4, 1
Let g be -5 + (-187)/68*(-2)/1. Solve -g + 3/4*c - 1/4*c**2 = 0.
1, 2
Let w(t) = t + 1. Let v(y) = 2 + y + 6*y**2 + y**4 - 242*y**3 + 238*y**3 + 4. Let c(h) = -v(h) + 5*w(h). Factor c(l).
-(l - 1)**4
Let s(v) = -2*v**2 - 9*v - 1. Let r be s(-4). Find y such that y**4 + r*y**2 + 3 - 9*y - 7*y**4 - 3*y**3 + 12*y**3 + 0 = 0.
-1, 1/2, 1
Let q be 8/(-90)*((-5)/15)/(36/162). Determine z, given that 4/5*z**2 + 6/5*z + 0 + q*z**3 = 0.
-3, 0
Let a(c) be the first derivative of 1/5*c**2 - 2/15*c**3 + 0*c + 14. Factor a(r).
-2*r*(r - 1)/5
Let s be (6/15)/(2/10). Factor -8*r**s + 12*r + 12*r**2 - 2 - 17 + 3.
4*(r - 1)*(r + 4)
Let f(u) = -2*u**3 + 13*u**2 - 5*u - 3. Let r be f(6). Factor j + 533 - 531 - j**r + 2*j.
-(j - 2)*(j + 1)**2
Let o(d) be the first derivative of d**6/14 - 3*d**5/5 + 45*d**4/28 - 13*d**3/7 + 6*d**2/7 + 88. Find b, given that o(b) = 0.
0, 1, 4
Let s(h) be the third derivative of -h**6/60 - h**5/10 - h**4/4 - h**3/3 - 2*h**2 + 101. What is k in s(k) = 0?
-1
Let j(s) = s**3 + 7*s**2 + 2*s - 9. Let p be j(-6). What is q in p*q**2 + 0*q + 5*q - 3*q - 5*q**3 + 3*q - 15 = 0?
-1, 1, 3
Let t be 30/(-33) + 2296/1848. Find f such that -5/6*f**3 - t - 2*f**2 - 3/2*f = 0.
-1, -2/5
Let b = 6 - 21. Let g = 18 + b. Factor 90*h**4 + 27*h**5 + 17*h - 19*h**3 + 130*h**g - 5*h + 60*h**2.
3*h*(h + 1)**2*(3*h + 2)**2
Let n be (-6)/2 + -1 + (0 - 0). Let g be ((-6)/n - -1)*(-68)/(-255). Solve -2/3*w - 2/3 + g*w**3 + 2/3*w**2 = 0.
-1, 1
Let t(d) be the first derivative of 3/2*d**2 - 1/30*d**5 - 4 + 0*d**3 + 0*d - 1/12*d**4. Let j(x) be the second derivative of t(x). Let j(i) = 0. Calculate i.
-1, 0
Let h(i) = 13*i**2 + i + 14. Let b(g) = 9*g**2 + g + 10. Let u(j) = -7*b(j) + 5*h(j). Let u(m) = 0. What is m?
0, 1
Let z be ((-2)/(84/(-45)))/(-1 + (-125)/(-105)). What is f in -27/4 - z*f**2 - 81/8*f - 1/8*f**4 - 11/8*f**3 = 0?
-3, -2
Suppose -8*q = 5*q + 208. Let f be q/(-60)*2*(-6)/(-4). What is l in 0 + 3/5*l + f*l**2 + 1/5*l**3 = 0?
-3, -1, 0
Let j(l) = -l**2 + 37*l + 2. Let g be j(37). Let w(r) be the first derivative of -3/4*r**g - 9/4*r - 4 - 1/12*r**3. Factor w(h).
-(h + 3)**2/4
Find k, given that -12*k - 3 + 99/4*k**4 + 141/2*k**3 + 147/4*k**2 = 0.
-2, -1, -2/11, 1/3
Let o be (2/(-4))/((-25)/90). Factor -6/5 - 24/5*m**2 - 21/5*m - o*m**3.
-3*(m + 1)**2*(3*m + 2)/5
Let n be 2*((3 - 5) + 10). Suppose 0 = 3*f + f - n. Factor 4*k**5 + 0*k**f - 4*k**4 + k**2 + 3*k**2 - 4*k**3.
4*k**2*(k - 1)**2*(k + 1)
Let q = -162 - -165. Let p(f) be the second derivative of 0 - 1/12*f**4 + 1/6*f**q - 2*f + 0*f**2. Suppose p(x) = 0. Calculate x.
0, 1
Let j(n) be the first derivative of -7 - 4/3*n + 2/9*n**3 + 1/3*n**2. Factor j(x).
2*(x - 1)*(x + 2)/3
Let b = 17/14 - -167/70. Factor -14/5*p**2 - 4/5 - b*p.
-2*(p + 1)*(7*p + 2)/5
Let b be 756/324 + -1 + 1. Let h be 2/6 - 2/(-6). Solve 7/3*u**2 - h*u**3 + 2/3 - b*u = 0 for u.
1/2, 1, 2
Let z(f) be the third derivative of f**6/20 + 14*f**5/15 + 3*f**4/4 + 26*f**2. Factor z(i).
2*i*(i + 9)*(3*i + 1)
Factor 4*d**2 - d - 3*d - 159 + 39 + 8*d.
4*(d - 5)*(d + 6)
Determine z, given that -34*z - 66*z**2 - 24*z + 10*z - 5*z**3 + 3*z**4 - 10*z**3 = 0.
-2, -1, 0, 8
Let c(u) = u**3 + 2*u**2 + u + 87. Let y be c(0). Let b be (-2 - y/(-42))*(3 - -1). Factor -b*k + 2/7*k**3 + 0*k**2 + 0.
2*k*(k - 1)*(k + 1)/7
Let r = 11 - 8. Find a such that 0*a**r + 6/7*a**4 - 6/7*a**2 + 0 + 3/7*a - 3/7*a**5 = 0.
-1, 0, 1
Let v(d) be the second derivative of d**7/63 - 13*d**6/45 - 17*d**5/30 + 41*d**4/18 + 16*d**3/9 - 28*d**2/3 + d - 34. Suppose v(o) = 0. What is o?
-2, -1, 1, 14
Let q(s) = 0*s**2 - 3*s**2 + 4*s + 0*s + 2*s**2 + 6. Let g be q(5). Factor 2 + 8*w**2 + g + 10*w + 2*w**3 + 1.
2*(w + 1)**2*(w + 2)
Let y(t) be the third derivative of t**5/12 - 205*t**4/24 - 35*t**3 - 134*t**2. Factor y(c).
5*(c - 42)*(c + 1)
Let b(u) be the second derivative of u**4/60 + 19*u**3/15 + 361*u**2/10 - 120*u. Find h such that b(h) = 0.
-19
Let n = -1570 + 1572. Let k(s) be the first derivative of 3/2*s**n - 1/3*s**3 + 8 + 4*s. Factor k(x).
-(x - 4)*(x + 1)
Let b be 1 + 0/(-1) + 5. Let l = b + -4. Factor 1/2 - 1/4*j**l + 1/4*j.
-(j - 2)*(j + 1)/4
Let s be (292/4672)/(1 - 3/4). Suppose -2*l + 4*x = -18, 0 = -4*x - x - 15. Suppose -s*j**l + 0*j - 1/4*j**2 + 0 = 0. What is j?
-1, 0
Suppose -42*l**4 - 93*l - 131*l**2 - 67*l**2 + 18*l**4 - 15 - 156*l**3 = 0. Calculate l.
-5, -1/2
Let t(p) = 2*p**2. Let q be t(1). Suppose -1 - 5 = -q*o. Determine u so that -u**2 + 2 + u**3 + u - 2*u**o + u**2 - 2*u**2 = 0.
-2, -1, 1
Solve -106*r**3 - 156*r**2 + 38*r - 22*r**4 + 68*r + 16 - 162*r = 0 for r.
-2, -1, 2/11
Let n(q) be the second derivative of -q**6/6 - 16*q**5/15 - 2*q**4/3 + 43*q**3/6 + 13*q. Let p(t) be the second derivative of n(t). Factor p(m).
-4*(m + 2)*(15*m + 2)
Let h(o) be the second derivative of 15*o - 4/9*o**4 + 0 - 2*o**3 - 4/3*o**2. Factor h(v).
-4*(v + 2)*(4*v + 1)/3
Let h be -4 + (1 - 20/(-4)). Let -2*x**h + 0*x**2 + 18*x + 0*x**2 - 50 + 2*x = 0. Calculate x.
5
Let m be 18/16*(-20)/(-6). Let s be ((96/28)/4)/(6*9/252). What is i in 3/4*i**3 - 3/4*i**s + m*i**2 + 0 + 9/4*i = 0?
-1, 0, 3
Determine v, given that 0*v + 182/9*v**3 + 4/9*v**2 + 0 = 0.
-2/91, 0
Let q be (-52)/(-5)*(-25)/10. Let l be ((-1)/(-1))/(q/(-39)). Determine k, given that -l*k + 3/4*k**2 + 3/4 = 0.
1
Suppose 8*j = 6*j + 22. Suppose 0 = j*p - 30 + 8. Suppose 3/2*v - 1/4*v**p - 9/4 = 0. Calculate v.
3
Let h = -4523 + 4527. Let -1/5*n**h + 1/5*n**5 + 1/5*n - 1/5 - 2/5*n**3 + 2/5*n**2 = 0. Calculate n.
-1, 1
Suppose -61*m + 2004*m**2 + 400 + 1506*m + 75*m + 196*m**4 + 1064*m**3 = 0. Calculate m.
-2, -5/7
Let k(s) be the second derivative of -s**7/140 + 15*s**2 + 18*s. Let p(g) be the first derivative of k(g). Factor p(v).
-3*v**4/2
Let 476*o - 3292*o**2 - 3 - 44*o - 4271*o**2 - 7989*o**2 = 0. Calculate o.
1/72
Let f(s) be the third derivative of s**8/4480 - s**4/6 + 16*s**2. Let m(k) be the second derivative of f(k). Solve m(x) = 0.
0
Factor -3/10*h**3 + 49/5*h**2 - 416/5*h + 256/5.
-(h - 16)**2*(3*h - 2)/10
Let y be (12/14)/(10/35). Solve y*h + 9*h - 15*h**3 - 18 - 2*h**4 + 18*h**2 + 5*h**4 - 6 = 0.
-1, 2
Let d(n) be the second derivative of -3/100*n**5 + 7/20*n**4 + 0 - 24/5*n**2 + 35*n - 4/5*n**3. Determine a, given that d(a) = 0.
-1, 4
Let p = -1822 - -1824. Let c(o) be the third derivative of 0 + 2*o**p + 0*o + 0*o**3 - 1/30*o**6 - 1/15*o**5 + 0*o**4 + 1/84*o**8 + 2/105*o**7. Factor c(r).
4*r**2*(r - 1)*(r + 1)**2
Let p(h) = -h**3 - 7*h**2 - 36*h - 22. Let u(s) = s**3 - s**2 + s - 1. Let m(b) = -5*p(b) - 10*u(b). What is t in m(t) = 0?
-2, -1, 12
Let m(o) = -o - 2. Let w be m(-8). Let n = w + 5. Let -i**2 - i**2 + n*i - 5*i - 4 = 0. What is i?
1, 2
Let c(j) be the first derivative of j**8/2016 + j**7/315 + 13*j**2 - j - 40. Let g(x) be the second derivative of c(x). Factor g(t).
t**4*(t + 4)/6
Let t(h) be the second derivative of h**5/30 + h**4/18 - h**3/9 - 9*h**2/2 + 5*h. Let m(f) be the first derivative of t(f). Factor m(y).
2*(y + 1)*(3*y - 1)/3
Let z be (-13)/38*(-496)/1612. Factor z*u**3 + 16/19*u**2 + 32/19*u + 0.
2*u*(u + 4)**2/19
Suppose 62 - 50 = -2*z - 4*u, -2*z - 5*u = 16. Suppose -3*f = -0*f. Solve 2/7*h**z + f - 2/7*h - 2/7*h**4 + 2/7*h**3 = 0.
-1, 0, 1
Suppose -5*u + 25 = 3*b, -10*b = -3*u - 15*b + 15. Let l(o) be the first derivative of 3/4*o**2 + 0*o + 7 + 9/10*o**u - 15/8*o**4 + 1/2*o**3. Factor l(a).
3*a*(a - 1)**2*(3*a + 1)/2
Let u(d) = -d**3. Let n(p) be the first derivative of -7*p**4/4 - 10*p**3/3 + 5*p**2/2 + 10*p - 6. Let o(y) = -n(y) + 2*u(y). Solve o(l) = 0.
-2, -1, 1
Let k(r) be the first derivative of -6*r + 2/3*r**3 + 2*r**2 + 14. Determine m so that k(m) = 0.
-3, 1
Let t(y) be th