k) be the second derivative of h(k). Factor x(l).
3*(l - 1)*(l + 2)
Let g(j) be the second derivative of -j**6/90 + j**5/3 - 25*j**4/6 - 2*j**3 + 6*j. Let u(v) be the second derivative of g(v). Find c, given that u(c) = 0.
5
Suppose 0 = 5*q - 10*q + 10. Find w, given that -12*w - 15*w**2 + 3*w**q + 16 + 2*w**2 = 0.
-2, 4/5
Find y such that 3*y**3 + 5913*y + 134325*y**2 - 134007*y**2 + 2823*y + 16224 = 0.
-52, -2
Let q(j) be the third derivative of 0*j**5 - 2/735*j**7 + 0*j**4 - 11*j**2 - 1/210*j**6 + 0 + 1/784*j**8 + 0*j**3 + 0*j. Factor q(n).
n**3*(n - 2)*(3*n + 2)/7
Suppose 0 = -6*t + 3*t - 213. Let h = t - -499/7. Factor 0 + 2/7*b**3 + 0*b**2 - h*b.
2*b*(b - 1)*(b + 1)/7
Let c(r) be the third derivative of -r**8/20160 + r**7/2520 + r**6/360 - r**5/45 - r**4/2 - r**2 - 4*r. Let m(p) be the second derivative of c(p). Factor m(k).
-(k - 4)*(k - 1)*(k + 2)/3
Suppose 4*l - l = 0. Factor 15*t - 39 - 9*t**2 + 33 + l*t**2.
-3*(t - 1)*(3*t - 2)
Let r(f) = 35*f**2 + 124*f - 43. Let h(l) = 35*l**2 + 122*l - 44. Let o(m) = 3*h(m) - 4*r(m). Suppose o(y) = 0. What is y?
-4, 2/7
Let p(c) be the first derivative of c**4/4 + 3*c**3 - c**2/2 - 5*c + 10. Let o be p(-9). Find n, given that -7/5*n**o - 19/5*n**3 + 0 - 8/5*n**2 + 4/5*n = 0.
-2, -1, 0, 2/7
Factor 4/11*l**2 - 2/11 + 0*l**3 - 2/11*l**4 + 0*l.
-2*(l - 1)**2*(l + 1)**2/11
Suppose 2*s - 6 = -2. What is d in 31*d + 27*d**s + 23 + 22 + 8*d**2 + 44*d + 5*d**3 = 0?
-3, -1
Factor -49/4 - 7/2*l - 1/4*l**2.
-(l + 7)**2/4
Let k = 67 + -63. Factor 9*i**4 + 3 + k*i - 15*i**2 - 3*i**3 + 4*i - 5*i + 3.
3*(i - 1)**2*(i + 1)*(3*i + 2)
Let x(p) be the third derivative of 5*p**8/448 + 11*p**7/140 + 7*p**6/40 + p**5/10 - 2*p**2 + 65. Factor x(a).
3*a**2*(a + 2)**2*(5*a + 2)/4
Factor 12/5*f - 2 - 2/5*f**2.
-2*(f - 5)*(f - 1)/5
Factor -63 + r**2 + 1305*r - 307 - 36*r**2.
-5*(r - 37)*(7*r - 2)
Let m(p) be the second derivative of -p**5/50 + p**4/15 + 13*p**3/15 + 2*p**2 + 86*p + 3. Find s, given that m(s) = 0.
-2, -1, 5
Let u(t) be the first derivative of -1/16*t**4 + t + 5/12*t**3 - t**2 + 5. Suppose u(w) = 0. What is w?
1, 2
Let y(j) be the first derivative of -2*j**4/9 - 10*j**3/9 - 4*j**2/3 + 8*j/9 + 51. Factor y(r).
-2*(r + 2)**2*(4*r - 1)/9
Let c = -356 - -359. Let o(m) be the second derivative of 0 - 4*m + 1/12*m**4 + 9/2*m**2 + m**c. What is s in o(s) = 0?
-3
Let j(v) be the first derivative of v**3/4 - 21*v**2/4 - 45*v/4 - 114. Determine w so that j(w) = 0.
-1, 15
Let v be 16 + -12*(-95)/(-75). Suppose -v*p**2 - 8/5*p**3 - 2/5*p**4 + 8/5*p + 6/5 = 0. Calculate p.
-3, -1, 1
Factor 1/3*j**2 - 2/3*j - 8.
(j - 6)*(j + 4)/3
Let p(c) = c + 7. Let n be p(-9). Let l be (n + 23)/3 - 3. Factor 30*r + 23*r**3 - 17*r + 2 + 4*r**4 + 27*r**2 + 3*r**l.
(r + 1)**3*(7*r + 2)
Let p = -350/3 + 118. Let x(j) be the first derivative of -1/2*j**4 - 16/5*j**5 - 3 + 5*j**2 + 14/3*j**3 - p*j**6 + 2*j. Find i such that x(i) = 0.
-1, -1/2, 1
Let s(g) be the first derivative of 20 + 5/3*g**3 + 0*g - 5/2*g**2. Factor s(v).
5*v*(v - 1)
Let j(o) be the second derivative of 0 + 31*o - 3*o**2 - 1/2*o**3 + 3/20*o**5 + 1/2*o**4. Factor j(b).
3*(b - 1)*(b + 1)*(b + 2)
Let v(l) be the third derivative of l**7/280 - 3*l**6/40 - 27*l**5/80 - 7*l**4/16 - 55*l**2. Factor v(p).
3*p*(p - 14)*(p + 1)**2/4
Let v(j) be the third derivative of 7*j**6/40 - 27*j**5/10 - 79*j**4/8 - 9*j**3 - j**2 + 29. Factor v(u).
3*(u - 9)*(u + 1)*(7*u + 2)
Let d(s) be the first derivative of 10/27*s**3 - 15 - 8/9*s - 8/9*s**2. Factor d(i).
2*(i - 2)*(5*i + 2)/9
Let o be 5/7 + (-4)/(-14). Suppose -o = 6*p - 13. Factor -7/2*d**p + 3/2*d**3 - 1/2 + 5/2*d.
(d - 1)**2*(3*d - 1)/2
Let y(t) = t**2 + t. Let q(o) = -8*o**3 - 404*o**2 - 5600*o - 2704. Let v(r) = -q(r) + 16*y(r). Find m, given that v(m) = 0.
-26, -1/2
Let y(r) be the third derivative of -r**5/240 - 3*r**4/32 + r**2 + 4*r. Find i, given that y(i) = 0.
-9, 0
Let i(s) be the second derivative of 16/7*s**3 + 10*s + 0 + 21/20*s**5 - 11/4*s**4 - 6/7*s**2. Factor i(l).
3*(l - 1)*(7*l - 2)**2/7
Let z(w) be the third derivative of 0 + 16*w**2 + 0*w - 2/315*w**7 - 1/40*w**6 - 1/30*w**5 - 1/72*w**4 + 0*w**3. Solve z(g) = 0 for g.
-1, -1/4, 0
Let c(x) = -18*x**2 - 230*x + 28. Let m(z) = 37*z**2 + 461*z - 58. Let l(u) = 11*c(u) + 6*m(u). Factor l(w).
4*(w + 10)*(6*w - 1)
Let p(k) be the first derivative of k**6/165 + k**5/22 + 2*k**4/33 + 9*k - 2. Let h(y) be the first derivative of p(y). Find x, given that h(x) = 0.
-4, -1, 0
Let h = 34 + -32. What is j in 5*j**2 - 4*j + 15*j**h - 6*j**2 - 10*j**3 = 0?
0, 2/5, 1
Let f(k) be the second derivative of k**4/54 + 2*k**3/27 - 5*k. Suppose f(n) = 0. Calculate n.
-2, 0
Factor 4/5*p**2 - 48*p + 720.
4*(p - 30)**2/5
Find z such that -7*z + 12 + 1/2*z**2 = 0.
2, 12
Let s be (-39)/(-30) - (-1)/5. Let a(y) be the first derivative of y**3 + s*y**2 - 6*y + 5. Let a(n) = 0. What is n?
-2, 1
Let z = 116 - 111. Suppose q = -z*q + 12. Factor -8/5 + 2*i - 2/5*i**q.
-2*(i - 4)*(i - 1)/5
Let x = -714 + 3572/5. Let a(b) be the first derivative of x*b**3 + 2/5*b**2 + 0*b - 4 + 1/10*b**4. Factor a(g).
2*g*(g + 1)*(g + 2)/5
Let a(m) be the second derivative of -m**7/42 - 2*m**6/15 + m**5/5 + 17*m**4/6 + 15*m**3/2 + 9*m**2 + 397*m + 1. Suppose a(r) = 0. What is r?
-3, -2, -1, 3
Let f(a) be the second derivative of -1/12*a**3 + 7/80*a**5 - 4*a - 5/168*a**7 + 1/16*a**4 + 0*a**2 - 1/40*a**6 + 0. Find t such that f(t) = 0.
-1, 0, 2/5, 1
Factor 28*c**3 + 66*c**3 + c**5 + 128 - 42913*c**2 - 96*c - 24*c**4 + c**5 + 42809*c**2.
2*(c - 4)**3*(c - 1)*(c + 1)
Let i(v) = v. Let w = -3 + 4. Suppose 2*b + w = -7. Let j(m) = m**3 - m**2 + 4. Let g(u) = b*i(u) + j(u). Factor g(x).
(x - 2)*(x - 1)*(x + 2)
Let o = 2/649 - -643/1947. Solve -4/3*i**4 + 0*i + o*i**5 + 4/3*i**3 + 0 + 0*i**2 = 0.
0, 2
Let u(i) be the second derivative of 0 - 4*i + 0*i**3 + 1/90*i**5 + 1/54*i**4 + 0*i**2. Factor u(r).
2*r**2*(r + 1)/9
Let z(w) be the first derivative of -w**6/24 - w**5/2 + w**4/8 + 5*w**3/3 - w**2/8 - 5*w/2 + 119. Solve z(n) = 0 for n.
-10, -1, 1
Let r(d) be the second derivative of d**4/42 + 4*d**3/3 - 724*d. Solve r(g) = 0 for g.
-28, 0
Let r be (8/10)/((-80)/(-200)). Let x(j) be the second derivative of -7*j + 3/20*j**4 - 9/10*j**3 + 0 - 1/100*j**5 + 27/10*j**r. Let x(c) = 0. What is c?
3
Let n(y) be the first derivative of 4*y**3/5 + 14*y**2/5 - 24*y/5 + 70. Factor n(r).
4*(r + 3)*(3*r - 2)/5
Factor 24389/5 + 2523/5*t + 87/5*t**2 + 1/5*t**3.
(t + 29)**3/5
Let o(k) be the third derivative of -4/15*k**5 + 0 - 1/84*k**8 + 4/105*k**7 + 0*k**3 + 1/10*k**6 + 11*k**2 + 0*k - 2/3*k**4. Suppose o(x) = 0. What is x?
-1, 0, 2
Let v = 3827 - 7651/2. Factor -3 - 3/4*u**4 + 3*u + 9/4*u**2 - v*u**3.
-3*(u - 1)**2*(u + 2)**2/4
Let k = -169 - -172. Let y be (3 + k - 3)*1/6. Determine f so that -1/2*f**2 + 1/4*f - 1/4*f**3 + y = 0.
-2, -1, 1
Let f(t) be the first derivative of t**6/36 - 2*t**5/15 + t**4/8 + 2*t**3/9 - t**2/3 + 29. Factor f(v).
v*(v - 2)**2*(v - 1)*(v + 1)/6
Suppose r = 5*b + 12, 5*r - b = 40 + 20. Let w = -9 + r. Factor -5*s + 2*s**3 - 3*s**3 + 4*s**w + 2*s.
3*s*(s - 1)*(s + 1)
Let c = -24925 + 124627/5. Let b = 3 - 1. Factor 2/5*u**b + c + 4/5*u.
2*(u + 1)**2/5
Let u(b) = -51*b**2 - 1767*b + 693. Let y(g) = 13*g**2 + 442*g - 174. Let i(a) = 2*u(a) + 9*y(a). Suppose i(n) = 0. Calculate n.
-30, 2/5
Let b(z) be the first derivative of -z**5/110 - z**4/33 + z**3/33 + 2*z**2/11 - 12*z + 9. Let j(p) be the first derivative of b(p). Factor j(v).
-2*(v - 1)*(v + 1)*(v + 2)/11
Let g(k) = -k**2 + 924*k**3 - 6*k**2 - 927*k**3. Let l(h) = -3*h**3 - 6*h**2. Let y(u) = 3*g(u) - 4*l(u). Let y(w) = 0. What is w?
-1, 0
Let m = -1988 + 1990. Factor 2/7*o**3 - 10/7*o + 2/7*o**m + 6/7.
2*(o - 1)**2*(o + 3)/7
Factor 48*x**2 + x**4 + 4*x**4 + 4*x**4 - 2*x**4 - 36*x - 21*x**3 - 4*x**4.
3*x*(x - 3)*(x - 2)**2
Let b = -23 - -25. Factor -3/2*p**b - 1 - 5/2*p.
-(p + 1)*(3*p + 2)/2
Let p(y) be the second derivative of y**5/24 - 20*y**4/9 + 475*y**3/12 - 375*y**2/2 + 112*y. Factor p(s).
5*(s - 15)**2*(s - 2)/6
Suppose g + 5 = 0, 0 = 3*w - 0*g + 5*g - 668. Let u be (-2)/(-11) - (-90)/w. Factor 2/7*b + u - 2/7*b**2.
-2*(b - 2)*(b + 1)/7
Factor 3/8*k - 3/8*k**3 + 165/4*k**2 - 165/4.
-3*(k - 110)*(k - 1)*(k + 1)/8
Let x = 43 + -41. Let 0*c**4 - 10 - 15*c