hird derivative of 56*c**2 + 0*c**4 + 0*c + 0 + 1/120*c**5 + 0*c**3. Factor u(b).
b**2/2
Let n(s) be the second derivative of s**7/1176 + s**6/360 + s**5/420 - 7*s**3/6 - s. Let f(a) be the second derivative of n(a). Suppose f(v) = 0. What is v?
-1, -2/5, 0
Let t(g) be the third derivative of -g**8/2880 + g**7/630 - g**6/720 - g**5/180 - 5*g**4/24 - 6*g**2. Let y(c) be the second derivative of t(c). Factor y(k).
-(k - 1)**2*(7*k + 2)/3
Let m(o) be the third derivative of 3*o**8/140 + 26*o**7/175 + 43*o**6/150 - 7*o**5/75 - 8*o**4/15 + 8*o**3/15 + 218*o**2 - 2. Let m(s) = 0. What is s?
-2, -1, 1/3
Let h(l) be the first derivative of -2*l**5/35 + 5*l**4/14 - 2*l**3/7 - 9*l**2/7 - 140. Factor h(u).
-2*u*(u - 3)**2*(u + 1)/7
Let l(k) = k**3 - 20*k**2 + 35*k + 16. Let t be l(18). Let z be ((t - 1)/(-1))/(6 + -2). What is w in 1/2 - z*w**3 - 1/4*w**4 + 3/4*w - 1/4*w**2 = 0?
-2, -1, 1
Let p = 5000 - 85045/17. Let x = p - -361/85. Determine a so that 8/5*a**2 + 0 + 2/5*a**3 + x*a = 0.
-2, 0
Let g = 19/13 - 31/39. Suppose -8/15*q**2 - 4/15 + g*q + 2/15*q**3 = 0. Calculate q.
1, 2
Let b = 2 + 1. Suppose 2*j = -4, -b*j = -3*u + 5 + 7. Solve 1 + c + c + 3 - u*c**2 = 0 for c.
-1, 2
Let b(k) be the first derivative of -8 + 3/20*k**4 + 1/15*k**3 + 1/25*k**5 - 2/5*k - 3/10*k**2. Factor b(q).
(q - 1)*(q + 1)**2*(q + 2)/5
Let i(k) be the first derivative of 1/15*k**3 + 7 + 6/5*k - 7/10*k**2. Find y, given that i(y) = 0.
1, 6
Let y(s) be the first derivative of s**5/105 - 6*s**2 + 4. Let c(u) be the second derivative of y(u). Solve c(l) = 0 for l.
0
Let n(s) = s**2 + 3*s - 3. Let k be n(-4). Let l = 3 + k. Solve 3*f**l - 5*f**3 + 3*f**4 - 2*f**5 + f**3 = 0.
0, 1, 2
Let w(g) be the third derivative of -g**5/12 - 35*g**4/24 - 25*g**3/3 - 60*g**2. Factor w(p).
-5*(p + 2)*(p + 5)
Suppose -2*m = -5*r - 11, -2*r + 4*r + 10 = -2*m. Let v = 0 - r. Determine x, given that 0 - 1/2*x - v*x**3 + 2*x**4 + 2*x**2 - 1/2*x**5 = 0.
0, 1
Factor -20/13*u**3 + 0 + 0*u**2 + 0*u - 2/13*u**4.
-2*u**3*(u + 10)/13
Let q(r) be the third derivative of -r**6/30 + 2*r**5/15 + 4*r**4/3 - 5*r**2 - 4*r. Factor q(c).
-4*c*(c - 4)*(c + 2)
Suppose 212*k - 324 - 6*k + 324*k**2 + 5*k**4 + 11*k**4 - 98*k + 132*k**3 = 0. Calculate k.
-3, 3/4
Let y(x) = x - 1. Let w be y(6). Solve -27*q - w*q**2 - 28 + 7*q + 8 = 0 for q.
-2
Let z = -31487/378 - -833/10. Let w(o) be the third derivative of 0*o**6 + 0*o**3 - 1/270*o**5 + 0 + 0*o**4 + z*o**7 + o**2 + 0*o. Factor w(c).
2*c**2*(c - 1)*(c + 1)/9
Let r = -104 + 122. Let k be 6*((-24)/r)/(-4). Find m, given that 1 + 5/2*m + 2*m**k + 1/2*m**3 = 0.
-2, -1
Suppose -6*d + 15937 = 15925. Factor 0 + 2/5*n**d + 2/5*n**3 + 0*n.
2*n**2*(n + 1)/5
Factor 67*x**2 + 91*x**2 + 11*x**3 + 24 + 110 + 3*x**3 + 296*x - 62.
2*(x + 2)*(x + 9)*(7*x + 2)
Let l(r) = -2*r**2 + 8*r - 6. Let p(x) = 4*x**2 - 16*x + 12. Let b = -19 - -13. Let s(a) = b*p(a) - 10*l(a). Determine k, given that s(k) = 0.
1, 3
Let g(w) be the second derivative of 0*w**2 + 1/57*w**3 + 1/114*w**4 + 0 - 14*w. Factor g(f).
2*f*(f + 1)/19
Let i(z) be the third derivative of z**7/2100 - z**6/900 - z**5/150 + 17*z**3/6 - 2*z**2. Let g(f) be the first derivative of i(f). Factor g(t).
2*t*(t - 2)*(t + 1)/5
Let s(y) = -3*y - 10. Let o be s(-5). Factor -2*l**3 - o*l**2 - 6*l**2 + 9*l**2.
-2*l**2*(l + 1)
Factor 2887*c + 36 + 3*c**3 - 5717*c + 2887*c + 24*c**2.
3*(c + 1)*(c + 3)*(c + 4)
Let m(t) be the first derivative of -t**7/840 + t**6/160 - t**5/240 - t**4/32 + t**3/12 + 5*t**2/2 + 24. Let a(z) be the second derivative of m(z). Factor a(o).
-(o - 2)*(o - 1)**2*(o + 1)/4
Let u = 242 + -240. Let t(w) be the second derivative of 0*w**u + 0 + 0*w**4 - 1/30*w**5 + 1/45*w**6 - 6*w + 0*w**3. Factor t(d).
2*d**3*(d - 1)/3
Let h = -1/332 - -1343/4980. Let d(u) be the second derivative of 0 + 1/3*u**3 - 2*u - h*u**6 + 0*u**2 - 2/3*u**4 + 1/21*u**7 + 3/5*u**5. Factor d(m).
2*m*(m - 1)**4
Suppose 5*n = 5*r - 45, n + 16 + 13 = 5*r. Let j(o) be the third derivative of 1/90*o**r + 3*o**2 + 0*o + 1/60*o**6 + 0*o**4 + 0 + 0*o**3. Solve j(w) = 0.
-1/3, 0
Let k(v) = 2*v**2 - 40*v + 4. Let d be 5*1 + (38 - 23). Let m be k(d). Factor -2/7*u**5 + 2/7*u**m + 0 - 10/7*u**2 + 6/7*u**3 + 4/7*u.
-2*u*(u - 1)**3*(u + 2)/7
Solve 67*i**2 + 1 - 3*i + 3*i**4 + 3*i**3 - 6 - 76*i**2 + 11 = 0 for i.
-2, -1, 1
Let g be 0 + -2 + (1 - (-4 + 0)). Factor -6*m**3 + 2*m**2 - 4 + 3*m + 5 - m**5 + 2*m**3 - 3*m**4 + 2*m**g.
-(m - 1)*(m + 1)**4
Let d be 190/(-4)*68/425 - -8. Let -1/10*c**2 + d*c - 3/10 = 0. Calculate c.
1, 3
Suppose 4*v - 53 = -3*c - 59, 0 = 3*v + 5*c + 10. Let j(q) be the first derivative of 0*q**4 + 0*q + v*q**2 + 1 - 3/25*q**5 + 1/5*q**3. Factor j(u).
-3*u**2*(u - 1)*(u + 1)/5
Let k(h) be the third derivative of -3*h**7/350 + h**6/40 + h**5/100 - h**4/8 + h**3/5 + h**2 + 57*h. Find j, given that k(j) = 0.
-1, 2/3, 1
Let c(m) = m**4. Let p(d) = -20*d**5 - 85*d**4 - 30*d**3 + 40*d**2 + 50*d + 15. Let o(w) = 30*c(w) + p(w). Suppose o(n) = 0. What is n?
-1, -3/4, 1
Let u(s) be the first derivative of s**6/51 - 6*s**5/85 - s**4/17 + 8*s**3/17 - 8*s**2/17 - 237. Suppose u(z) = 0. What is z?
-2, 0, 1, 2
Let a be -3 - (-1)/(3/42). Suppose 0 = -4*r + a - 3. Let 0 + 3/5*w + 9/5*w**4 + 3/5*w**r - 3*w**3 = 0. What is w?
-1/3, 0, 1
Let v(o) be the second derivative of o**4/18 - 3*o**2 - 139*o + 2. Solve v(w) = 0 for w.
-3, 3
Let v(c) = c**3 - 4*c**2 - 2*c - 8. Let t be v(5). Let p(l) be the first derivative of 1/22*l**4 + 0*l + t + 2/11*l**3 + 2/11*l**2. Solve p(k) = 0.
-2, -1, 0
Factor -9/5*c**2 - 4/5*c + 6/5*c**3 - 1/5*c**4 + 12/5.
-(c - 3)*(c - 2)**2*(c + 1)/5
Suppose -13 - 235 = -62*n. Let v(o) be the first derivative of 0*o + 0*o**3 - 2/35*o**5 - 1/14*o**n + 0*o**2 - 2. Factor v(w).
-2*w**3*(w + 1)/7
Let q(k) be the third derivative of -2/7*k**3 + 1/210*k**5 + 0 + 0*k + 28*k**2 - 5/84*k**4. Factor q(a).
2*(a - 6)*(a + 1)/7
Let d(q) be the third derivative of q**5/240 + q**4/48 + q**3/24 - 4*q**2 - 41. Find w, given that d(w) = 0.
-1
Factor -16/3*c**2 - 380/9*c**4 + 0 - 256/9*c**3 - 100/9*c**5 + 0*c.
-4*c**2*(c + 3)*(5*c + 2)**2/9
Let s(q) be the first derivative of -4*q - 4 - 52/3*q**3 - 12*q**4 - 12*q**2 - 16/5*q**5. Suppose s(l) = 0. Calculate l.
-1, -1/2
Let r(z) = -z**3 - 10*z**2 - 9*z - 4. Let n(s) = 2*s**2 + 1. Let g(q) = -24*n(q) - 3*r(q). Factor g(a).
3*(a - 4)*(a - 1)**2
Let z(j) be the first derivative of 2*j**3/15 + 4*j**2/5 + 8*j/5 - 83. Determine v so that z(v) = 0.
-2
Let u be 7 + -1 + (10/(-5))/2. Suppose -15 = -5*k - 2*l, -2*k + 6 = u*l - 4*l. Factor -3/2*v**2 + 0 + 0*v**k + 1/2*v**4 - v.
v*(v - 2)*(v + 1)**2/2
Solve 29 + 174*h**2 - h**3 - 29 + 9*h**3 - 50*h**2 + 60*h = 0.
-15, -1/2, 0
Let h(d) be the second derivative of -d**4/12 + 7*d**3/6 + 4*d**2 - 2*d - 41. Let u be h(8). Factor -2/3*f + u + 1/3*f**3 - 1/3*f**2.
f*(f - 2)*(f + 1)/3
Let b(n) be the second derivative of n**7/1260 - n**6/120 - n**4/6 + 3*n. Let a(w) be the third derivative of b(w). Factor a(m).
2*m*(m - 3)
Let s(p) be the first derivative of p**5/15 - 5*p**4/12 - p**3/9 + 17*p**2/6 + 4*p - 97. What is u in s(u) = 0?
-1, 3, 4
Solve -5*j**2 - 4*j + j**2 - 4*j**4 + 5*j**2 + 3*j**3 + 3*j**2 + j**5 = 0.
-1, 0, 1, 2
Let g(j) = 6*j - 34. Let n be g(6). Factor 4*f**5 - 12*f**3 + 4*f**2 - 15*f**2 + 3*f**n.
4*f**2*(f - 2)*(f + 1)**2
Let c be (-4 - 40/(-6)) + (-58)/24. Find k, given that 0*k + 0 - c*k**3 + 0*k**2 = 0.
0
Suppose 0 = -5*c + 4*v + 10, -4*c - 11 = -4*v - 19. Suppose q - 2*m = 0, -q - c*m = -3*m - 1. Solve -1/5*i**q + 0*i + 0 = 0.
0
Let u(j) be the first derivative of 3/2*j**2 + j**3 - 15 - 6*j. Factor u(i).
3*(i - 1)*(i + 2)
Let n be 5 + -2 + 48*-1. Let r be 6/45 + (-129)/n. Factor r + 2*w**5 + 4*w**3 - 6*w**2 + 10*w**2 - 1 - 6*w - 2*w**4 - 4*w**4.
2*(w - 1)**4*(w + 1)
Let l = 9883/1464 + -1/1464. Factor -63/4*v**2 - l*v**3 - 9/2 - 57/4*v - 3/4*v**4.
-3*(v + 1)**3*(v + 6)/4
Let i(y) be the third derivative of y**6/840 + 2*y**5/105 + 5*y**4/42 + 8*y**3/21 + y**2 + 3. Factor i(n).
(n + 2)**2*(n + 4)/7
Let -3*b**3 - 24*b**2 + 59*b + 10*b**3 - 32 - 3*b**3 - 11*b = 0. Calculate b.
2
Let w(r) = -r**4 + r + 1. Let n(g) = -5*g**4 + 35*g**3 - 51*g**2 - 313*g - 96. Let h(i) = -3*n(i) + 6*w(i). Factor h(z).
3*(z - 7)**2*(z + 2)*(3*z + 1)
Let c(i) be the first derivative 