
Suppose 0 = 5*s + s - 30. Let y(c) be the third derivative of 3*c**2 + 0 + 1/24*c**s + 0*c + 1/6*c**3 + 7/48*c**4. Factor y(h).
(h + 1)*(5*h + 2)/2
Let n(i) be the first derivative of 0*i - 4/9*i**3 + 1/2*i**2 + 8. Factor n(x).
-x*(4*x - 3)/3
Let w(j) = -1. Let x(f) = 17*f**2 - 110*f + 603. Let y(v) = 4*w(v) + x(v). Let r(t) = 70*t**2 - 440*t + 2395. Let z(b) = 6*r(b) - 25*y(b). Factor z(g).
-5*(g - 11)**2
Suppose 9 = 2*l + s, 9*l - 14*l + 3*s = -6. Let z(q) be the first derivative of -1/9*q**2 - 1/18*q**4 + 0*q + 4/27*q**l - 6. Solve z(h) = 0 for h.
0, 1
Let v(k) = -11*k**2 + 5*k + 7. Let p(m) = 5*m**2 - 3*m - 3. Let i(a) = -7*p(a) - 3*v(a). Determine b so that i(b) = 0.
0, 3
Let o(s) = s**2 - 26*s + 3. Let j(k) = -k**2 - 1. Let x(n) = 3*j(n) + o(n). Suppose x(h) = 0. Calculate h.
-13, 0
Let f(o) be the first derivative of o**7/210 - o**5/10 - o**4/3 - 6*o**3 - 15. Let j(g) be the third derivative of f(g). Determine m so that j(m) = 0.
-1, 2
Let o(i) be the third derivative of 0 - 125/8*i**5 - 25/16*i**6 - 3125/32*i**4 + 0*i - 1/448*i**8 - 5/56*i**7 + 21*i**2 - 3125/8*i**3. Factor o(f).
-3*(f + 5)**5/4
Let s = 479/790 - 1/158. Let m = -50054 - -250273/5. What is w in -m - 9/5*w**2 - s*w**3 - 9/5*w = 0?
-1
Let f = -146/21 + 313/42. Let v = -19/22 + 26/11. Suppose -v*b + f*b**2 + 1 = 0. What is b?
1, 2
Let w = 46 - 43. Let -4*m**3 + 17*m**3 - 16*m**3 - w*m**2 = 0. What is m?
-1, 0
Factor 0 + 3/5*a**5 - 2/5*a + 3/5*a**2 + 3/5*a**3 - 7/5*a**4.
a*(a - 1)**3*(3*a + 2)/5
Factor -2*v**3 - 5/4*v**2 - v**4 + 0 - 1/4*v.
-v*(v + 1)*(2*v + 1)**2/4
Suppose -10*l + 49 = -1. Let r(j) be the second derivative of 1/75*j**6 + 2/15*j**3 + 0*j**2 + 0*j**5 + 0 - 1/10*j**4 + l*j. Factor r(u).
2*u*(u - 1)**2*(u + 2)/5
Suppose -3*y - 6 = -3*m, 3*m = -12*y + 10*y - 4. Factor 3/8*f**5 + 3/8*f**4 + 0*f**3 + 0 + 0*f**2 + m*f.
3*f**4*(f + 1)/8
Find q such that -164/7*q + 6724/7 + 1/7*q**2 = 0.
82
Let j(s) be the first derivative of 19 + 1/2*s**4 + 4/3*s**6 + 10/3*s**3 - 16/5*s**5 - s**2 - 2*s. Factor j(c).
2*(c - 1)**3*(2*c + 1)**2
Let x(u) be the third derivative of -u**9/22680 + u**8/5040 + u**7/1260 - u**6/270 + u**5/6 - u**2 - 6. Let h(o) be the third derivative of x(o). Factor h(i).
-4*(i - 2)*(i + 1)*(2*i - 1)/3
Let s(p) = 2*p**2 + 14*p + 23. Let v be s(-2). Let q(o) be the first derivative of -9/2*o**2 + 6*o + o**v + 3. Find l, given that q(l) = 0.
1, 2
Suppose -4*u + 2*u = -68. Factor -u*f**2 - 44*f**3 - 12*f**2 - 41*f**2 - 24*f - 8*f**4 + 19*f**2.
-4*f*(f + 2)*(f + 3)*(2*f + 1)
Factor -16/3*c - 4*c**2 - 2/3*c**3 + 0.
-2*c*(c + 2)*(c + 4)/3
Let d(z) = 2*z**4 - z**2. Let l(a) = 3*a**4 + 5*a**3 + 15*a**2 - 21*a. Let q(n) = 4*d(n) - 2*l(n). Find v, given that q(v) = 0.
-3, 0, 1, 7
Let w be (-1 + -8 + 9)/(-1). Factor 1/2*y**4 + 1/2*y**3 - 1/2*y**2 + w - 1/2*y.
y*(y - 1)*(y + 1)**2/2
Suppose 149 = 6*b - 5*m, -4*b - 6*m = -3*m - 93. Solve 12*l + 3/2*l**2 + b = 0.
-4
Let a(l) be the second derivative of l**6/900 - l**5/150 + l**4/90 - 26*l**2 + 5*l. Let t(d) be the first derivative of a(d). Let t(j) = 0. What is j?
0, 1, 2
Factor -v**2 + 0*v**2 + 2*v**2 + 4*v + 27*v**2 - 4*v**3 - 28.
-4*(v - 7)*(v - 1)*(v + 1)
Let 56*n - 8*n**2 - 46*n**3 + 2*n**5 - 176*n - 7*n**4 + 136*n**3 + 43*n**4 = 0. What is n?
-15, -2, 0, 1
Let t(a) be the first derivative of a**4/28 + a**3/7 + 3*a**2/14 + 10*a + 36. Let q(l) be the first derivative of t(l). Factor q(g).
3*(g + 1)**2/7
Solve 39/4*f**2 - 1/4*f**3 + 37/4 - 75/4*f = 0 for f.
1, 37
Let v(g) be the first derivative of g**4/12 - 16*g**3/9 + 85*g**2/6 - 50*g + 465. Factor v(i).
(i - 6)*(i - 5)**2/3
Let v(f) be the third derivative of -f**6/72 + f**5/24 - 2*f**3/3 - 5*f**2. Let p(u) be the first derivative of v(u). Factor p(s).
-5*s*(s - 1)
Let h(d) be the first derivative of 5*d**3/12 - 139*d**2/4 - 28*d - 157. Factor h(a).
(a - 56)*(5*a + 2)/4
Let y(f) be the first derivative of 0*f - f**2 + 1/40*f**4 + 1/200*f**6 + 0*f**3 - 6 - 1/50*f**5. Let v(q) be the second derivative of y(q). Factor v(c).
3*c*(c - 1)**2/5
Suppose 19 + 1/4*k**2 - 77/4*k = 0. What is k?
1, 76
Suppose -5*d = -32 + 82. Let n(p) = 2*p**2 - 12*p + 23. Let j(w) = w**2 - 6*w + 12. Let r(a) = d*j(a) + 6*n(a). Determine g so that r(g) = 0.
3
Let f = -433/66 - -74/11. Let j(p) be the first derivative of -1/9*p**3 - 2 + 1/3*p + 1/3*p**2 - f*p**4. Solve j(v) = 0 for v.
-1, -1/2, 1
Let s be 3*12/(-72) + 14/24. Let x(b) be the second derivative of -13/48*b**4 - 1/24*b**7 - 27/80*b**5 - 6*b + 0*b**2 - 23/120*b**6 - s*b**3 + 0. Factor x(y).
-y*(y + 1)**3*(7*y + 2)/4
Let g(q) be the third derivative of q**8/448 - 3*q**7/140 - q**6/20 + 3*q**5/40 + 7*q**4/32 + 12*q**2 + 2*q. Suppose g(d) = 0. What is d?
-1, 0, 1, 7
Let m(a) = -a**2 - 8*a + 14. Let z be m(-9). Let i(g) be the first derivative of z - 2*g**3 + 2/5*g**5 + 1/2*g**4 + 4*g - g**2. Factor i(b).
2*(b - 1)**2*(b + 1)*(b + 2)
Suppose -3*d = 3*a - 4*a - 10, -d = -3*a - 6. Suppose 0 = -d*m - 5*h + 329, -m + 325 = 2*m + h. Find u, given that 0*u - 9*u - 12 - m*u**2 + 111*u**2 = 0.
-1, 4
Let c(j) = 3*j**3 + 30*j**2 - 304*j + 1000. Let h(m) = m**3 - m. Let r(n) = c(n) - 4*h(n). Suppose r(f) = 0. What is f?
10
Let d(i) be the second derivative of -i**7/280 + i**6/120 + i**4/2 - 3*i. Let f(w) be the third derivative of d(w). Determine n, given that f(n) = 0.
0, 2/3
Suppose -8 = -0*l + 2*l. Let q(v) = v**3 + 3*v**2 - 4*v + 2. Let y be q(l). Let 2*a**y - a + 3 + 0*a - 4 = 0. Calculate a.
-1/2, 1
Let i(c) be the first derivative of 2*c**3/3 + 15*c**2 + 88*c + 378. Solve i(m) = 0 for m.
-11, -4
Let o(r) = 26*r**2 - 234*r + 2. Let l be o(9). Let m = 23/2 + -67/6. Factor m + 0*n - 1/3*n**l.
-(n - 1)*(n + 1)/3
Let f = 30 - 29. Let b be 4 - f - 1 - -1. Factor b*g**5 + 17*g**3 - 14*g**3 - 2*g**5 - 4*g**5.
-3*g**3*(g - 1)*(g + 1)
Factor -1/8*y**3 + 117/8 - 87/8*y + 19/8*y**2.
-(y - 13)*(y - 3)**2/8
Let l(v) be the third derivative of v**6/30 + 2*v**5/15 - 5*v**4/6 - 4*v**3 + 3*v**2 + 82*v. What is i in l(i) = 0?
-3, -1, 2
Let m(g) be the third derivative of 0*g**3 + 0*g + 1/9*g**4 + 1/45*g**5 + 0 - 1/45*g**6 - 10*g**2 - 2/315*g**7. Factor m(l).
-4*l*(l - 1)*(l + 1)*(l + 2)/3
Let o be (-2)/(-3) + (896/24)/16. Let h(k) be the third derivative of 0 - 1/210*k**5 + 0*k + 4*k**2 - 2/21*k**o + 1/28*k**4. Factor h(z).
-2*(z - 2)*(z - 1)/7
Let i(a) be the third derivative of 4/3*a**3 + 1/9*a**5 - 26*a**2 + 0 + 0*a - 17/18*a**4. Suppose i(y) = 0. Calculate y.
2/5, 3
Determine o so that -18/5*o - 57/5*o**2 + 0 + 21/5*o**3 = 0.
-2/7, 0, 3
Let w(f) be the first derivative of -8*f - 17/2*f**2 - 3 - 4*f**3. Let u(l) = -l - 1. Let o(b) = -5*u(b) + w(b). Determine s so that o(s) = 0.
-1/2
Find b such that -6*b**2 + 5*b**2 + 35 + 4*b**2 + 2*b**2 + 15 - 35*b = 0.
2, 5
Let y = 11/36 + -17/63. Let j(n) be the third derivative of -y*n**4 + n**2 + 2/21*n**3 + 0 + 0*n + 0*n**5 + 1/420*n**6. Factor j(p).
2*(p - 1)**2*(p + 2)/7
Let z(t) be the third derivative of -t**5/20 + t**4/3 - 2*t**3/3 + t**2 + 17*t. Find y, given that z(y) = 0.
2/3, 2
Let k(f) = 5*f**5 - 9*f**3 - 4*f**2 + 3*f. Let v(j) = -19*j**5 + 35*j**3 + 16*j**2 - 11*j. Let n(p) = -22*k(p) - 6*v(p). Determine t, given that n(t) = 0.
-1, 0, 2
Let z be 0 - ((-781)/55 + 13). Factor z*n - 2/5 + 2/5*n**3 - 6/5*n**2.
2*(n - 1)**3/5
Suppose 8*v - 86 = 9*v. Let u = v - -175/2. Solve 2*m**3 + 0 - m - u*m**4 + 1/2*m**2 = 0.
-2/3, 0, 1
Let v(r) = 2*r**3 - 41*r**2 - 21*r + 5. Let p be v(21). Suppose -j + 7/2*j**2 - 9/2*j**3 + 5/2*j**4 - 1/2*j**p + 0 = 0. Calculate j.
0, 1, 2
Let k(b) = -105*b**3 + 630*b**2 - 595*b + 170. Let o(d) = -26*d**3 + 157*d**2 - 149*d + 42. Let f(g) = 6*k(g) - 25*o(g). Find z such that f(z) = 0.
1/4, 1, 6
Let q = -69/280 + 13/35. Let j(f) be the second derivative of 4*f + 0*f**3 + 3/4*f**2 - q*f**4 + 0. Factor j(b).
-3*(b - 1)*(b + 1)/2
Let b be (-12)/(-8)*(-32)/(-36). Suppose 0 = 3*p + 3*i - 24, 0 = 2*p - 0*p - 5*i + 12. Find k, given that 2/3 + 3*k - b*k**p - 3*k**3 + 2/3*k**2 = 0.
-2, -1, -1/4, 1
Let v(t) = 3*t**3 + 16*t**2 - 18*t - 31. Let u be v(-6). Solve -2/11*c**u - 2/11*c - 8/11*c**2 - 12/11*c**3 - 8/11*c**4 + 0 = 0.
-1, 0
Factor 2*s**4 + 134*s**2 - 152*s**2 + s - 16*s**3 - s.
2*s**2*(s - 9)*(s + 1)
Let m(v) be the second derivative of v**7/231 - 3*v**5/22 + 5*v**4/33 + 8*v**3/11 -