-5*h**2*(h - 1)**2
Let j(l) = -2*l**5 + 14*l**4 - 17*l**3 - 2*l**2 + 7*l. Let f(d) = -d**5 + d**4 + d**3 - d. Let w(b) = -10*f(b) - 5*j(b). Find v such that w(v) = 0.
-1/2, 0, 1, 5/2
Let c(r) be the first derivative of r**3/12 + 13*r**2/8 + 20. Let c(w) = 0. Calculate w.
-13, 0
Let z(s) = s**3 + 9*s**2 + 7*s + 23. Let y be z(-7). Suppose y*n - 68*n = 8. Factor 2/11*j**3 + 8/11*j**n + 10/11*j + 4/11.
2*(j + 1)**2*(j + 2)/11
Let l(b) be the third derivative of -3/10*b**5 - 1/8*b**4 - 1/20*b**6 + 3/112*b**8 + 0 + 1/14*b**7 + 1/2*b**3 + 0*b - 9*b**2. Factor l(i).
3*(i - 1)*(i + 1)**3*(3*i - 1)
Let n = 1279/9705 + 1/647. Let m(q) = q**3 + 13*q**2 - 13*q + 14. Let x be m(-14). Let -2/15*k + x - n*k**2 = 0. Calculate k.
-1, 0
Let p(x) = -5*x**4 - 9*x**3 - 5*x**2 + 3*x + 7. Let b(w) = 44*w**4 + 80*w**3 + 44*w**2 - 28*w - 62. Let k(j) = -6*b(j) - 52*p(j). Find y, given that k(y) = 0.
-2, -1, 1
Let u(b) = -b**2 - 3*b + 4. Let y be u(-5). Let i(z) = 18*z**3 + 8*z + 26. Let a(w) = -2*w**3 - w - 3. Let d(x) = y*i(x) - 52*a(x). Suppose d(n) = 0. What is n?
-1, 0, 1
Suppose 0 = -5*n + 3*u + 144, 2*n - u = 2*u + 54. Find k, given that -n*k - 25*k + 35*k**2 + 25 - 1092*k**3 + 1087*k**3 = 0.
1, 5
Let a = -5454/119 - -784/17. Find h, given that 2/7*h**3 + 4/7 + 2/7*h**4 - a*h - 6/7*h**2 = 0.
-2, -1, 1
Factor 3/7*g**4 + 0*g**2 - 1/7*g**5 + 0 - 2/7*g**3 + 0*g.
-g**3*(g - 2)*(g - 1)/7
Let s(k) be the second derivative of k**6/105 + 9*k**5/35 + 11*k**4/6 - 24*k**3/7 - 324*k**2/7 + 20*k. Solve s(z) = 0 for z.
-9, -2, 2
Suppose b + 3 = -5*g, 48*b = 2*g + 45*b - 9. Let w(m) be the first derivative of 8/11*m - 2/33*m**3 + g*m**2 + 2. Factor w(l).
-2*(l - 2)*(l + 2)/11
Factor 10 + 148/5*t - 2/5*t**4 + 144/5*t**2 + 44/5*t**3.
-2*(t - 25)*(t + 1)**3/5
Let z(y) be the third derivative of y**8/672 + y**7/210 - y**6/240 - y**5/60 - 929*y**2. Solve z(f) = 0 for f.
-2, -1, 0, 1
Determine t so that 8 - 2*t**2 + 10 + 10 - t - 9*t = 0.
-7, 2
Let k be (-4)/(-6) - 6640/10050. Let p = 1679/670 - k. Factor 0 - 5/4*o**2 - p*o.
-5*o*(o + 2)/4
Suppose 218*v = 71*v + 294. Factor -15/4*a - 3/2 + 21/4*a**v.
3*(a - 1)*(7*a + 2)/4
Solve -24/5*x**5 + 26/5*x**4 - 16/5*x - 3*x**2 + 4/5 + 11*x**3 = 0.
-1, -2/3, 1/4, 1/2, 2
Suppose -5*d = -4*v - 14, -3*d + 6*d = -5*v + 38. Let c be 340/322 - d/(-69). Determine b so that -34/7*b - c*b**2 - 8/7 = 0.
-4, -1/4
Let j(k) be the second derivative of k**6/1260 + k**5/210 + k**4/84 + 7*k**3/3 - 15*k. Let d(p) be the second derivative of j(p). Solve d(n) = 0 for n.
-1
Let d(m) be the first derivative of -3*m**5/5 + 15*m**4/4 + 8*m**3 - 72*m**2 + 184. Factor d(j).
-3*j*(j - 4)**2*(j + 3)
Let n(k) = 2*k**2 + 6*k - 3. Suppose -5*w + 18 + 2 = 0. Let a(i) = i**2 + 5*i - 2. Let f(j) = w*n(j) - 6*a(j). Determine c so that f(c) = 0.
0, 3
Let q(w) be the first derivative of 2*w**6/3 - 4*w**5 - 7*w**4 + 20*w**3/3 + 12*w**2 + 96. Factor q(l).
4*l*(l - 6)*(l - 1)*(l + 1)**2
Let t = -1 - 0. Let g be (-52)/(-8) + t/2. Factor g + 4 - x - x**2 - 8.
-(x - 1)*(x + 2)
Let d(g) be the second derivative of 0*g**2 - g + 5/3*g**3 + 0 + 1/12*g**4. Let d(p) = 0. What is p?
-10, 0
Let j(i) be the second derivative of -1/32*i**4 + 0*i**5 + 1/480*i**6 + 2*i**2 + 0 + 5*i - 1/12*i**3. Let o(f) be the first derivative of j(f). Factor o(b).
(b - 2)*(b + 1)**2/4
Let p(b) be the second derivative of -b**6/30 - b**5/10 + 7*b**4/12 + 10*b**3/3 + 6*b**2 - 45*b. Suppose p(s) = 0. Calculate s.
-2, -1, 3
Let g = 15 + -40/3. Factor -g*h + h**2 - 2/3.
(h - 2)*(3*h + 1)/3
Suppose -3*h - h + 12 = 0. Suppose 7 = -x + 2*g, x = -h*g + 9 + 9. Let x*u + 4 - 3*u**3 - 6*u**2 - 1 + 3 = 0. Calculate u.
-2, -1, 1
Suppose -4*r = 2*h + 16, -5*r = h + 4*h + 15. Factor -8 + 19 - 1 - 2*j**3 + h*j - 8 - 2*j**2.
-2*(j - 1)*(j + 1)**2
Suppose 4*p - 22 = -3*g, -5*p + 2*g = -10*p + 24. Let q = 540 - 1598/3. Find a such that 2/3*a - 7*a**p + 0 + 1/3*a**2 - q*a**3 = 0.
-1, -1/3, 0, 2/7
Let z(x) = -x**2 + 12*x - 15. Let w be z(9). Suppose -15 = -w*v + 7*v. Factor 4*r**2 - r**v - 4*r**4 + 3*r**5 - 7*r**5 + 5*r**3.
-4*r**2*(r - 1)*(r + 1)**2
Let a(t) be the third derivative of 1/350*t**7 - 1/200*t**6 + 29*t**2 - 3/100*t**5 + 1/40*t**4 + 0*t + 1/5*t**3 + 0. Factor a(k).
3*(k - 2)*(k - 1)*(k + 1)**2/5
Let a be (12/126)/(10/70). Factor 2 - 8/3*i + a*i**2.
2*(i - 3)*(i - 1)/3
Let q(t) be the second derivative of 14*t**6/3 + 138*t**5/5 + 97*t**4/3 - 4*t**3 + 2*t + 21. Factor q(d).
4*d*(d + 1)*(d + 3)*(35*d - 2)
Let m(g) = -2*g**2 - 4*g + 6. Let o(i) = 2 + 3 + 14 - 11*i - i**3 - 7*i**2. Let w(r) = 7*m(r) - 2*o(r). Solve w(c) = 0 for c.
-2, 1
Let a(o) be the first derivative of -3*o**5/5 - 165*o**4/2 - 3133*o**3 - 8910*o**2 - 8748*o - 334. Factor a(v).
-3*(v + 1)**2*(v + 54)**2
Let k be (80/27 - 3)/(3/(-6)). Let b(w) be the second derivative of -4*w + 1/54*w**4 + 1/9*w**2 - k*w**3 + 0. Factor b(g).
2*(g - 1)**2/9
Let n be (20/(-420))/(4/(-72)). Find s such that 10/7*s - 2/7*s**3 - 4/7 - n*s**2 + 2/7*s**4 = 0.
-2, 1
Let k(l) = -l**2 - 9*l - 12. Let s be k(-7). Let h = -2/11 + 36/77. Factor -h*i - 2/7*i**s + 2/7*i**4 + 0 + 2/7*i**3.
2*i*(i - 1)*(i + 1)**2/7
Let a be 14*6/4 - 0/4. Let x be (2/a*-6)/(20/(-14)). Factor 2/5*g**4 + x + 0*g**3 - 4/5*g**2 + 0*g.
2*(g - 1)**2*(g + 1)**2/5
Let s(j) be the second derivative of j**6/45 + 4*j**5/15 - j**4/2 - 224*j - 2. Solve s(c) = 0.
-9, 0, 1
Let v(m) = 550*m + 6654. Let w be v(-12). Factor -18*g - w - 3/2*g**2.
-3*(g + 6)**2/2
Let d(l) be the third derivative of -l**6/30 + 7*l**5/15 - 11*l**4/6 + 10*l**3/3 + 20*l**2 + 10. Let d(i) = 0. Calculate i.
1, 5
Let h = 20 + -18. Suppose -f = -4*f + 9. Suppose 3/5*i**h + 0 + 2/5*i + 1/5*i**f = 0. Calculate i.
-2, -1, 0
Factor 21*o**2 + 4*o**4 + 336*o + 21*o**2 + 288 - 34*o**2 - 36*o**3.
4*(o - 6)**2*(o + 1)*(o + 2)
Suppose -20*i + 15*i + 25 = 0. What is l in -20*l**4 + 5*l**2 + 8*l**i - 16*l + 11*l**2 + 3 + 8*l**3 + 1 = 0?
-1, 1/2, 1
Let d(n) be the second derivative of 169*n**6/15 - 689*n**5/30 + 5*n**4 + 28*n**3/3 + 8*n**2/3 + 41*n. Determine l so that d(l) = 0.
-2/13, 2/3, 1
Factor 19/3*d**2 + 27 + 1/3*d**3 + 33*d.
(d + 1)*(d + 9)**2/3
Let b(t) be the second derivative of 5*t**7/28 + 29*t**6/60 + 13*t**5/40 - t**4/24 - 126*t. Factor b(a).
a**2*(a + 1)**2*(15*a - 1)/2
Let w(y) be the third derivative of -y**7/2520 + y**6/90 - y**5/10 + 5*y**3 + 8*y**2 - 2. Let d(c) be the first derivative of w(c). Factor d(u).
-u*(u - 6)**2/3
Suppose -10*l + 17*l - 665 = 0. Factor 3*p**2 - 48*p + l*p - 49*p - p**3.
-p*(p - 2)*(p - 1)
Let b(h) be the second derivative of -5/18*h**3 + 34*h + 0 - h**2 + 1/36*h**4. Factor b(p).
(p - 6)*(p + 1)/3
Let j be (-10)/(-25) - (-242)/55. Factor -3*g**3 + 0 - 12/5*g - j*g**2 - 3/5*g**4.
-3*g*(g + 1)*(g + 2)**2/5
Factor 0 + 0*g**3 - g - 1/2*g**4 + 3/2*g**2.
-g*(g - 1)**2*(g + 2)/2
Let b = -36 + 43. Let k be b/(-14) - (-4)/2. Solve 15/4*i**2 - k*i**5 - 5/2*i**3 + 4*i - 19/4*i**4 + 1 = 0 for i.
-2, -1, -2/3, -1/2, 1
Let r(j) be the first derivative of -2*j**6/3 - 56*j**5/5 - 33*j**4 + 448*j**3/3 - 128*j**2 + 22. Solve r(b) = 0 for b.
-8, 0, 1
Factor -7*x + 25*x - 13*x - 7*x**2 + 5*x**3 - 3*x**2.
5*x*(x - 1)**2
Let u(y) be the first derivative of -10 - 1/3*y**4 - 2*y - 2*y**3 - 4*y**2. Let z(d) be the first derivative of u(d). Find t, given that z(t) = 0.
-2, -1
Let s(j) = j**2 + j - 1. Let v(i) = 8*i**2 + 273*i + 3642. Let a(q) = -3*s(q) + v(q). Factor a(p).
5*(p + 27)**2
Let o = -47 - -50. Factor 315*a**2 + 2*a**5 - 311*a**2 - 4*a**o - 2*a**3.
2*a**2*(a - 1)**2*(a + 2)
Let q(o) be the second derivative of 5*o**7/98 - 6*o**6/35 - 33*o**5/140 + 13*o**4/14 + 6*o**3/7 - 12*o**2/7 + 94*o. Let q(t) = 0. What is t?
-1, 2/5, 2
Factor -9/8*n**4 + 15/8 + 27/8*n + 3/8*n**5 - 3/4*n**2 - 15/4*n**3.
3*(n - 5)*(n - 1)*(n + 1)**3/8
Let t(i) be the second derivative of -i**5/25 - 7*i**4/15 - 2*i**3 - 18*i**2/5 + 289*i. Let t(u) = 0. Calculate u.
-3, -1
Factor -1/6*f**3 + 29/3*f**2 + 10 + 119/6*f.
-(f - 60)*(f + 1)**2/6
Let u(b) be the first derivative of b**6/20 - 13*b**5/60 + b**4/12 + 11*b**2 - 35. Let z(s) be the second derivative of u(s). Factor z(o).
o*(o - 2)*(6*o - 1)
Let i(c) be the third derivative of -c**6/120 - 43*c**5/30 - 220*c**4/3 + 1936*c**3/3 - 634*c**2. Suppose i(o) = 0. Calculate o.
-44, 2
Let k(g) = -10*g**3 + 474*g**2 - 27