hird derivative of c**5/60 - c**3/6 + c**2 - 6*c. Factor m(i).
(i - 1)*(i + 1)
Suppose -4*a - 3*n + 10 = 8, -3*a - 3*n = 0. Find w, given that -7/6*w - 5/6*w**a + 1/3 + 2/3*w**3 = 0.
-1, 1/4, 2
Suppose -j + 9 = 3*x, 4*x - 3*j - 1 = -2. Factor 5*u**2 - 2*u**2 + x + 15*u - 6*u**3 + 1 + 3.
-3*(u - 2)*(u + 1)*(2*u + 1)
Let a(d) be the first derivative of -d**9/3024 - d**8/840 + d**6/180 + d**5/120 + 5*d**3 + 28. Let r(h) be the third derivative of a(h). Factor r(l).
-l*(l - 1)*(l + 1)**3
Factor 1/2*h**4 + 21/2 + 16*h + h**2 - 4*h**3.
(h - 7)*(h - 3)*(h + 1)**2/2
Factor 1/7*s**2 + 0 + 8/7*s.
s*(s + 8)/7
Determine v so that 26*v**5 - 124*v**2 - 212*v**4 - 73*v**5 - 72 + 289*v**3 - 708*v - 1258*v**2 - 1232*v**3 + 32*v**5 = 0.
-6, -1, -2/15
Let g(n) = n**3 + n**2 - 3*n + 2. Let y be g(-3). Let v(o) = -o**2 - 8*o - 5. Let m be v(y). Factor -i**4 + 0*i**4 - 2 + 3*i**3 - 9*i**2 + m*i**3 + 7*i.
-(i - 2)*(i - 1)**3
Let s(a) be the third derivative of -a**10/75600 + a**9/30240 + a**8/10080 - a**7/2520 - a**5/6 - 8*a**2. Let l(r) be the third derivative of s(r). Factor l(b).
-2*b*(b - 1)**2*(b + 1)
Let g(w) = -3471*w + 3477. Let d be g(1). Factor 0 + d*u**2 - 8*u + 15/8*u**3 + 1/8*u**4.
u*(u - 1)*(u + 8)**2/8
Let n(g) = 7*g**3 - 10*g**2 + 11*g + 63. Let m(c) = -6*c**3 + 10*c**2 - 10*c - 54. Let a(q) = 5*m(q) + 4*n(q). Factor a(j).
-2*(j - 3)**2*(j + 1)
Let d = 2 + 0. Let u be 6 - (-20)/(-35)*10. Factor 0*k - u + 2/7*k**d.
2*(k - 1)*(k + 1)/7
Factor 0 - 2/7*x**4 + 2/7*x**2 - 4/7*x + 4/7*x**3.
-2*x*(x - 2)*(x - 1)*(x + 1)/7
Let l be ((-16)/(-55))/((-87)/(49590/(-76))). What is t in 272/11*t**3 + 170/11*t**2 + 70/11*t**4 - l - 56/11*t = 0?
-3, -1, -2/7, 2/5
Factor -28*i**4 + 9*i**4 - i**3 + 17*i**4 + 29*i**3.
-2*i**3*(i - 14)
Suppose 25 = -r + 5. Let j be (-81)/(-105) + (16/r)/4. Factor 2/7*z**2 + j + 6/7*z.
2*(z + 1)*(z + 2)/7
Let m = 23 - 19. Factor -l**2 + m*l - l - 2*l + 0*l.
-l*(l - 1)
Suppose 0 = -11*x - 83 + 127. Let g(j) be the first derivative of 1/24*j**x - 2/9*j**3 + 5/12*j**2 - 1/3*j - 1. Let g(a) = 0. Calculate a.
1, 2
Determine h, given that 1/4*h**2 + 64 - 8*h = 0.
16
Let s(v) be the second derivative of -v**9/7056 - v**8/1960 - v**7/1960 - 4*v**3/3 - 10*v. Let g(y) be the second derivative of s(y). Solve g(h) = 0 for h.
-1, 0
Let f(w) be the second derivative of 5*w**7/84 + 23*w**6/10 + 167*w**5/20 + 28*w**4/3 - 9*w**3/4 - 25*w**2/2 + 78*w. Determine b so that f(b) = 0.
-25, -1, 2/5
Factor -50*r**3 + 15*r**4 + 88708*r - 88708*r + 5*r**5.
5*r**3*(r - 2)*(r + 5)
Let s be ((-108)/55 - -2)/((-15)/(-300)). Factor 6*q**2 + 50/11*q**3 + s + 38/11*q + 14/11*q**4.
2*(q + 1)**3*(7*q + 4)/11
Suppose -62 + 22 = -2*f. Determine q, given that -9 - 5*q + f*q**2 - 8 - 10*q**4 - 5*q**5 + 7 + 10*q**3 = 0.
-2, -1, 1
Let b = 180 + -301. Let d be 22/b - 167/(-11). Factor 6*u**2 - 9*u**4 - u**5 + 9*u**3 - 2*u**5 + 9*u + 3 - d*u**3.
-3*(u - 1)*(u + 1)**4
Let y be (-1)/5*(-75)/180*6. Find f, given that 3/4*f**4 + 3/4*f + 1/2 - 5/4*f**2 - 5/4*f**3 + y*f**5 = 0.
-2, -1, -1/2, 1
Let o(p) be the first derivative of p**7/140 - p**6/10 + 2*p**5/5 + 5*p**2/2 + 6. Let c(t) be the second derivative of o(t). Factor c(h).
3*h**2*(h - 4)**2/2
Factor -2/11*p**5 - 4/11*p**2 + 0 + 0*p**3 + 2/11*p + 4/11*p**4.
-2*p*(p - 1)**3*(p + 1)/11
Let v(h) = 98*h**3 - 250*h**2 + 115*h + 13. Let w(d) = 49*d**3 - 124*d**2 + 58*d + 6. Let l(m) = -6*v(m) + 13*w(m). Factor l(k).
k*(7*k - 8)**2
What is k in 27*k**5 - 30*k**5 + 91*k**2 - 166*k**2 - 45*k**3 + 27*k**4 = 0?
-1, 0, 5
Suppose 27*i + 10 - i**2 - 4*i - 7*i - 5*i + 2 = 0. What is i?
-1, 12
Suppose 4*m - 22*m - 10*m = 10*m. Find t such that -2/9*t**2 + 0 + m*t = 0.
0
Let j(q) be the third derivative of 0 + 0*q - 2/9*q**3 + 1/12*q**4 - 1/90*q**5 + 4*q**2. Solve j(l) = 0.
1, 2
Let r(m) be the third derivative of -m**6/200 - 3*m**5/100 - m**4/20 + 2*m**2 - 7*m. Factor r(j).
-3*j*(j + 1)*(j + 2)/5
Let o(s) be the second derivative of s**4/12 + 2*s**3/3 + 5*s**2/2 + 8*s. Let l be o(-3). Find a, given that 3/4*a**3 + 0*a**l - 3/4*a + 0 = 0.
-1, 0, 1
Let b(m) = 16*m**3 + 22*m**2 - 2*m + 2. Let n(h) = -h**4 + 81*h**3 + 109*h**2 - 11*h + 11. Let y(o) = -11*b(o) + 2*n(o). Determine t, given that y(t) = 0.
-4, -3, 0
Suppose 2*d + 2 = 10. What is p in 0*p**2 - 12*p + 11*p**3 + p**3 - 4 + 0*p**2 + d*p**2 = 0?
-1, -1/3, 1
Let k = -4855 + 4855. What is l in -1/9*l**2 + k + 4/9*l**5 + 0*l + 2/3*l**3 - l**4 = 0?
0, 1/4, 1
Let y(j) be the third derivative of 5*j**8/336 - 11*j**7/42 + 7*j**6/4 - 9*j**5/2 - 45*j**4/8 + 135*j**3/2 - 154*j**2. Determine x, given that y(x) = 0.
-1, 3
Let s(i) be the first derivative of 5*i**3/3 - 265*i**2 + 14045*i + 261. Solve s(l) = 0.
53
Let j(p) be the first derivative of -2*p**5/5 + p**4 - 2*p**2 + 2*p + 123. Factor j(v).
-2*(v - 1)**3*(v + 1)
Let n = 511/15 - 12/5. Let w = 32 - n. Find p, given that -1/3*p**2 + 0 + 0*p + w*p**3 = 0.
0, 1
Let m(k) = 8*k + 5. Let j be m(3). Let 40*g - j*g**4 + 5*g**5 + 20*g**2 + 12*g**4 + 12*g**4 - 30*g**3 = 0. Calculate g.
-2, -1, 0, 2
Let y(g) be the first derivative of -g**4/24 + g**3/12 - 10*g + 16. Let h(c) be the first derivative of y(c). Suppose h(a) = 0. What is a?
0, 1
Find s such that 93*s - 87*s + 4 + 2*s**2 - s**2 + s**2 = 0.
-2, -1
Let v(h) = h**2 - 8*h + 16. Let b be v(8). Factor b + 3*p**4 + 6*p**3 - 7 - 9 + 3*p**2.
3*p**2*(p + 1)**2
Suppose 28*t = 40*t - 36. Let j(i) be the first derivative of -10/3*i**t + 8*i**2 - 8*i - 3 + 1/2*i**4. Solve j(m) = 0 for m.
1, 2
Let b(s) be the second derivative of -s**7/42 + 13*s**6/30 - 8*s**5/5 + 5*s**4/3 + 2*s + 99. What is l in b(l) = 0?
0, 1, 2, 10
Let i be (33/66)/(4/16). Let k(j) be the first derivative of 0*j**i + 12 + 0*j + 8/3*j**3 - 4/5*j**5 - j**4. Solve k(w) = 0 for w.
-2, 0, 1
Let q = 98 - 103. Let p be (-2)/(-1)*q/(-40). Factor p*j**5 + 2 + j**4 - j - 5/2*j**2 + 1/4*j**3.
(j - 1)**2*(j + 2)**3/4
Suppose -5*x = -3*b - 12, -9 = -4*x + b + 2*b. Suppose -43 = -x*p - 10. Find t, given that -19 + p - 16*t**2 + 20*t + 0*t + 4*t**3 = 0.
1, 2
Suppose l + 144 = 3*l. Let u be (-46)/(-12) + 12/l. Factor 0 + 4 + 0 - 8*d - u*d**2 + 2*d.
-2*(d + 2)*(2*d - 1)
Suppose -5*h - 18 = -38. Find w such that 5*w**h - 5*w**2 - 12*w**2 + 10*w + 2*w**2 = 0.
-2, 0, 1
Suppose -5*b = k - 17, -26*k - 16 = -31*k - 2*b. Factor 4/9*d**2 - k*d**3 - 16/9 + 8*d.
-2*(d - 2)*(d + 2)*(9*d - 2)/9
Let y be ((-800)/48)/(8/(-6)) + -12. Solve -y + p**4 - p**3 - 1/4*p**5 - 1/2*p**2 + 5/4*p = 0.
-1, 1, 2
Factor -1760*u - 5*u**3 + 75 - 49 + 753 + 3061 + 175*u**2.
-5*(u - 16)**2*(u - 3)
Let c(i) = -18*i**2 - 15*i + 1. Suppose -4*t = 4*q + 4, q + 12 = -3*t - 1. Let o(v) = -v + 1. Let n(l) = t*o(l) + 2*c(l). Factor n(b).
-4*(3*b + 1)**2
Let a(d) be the third derivative of -d**9/20160 - d**8/2240 - d**7/672 - d**6/480 + 5*d**4/24 - 29*d**2. Let b(r) be the second derivative of a(r). Factor b(k).
-3*k*(k + 1)**2*(k + 2)/4
Let i(o) be the second derivative of 7*o**7/6 + 161*o**6/15 + 613*o**5/20 + 23*o**4 + 6*o**3 - 2*o - 12. Factor i(z).
z*(z + 3)**2*(7*z + 2)**2
Let s(m) be the first derivative of m**4/22 - 3*m**3/11 + 6*m**2/11 + 6*m + 24. Let y(i) be the first derivative of s(i). Let y(c) = 0. Calculate c.
1, 2
Let z(l) be the third derivative of 0*l - 5/3*l**4 + 6*l**2 - 5/12*l**5 - 1/24*l**6 + 0 - 10/3*l**3. Factor z(i).
-5*(i + 1)*(i + 2)**2
Let x = 17/31 + 515/248. Let u = x + -17/8. Let q**2 - 1 - u*q + 1/2*q**3 = 0. Calculate q.
-2, -1, 1
Suppose 2*n - 2 = 2*l, 2*n - 4 - 4 = 0. What is x in 148*x - 3*x**l - 143*x - 6*x**3 + 4*x**3 = 0?
-1, 0, 1
Suppose 137*i + 15 = 142*i. Let s(l) be the first derivative of l**2 - l - 1/3*l**i + 4. Suppose s(x) = 0. Calculate x.
1
Let z(s) = -3*s**3 - 24*s**2 - 70*s - 47. Let q(x) = -47*x - 11 - 20 - 4*x**3 - 16*x**2 - 3*x**3 + 5*x**3. Let m(l) = 7*q(l) - 5*z(l). Let m(c) = 0. What is c?
-3, -2
Suppose 0 = 2*u + 95 - 99. Let s(t) = 0*t**2 + 2*t**2 - t + 2*t**2 - 5*t**3. Let l(j) = -16*j**3 + 11*j**2 - 2*j. Let z(b) = u*l(b) - 7*s(b). Factor z(v).
3*v*(v - 1)**2
Suppose 24 = 9*s - s. Let n = -9/52 + 12/13. Factor -s*b + 0 + 0*b**2 + n*b**3.
3*b*(b - 2)*(b + 2)/4
Let k(c) = c - 1. Let a(w) = w**3 + 10*w**2 - 30*w - 10. Let l(n) = -a(n) - 5*k(n). Let v be l(-12). Find j, given that 4/3 + 5/3*j**2 - 1/3*j**v - 8/3*j = 0.
1, 2
Suppose 0 = 2*b