)*(c + 2)/7
Let f(s) be the third derivative of 0*s + 11*s**2 + 0*s**3 - 5/24*s**4 + 31/84*s**7 + 9/16*s**6 + 55/672*s**8 + 5/24*s**5 + 0. Factor f(m).
5*m*(m + 1)**3*(11*m - 2)/2
Let p be (-1 - -1)/(0 + 2). Suppose p*a = 5*t + 4*a + 2, -3*t = -3*a - 15. Determine q, given that 2*q**t - 6*q**2 - 7 + 5 + 16*q - 14 = 0.
2
Factor -2*b**5 + 62*b**2 + 3*b**5 + 0*b**4 - b + 2*b**4 - 64*b**2.
b*(b - 1)*(b + 1)**3
Let p(g) = 2*g**5 - g**3 + g**2 + 1. Let f(a) = 10*a**5 - 10*a**4 - 26*a**3 - 14*a**2 - 10*a + 4. Let q(y) = -f(y) + 6*p(y). Find i such that q(i) = 0.
-1
Let i(s) be the third derivative of s**6/30 - 2*s**5 + 42*s**4 - 784*s**3/3 - 212*s**2. Factor i(y).
4*(y - 14)**2*(y - 2)
Let k(t) be the first derivative of t**3/7 - 15*t**2/7 + 9*t + 137. Solve k(c) = 0.
3, 7
Let c(i) = -i**2 + i + 1. Let l = -10 + 15. Suppose -2*p = -l*p + 9. Let b(x) = -6*x**2 + 3. Let z(k) = p*c(k) - b(k). Factor z(g).
3*g*(g + 1)
Let b(m) be the first derivative of 1/2*m**5 + 15/16*m**4 - 9 + 0*m - 5/24*m**6 + 0*m**2 + 0*m**3. Find o, given that b(o) = 0.
-1, 0, 3
Factor -76 - 4*j**2 - 539142*j + 539222*j + 0*j**2.
-4*(j - 19)*(j - 1)
Suppose -8 = 4*f - 2*a, -29*a + 31*a - 8 = -3*f. Find h, given that 2/3*h**2 + f*h - 2/3 = 0.
-1, 1
Let r be (1*(-32)/(-20))/((-6)/(-15)). Suppose -r*a + 8 = -0*a. Factor -24/5*o**a - 21/5*o - 9/5*o**3 - 6/5.
-3*(o + 1)**2*(3*o + 2)/5
Let m(g) be the third derivative of -g**8/1680 + 2*g**7/525 + g**6/50 - 5*g**2 + 38*g. Factor m(h).
-h**3*(h - 6)*(h + 2)/5
Let v(t) = -2*t**3 - 2*t - 1. Let d be v(-1). Let r be 2 + (-24)/10 - 132/(-30). Find i, given that -r*i**3 - 3*i**d + 5*i**3 - 3*i**4 - i**3 = 0.
-1, 0
Let v(z) be the second derivative of -6*z + 0*z**2 + 1/9*z**3 + 0 - 1/18*z**4. What is i in v(i) = 0?
0, 1
Let w(b) = 4*b**4 + 12*b**3 - 22*b**2 + 6*b - 7. Let v(m) = 3*m**4 + 8*m**3 - 15*m**2 + 4*m - 5. Let h = 31 + -26. Let j(y) = h*w(y) - 7*v(y). Factor j(z).
-z*(z - 2)*(z - 1)**2
Let j = -272/705 + -2/141. Let b = j - -1. Suppose -b*h**3 + 0*h**2 + 4/5*h - 1/5*h**4 + 0 = 0. What is h?
-2, 0, 1
Let l(u) = -u - 1. Let d(o) = 4*o**2 + 94*o + 490. Let a(i) = -d(i) - 6*l(i). Factor a(p).
-4*(p + 11)**2
Suppose 3*a - 9 = -0. Let p be a*(2 - 12/15) - 0. Factor p*v - 4/5 - 8/5*v**2.
-2*(v - 2)*(4*v - 1)/5
Let n(f) = f**3 - 8*f**2 - 7*f + 2. Let l be n(9). Let a = -18 + l. Solve 10*d**3 - 9*d**2 - 5*d**a - d**3 + 5*d**2 - 3*d**4 + 3*d = 0 for d.
0, 1
Suppose 3*y + 2 = 11. Factor -131*p**3 + 141*p**y - p**5 + 6*p**5 - 15*p**4.
5*p**3*(p - 2)*(p - 1)
Solve 2/15*q**4 - 46/15*q**3 + 46/15*q + 0 - 2/15*q**2 = 0.
-1, 0, 1, 23
Let a(s) = -s**3 - 7*s**2 + s - 6. Let l be a(-7). Let y = 15 + l. Factor -7*d**y - 4*d**3 - 4*d**3 + 4*d**2 + 5*d**3.
-3*d**2*(d + 1)
Let y(d) be the third derivative of -33*d**2 - 85/12*d**4 - 1/168*d**8 - 29/30*d**6 + 25/3*d**3 + 13/105*d**7 + 0*d + 53/15*d**5 + 0. Factor y(a).
-2*(a - 5)**2*(a - 1)**3
Suppose -44/5*w**3 + 4/5*w**4 + 156/5*w**2 + 0 - 36*w = 0. Calculate w.
0, 3, 5
Suppose 39*h = 38*h + 5. Solve h*f + f**2 + 177 - 29*f - 33 = 0.
12
Let s(l) be the third derivative of l**7/1155 - 8*l**6/165 + 15*l**2 - 18. Factor s(t).
2*t**3*(t - 32)/11
Let m(f) = f**2 - f. Let l(r) = -58*r**3 + 123*r**2 - 8*r. Let d(q) = l(q) - 6*m(q). Find u such that d(u) = 0.
0, 1/58, 2
Let c(f) be the first derivative of 7*f**3/2 + 9*f**2 - 6*f + 62. Let c(t) = 0. Calculate t.
-2, 2/7
Suppose 2*i**2 + 32/11*i**3 + 4/11*i + 14/11*i**4 + 0 = 0. What is i?
-1, -2/7, 0
Let l(s) be the first derivative of -s**4/6 + 2*s**3/3 + 4*s**2/3 - 214. Find c, given that l(c) = 0.
-1, 0, 4
Let l(t) = -6*t**4 - 2*t**3 - 6*t**2 + 2*t - 4. Let a(z) = -5*z**4 - 2*z**3 - 4*z**2 + 2*z - 3. Let y(w) = 4*a(w) - 3*l(w). Factor y(c).
-2*c*(c - 1)*(c + 1)**2
Let i(q) = -q**3 - 26*q**2 + 6. Let v be i(-26). Suppose -4*k = -4, 2*h - k - 3 = -0*h. Determine c so that 2*c**3 + 1 + 4*c - v*c + c**4 - h = 0.
-1, 1
Let x be ((-8)/(-12))/1*18. Suppose 8 + x*z**3 - 4*z**4 - 3*z**2 + 9*z - 21*z - z**2 = 0. What is z?
-1, 1, 2
Let 16*i**3 + 20 + 3 - 12*i - 4*i**5 - 8*i**2 - 15 = 0. What is i?
-2, -1, 1
Let h(s) be the third derivative of -s**8/112 - 6*s**7/35 + 9*s**6/8 - s**5/5 - 15*s**4/2 + 106*s**2 + 2. Find l such that h(l) = 0.
-15, -1, 0, 2
Let g(z) = -46*z - 89. Let c be g(-2). Let x(b) be the first derivative of -1/7*b**c - 12/7*b + 6/7*b**2 + 7. Factor x(f).
-3*(f - 2)**2/7
Determine m, given that -19*m**3 + 2*m**2 + 17*m**3 + 2*m**4 + 2*m**5 - 4*m**2 = 0.
-1, 0, 1
Determine j so that 14/9*j**3 + 4/9*j + 0 - 2*j**2 = 0.
0, 2/7, 1
Let l = 13 + -9. Factor 16*f**3 + 3*f**4 - 12*f + f**l - 7*f**3 - f**4.
3*f*(f - 1)*(f + 2)**2
Let t = -240/511 - -5288/2555. Factor t*j**3 + 0*j + 0 + 2*j**2 - 2/5*j**4.
-2*j**2*(j - 5)*(j + 1)/5
Suppose 5*j = 4*l + 27, -5*l - 18 = -4*l - 5*j. Let g be (2 - 1)*(2 - l). Find y, given that 0 + 4*y**3 + 12*y**g + 6*y**2 - 4/3*y - 62/3*y**4 = 0.
-1/2, 0, 2/9, 1
Let v(m) = m**3 - 6*m**2 - m - 5. Suppose 4*a + 120 = 32. Let g(i) = -1. Let c(x) = a*g(x) + 2*v(x). Factor c(k).
2*(k - 6)*(k - 1)*(k + 1)
Suppose -27*b + 30 = -12*b. Let p(i) be the second derivative of -3/40*i**5 + 0*i**b - 2*i + 0*i**3 - 3/20*i**6 - 1/14*i**7 + 0 + 0*i**4. Factor p(d).
-3*d**3*(d + 1)*(2*d + 1)/2
Let z be -6*5/15*1. Let d be (32/(-14))/z - (-30)/30. Suppose -9/7 - 3*f - d*f**2 - 3/7*f**3 = 0. What is f?
-3, -1
Let s = -2701 - -2705. Let v(x) be the third derivative of -3*x**2 - 1/24*x**s - 1/14*x**3 - 1/840*x**6 + 0*x - 1/84*x**5 + 0. Factor v(k).
-(k + 1)**2*(k + 3)/7
Let d(p) be the third derivative of -p**11/110880 + p**5/15 + 10*p**2. Let l(k) be the third derivative of d(k). Factor l(g).
-3*g**5
Let m(a) be the third derivative of 5/42*a**7 + 0*a**4 - 10 + a**2 + 0*a**5 + 0*a**3 + 0*a - 1/12*a**6. What is l in m(l) = 0?
0, 2/5
Let h(p) = -2*p**4 + 4*p**3 + 39*p**2 - 41*p - 54. Let f(g) = -g**4 + 2*g**3 + 21*g**2 - 21*g - 27. Let d(b) = 10*f(b) - 6*h(b). Solve d(u) = 0 for u.
-3, -1, 3
Let b be (254/(-6))/(4 + 28/(-12)). Let d = -25 - b. Factor -2*n + 4/5 + 8/5*n**2 - d*n**3.
-2*(n - 2)*(n - 1)**2/5
Let i = 1 + -1. Suppose 7*v + 28*v = 85*v - 200. Factor 3/4*j**5 + i + 15/4*j**3 - 11/4*j**v + 1/2*j - 9/4*j**2.
j*(j - 1)**3*(3*j - 2)/4
Suppose -8*w + 126 - 231 = -43*w. Factor -172/5*p**w - 224/5*p + 292/5*p**2 + 64/5 - 4/5*p**5 + 44/5*p**4.
-4*(p - 4)**2*(p - 1)**3/5
Let i(n) be the second derivative of -5*n**5/24 + 5*n**4/4 + 13*n**3/12 + n**2/3 + 23*n. Factor i(g).
-(g - 4)*(5*g + 1)**2/6
Suppose 41 = 3*k - 157. Factor 45*o**2 + 15*o**3 - 3*o**4 + 4*o - o + 6*o - k*o**2.
-3*o*(o - 3)*(o - 1)**2
Suppose -4*b + 11 = 5*z, 0*b + 2*z = 4*b - 18. Suppose -15 = -2*x - 5*n, -x - n = -b + 1. Factor -1/4*d**3 + x*d**2 + 0 + 1/4*d.
-d*(d - 1)*(d + 1)/4
Let p(d) = d**2 - 5*d. Let g be p(5). Suppose g = -c + 5 + 4. Factor -12*o - 1 + c*o**2 + 6*o**3 - 1 - 13 + 3 - 3*o**4.
-3*(o - 2)**2*(o + 1)**2
Let t(g) be the first derivative of 1/80*g**5 + 12 - 9*g + 1/24*g**4 + 0*g**2 + 1/24*g**3. Let b(m) be the first derivative of t(m). Factor b(i).
i*(i + 1)**2/4
Let h(p) = -p**3 + 8*p**2 - 8*p + 10. Let x be h(7). Let 9*c**2 + 8*c**3 + 8*c**x + 5*c**3 - 6*c**3 - 27*c + 3*c**4 = 0. What is c?
-3, 0, 1
Let g(r) = -3*r**2 - 15*r - 2. Let d(k) = 20*k**2 + 105*k + 10. Let c(x) = -2*d(x) - 15*g(x). Determine n, given that c(n) = 0.
-2, -1
Let r(c) be the second derivative of -c**4/21 + 2*c**3/7 + 36*c**2/7 - 917*c. Factor r(m).
-4*(m - 6)*(m + 3)/7
Let g(s) = s**5 - 5*s**4 - 5*s**3 + 9*s**2 - 8*s. Let m(l) = -l**4 - l**3 + l**2 - l. Let h = -17 - -14. Let t(v) = h*g(v) + 24*m(v). Factor t(a).
-3*a**2*(a + 1)**3
Let f(u) = -u - 16. Let l(w) = 4. Let n(o) = -4*f(o) - 12*l(o). Let t be n(-4). Factor 0*b**3 - 2/7*b**4 + t + 6/7*b**2 - 4/7*b.
-2*b*(b - 1)**2*(b + 2)/7
Let d(o) be the second derivative of -o**5/270 + o**4/54 - 7*o**2 + 7*o. Let a(v) be the first derivative of d(v). Let a(p) = 0. Calculate p.
0, 2
Let c(g) be the third derivative of g**8/112 - 3*g**6/40 + g**5/10 - 249*g**2. Factor c(r).
3*r**2*(r - 1)**2*(r + 2)
Let h = -3074 - -3077. Factor -2/3*m**h + 2*m**2 + 2/3*m - 2.
-2*(m - 3)*(m - 1)*(m + 1)/3
Suppose -9*k + 4 = -8*k. Factor k*y**5 + y - 4*y + 4*y**3 - 6*y + y - 12*y**4 + 12*y**2.
4*y*(y - 2)*(y - 1)**2*(y + 1)
Let u(p) be the third derivative of -p**8/84 - 1