d derivative of s**5/20 + s**4/12 + s**2/2 + 9*s. Let d(f) = -36*b(f) - 4*o(f). Factor d(t).
4*(t - 5)*(t - 2)*(t - 1)
Factor 120*k - 243*k**3 + 7*k**4 - 936*k**2 - k**4 + 1053*k**2.
3*k*(k - 40)*(k - 1)*(2*k + 1)
Suppose 2*c = -2*n + 36 + 2, -4*n = -2*c - 70. Factor 9*p**3 - 62*p**2 - 4*p**4 + 14*p**2 + 32*p + n*p**3 - 3*p**3.
-4*p*(p - 2)**3
Factor -100 + 71*x + 131*x + 33*x + 45*x**2 + 205*x.
5*(x + 10)*(9*x - 2)
Let c = -907/630 + 13/9. Let s(n) be the third derivative of -n**2 + 1/420*n**6 + 0*n + 0 - 5/84*n**4 + 1/7*n**3 + c*n**5. Factor s(y).
2*(y - 1)**2*(y + 3)/7
Let c = -23 - -25. Factor -26 - 30*u + 9*u**c - 5*u**3 + 34 + 18*u**2.
-(u - 4)*(u - 1)*(5*u - 2)
Suppose -4*q - 8 = -5*f, 21*f - 24*f = -4*q. Factor 1/2*w**4 + 1/2*w**5 + 0*w + 0 - 1/2*w**q - 1/2*w**2.
w**2*(w - 1)*(w + 1)**2/2
Let u be (-6)/32*(13 + 301/(-21)). Find i such that 0 - u*i**5 - 1/4*i**4 + 1/4*i**2 + 1/4*i**3 + 0*i = 0.
-1, 0, 1
Let w(k) be the third derivative of 2/7*k**3 - 1/14*k**4 - 1/140*k**5 + 0 + 0*k + 1/280*k**6 + 20*k**2. Factor w(i).
3*(i - 2)*(i - 1)*(i + 2)/7
Suppose -5 = 10*y - 7*y + 5*w, 0 = -w + 2. Let t be (-6)/40*y + (-4)/16. Find x such that 3/8*x**4 + 1/8*x**2 + t*x**3 + 0*x + 0 = 0.
-1, -1/3, 0
Suppose -5*s + 6 = -2*s. Let i(z) = z**3 - 2*z**2 - 8*z + 3. Let x be i(4). Factor 3/7*b**x + 6/7*b**s + 3/7*b + 0.
3*b*(b + 1)**2/7
Let o(m) = 156*m - 156. Let p be o(1). Let a be -2*2/(-4) + -1. Factor 0*b - 4/5*b**4 + a + 0*b**3 - 4/5*b**5 + p*b**2.
-4*b**4*(b + 1)/5
Let h be (-1 - -2)*1 + 1. Let g = -4238 + 4242. Factor 0 - 4/15*o + 2/15*o**g - 2/15*o**h + 4/15*o**3.
2*o*(o - 1)*(o + 1)*(o + 2)/15
Suppose 3*p - 4 + 10 = 0. Let w be p/5 + -579*6/(-360). Determine h, given that 11*h + w*h**3 + 2 + 7/4*h**4 + 33/2*h**2 = 0.
-2, -1, -2/7
Factor 4*p**2 - 3*p**3 + 0 - 5/2*p**4 + 0*p.
-p**2*(p + 2)*(5*p - 4)/2
Let z be (-21)/(-9) - (-1)/(-3). Let m be 12*(3 - (-2 + z)). Find p, given that -5*p**2 - 7 + 4*p**4 - p**4 + 34 - p**2 + 12*p**3 - m*p = 0.
-3, 1
Let v = -17306/3 + 5769. Determine t so that 2*t**2 + v*t**3 - 2/3 + 1/3*t - 2/3*t**4 = 0.
-1, 1/2, 2
Let m(f) be the first derivative of 0*f + 0*f**2 - 1/12*f**4 + 1/9*f**3 - 17. Factor m(t).
-t**2*(t - 1)/3
Let o(g) be the third derivative of -g**6/360 + 11*g**5/180 - 19*g**4/72 + g**3/2 + 2*g**2 - 88*g. Suppose o(n) = 0. Calculate n.
1, 9
Let d(s) be the first derivative of -5*s**5/4 + 45*s**4/8 - 15*s**3/4 + 136. Factor d(p).
-5*p**2*(p - 3)*(5*p - 3)/4
Let r(p) = p**4 + p - 1. Let m(c) = 7*c**4 + 3*c**3 + 3*c**2 + 7*c - 6. Let i be (52/20 + -3)*15. Let n(f) = i*r(f) + m(f). Suppose n(v) = 0. Calculate v.
-1, 0
Let d be (-6)/2 + 3 - 0. Suppose -3*z = -0*q - 4*q, d = -3*q - 2*z + 17. Factor -2*l**4 - 4*l - 26*l**2 + 3*l**3 + l**q - 2*l**4 + 30*l**2.
-4*l*(l - 1)**2*(l + 1)
Let r be (7 + -5)*2*2. Let d = 11 - r. Find s, given that -4*s**5 - 30*s**d + 4*s**4 + 34*s**3 + 5*s**5 = 0.
-2, 0
Let f = -7/17 + 185/408. Let u(o) be the third derivative of -1/840*o**7 - 2*o**2 + f*o**4 + 0 - 1/40*o**5 + 1/120*o**6 - 1/24*o**3 + 0*o. Factor u(j).
-(j - 1)**4/4
Let c = 898/7 + -128. Let f be (-17)/(-42) + (-285)/(-90) + -3. Find h, given that -6/7*h - c*h**2 - f = 0.
-2, -1
Let d be (14/12 - 1)/(3/6). Suppose -4*t - 3*q - 25 = -8*q, 3*q = -3*t + 15. Factor -d*c**3 + t - c - 4/3*c**2.
-c*(c + 1)*(c + 3)/3
Solve 2/5*c**3 - 14/5 - 2*c**2 - 26/5*c = 0.
-1, 7
Let j = -779 - -787. Let b(w) be the third derivative of 0*w - 1/448*w**8 + 0 - 3/2*w**4 - 1/5*w**6 - 9/280*w**7 - 2*w**3 - 7/10*w**5 + j*w**2. Factor b(a).
-3*(a + 1)*(a + 2)**4/4
Let u be 2 + (-7)/(14/(-54)). Let b = u + -24. Suppose b*s - 8*s - s - 3*s**2 - 2*s = 0. What is s?
-2, 0
Suppose -1 = -9*z + 44. Factor 8*t**3 - 5*t**5 - 5*t - 3*t**3 + z*t**3.
-5*t*(t - 1)**2*(t + 1)**2
Suppose -b - 3*c + 6 = 0, 18*b - 16*b - c = -2. Factor 5*x**3 + 0 + b*x - 5/2*x**2 - 5/2*x**4.
-5*x**2*(x - 1)**2/2
Let d = -245 + 248. Let k(z) be the first derivative of 0*z - 23/5*z**5 - 4 - 7/6*z**6 - 27/4*z**4 - 13/3*z**d - z**2. Factor k(f).
-f*(f + 1)**3*(7*f + 2)
Find d, given that -6*d**5 - 6*d**5 - 1750*d**2 - 15*d**4 + 1765*d**2 + 3*d + 9*d**3 = 0.
-1, -1/4, 0, 1
Factor 8/5*a + 2/5*a**3 + 32/15*a**2 - 32/15.
2*(a + 2)*(a + 4)*(3*a - 2)/15
Let z(n) be the second derivative of n**7/126 + 7*n**6/90 + 3*n**5/20 - 7*n**4/36 - 5*n**3/9 - 95*n. Let z(b) = 0. Calculate b.
-5, -2, -1, 0, 1
Let k(r) = 21*r**2 + 3*r + 4. Let h be k(-3). Let z be 10/70 - 1*h/(-35). Find n such that 21/5*n**2 + 9*n + 3/5*n**3 + z = 0.
-3, -1
Let f(i) be the second derivative of i**7/1980 + i**6/1980 - i**4/6 + 6*i. Let n(t) be the third derivative of f(t). What is y in n(y) = 0?
-2/7, 0
Let j(d) = 2*d**2 - 5*d + 4. Let b be j(4). Let h(r) = -r**3 + 17*r**2 - 15*r - 14. Let u be h(b). What is k in 0*k**u + 1/3*k**3 - 2/3 - k = 0?
-1, 2
Suppose -2*u + g - 8 = 3*g, 4 = 2*g. Let v be 3/u - (-30)/44. Factor v*b**3 + 4/11 + 0*b**2 - 6/11*b.
2*(b - 1)**2*(b + 2)/11
Let y(o) be the third derivative of 0 + 1/24*o**6 + 0*o**3 + 0*o**4 + 0*o**5 + 1/42*o**7 + 22*o**2 + 0*o. Factor y(j).
5*j**3*(j + 1)
Let l(h) be the first derivative of -3*h**4/4 + 20*h**3 + 138*h**2 + 288*h - 57. Factor l(a).
-3*(a - 24)*(a + 2)**2
Let y be 117/(-1014)*4/(-12). Let m(p) be the first derivative of 14 - y*p**4 + 0*p - 1/13*p**2 - 4/39*p**3. Determine g so that m(g) = 0.
-1, 0
Let n(u) = -u - 8. Let k(t) = t**2 - t - 9. Let m(d) = -4*k(d) + 5*n(d). Let b(g) = 7*g**2 + g + 7. Let q(h) = -3*b(h) - 5*m(h). What is p in q(p) = 0?
1
Let j(b) be the third derivative of 3*b**2 + 0*b + 0*b**3 + 5 - 1/60*b**5 - 1/600*b**6 + 0*b**4. Factor j(s).
-s**2*(s + 5)/5
Factor -57*n - 3*n**2 + 9*n + 48 + 10*n + 7*n + 13*n.
-3*(n - 2)*(n + 8)
Let d = -457/18 + 5977/234. Factor 0*a**2 - d*a**3 + 0*a + 0.
-2*a**3/13
Let o(k) be the second derivative of -169*k**5/40 - 91*k**4/24 + 23*k**3/4 - 9*k**2/4 + 72*k. Factor o(l).
-(l + 1)*(13*l - 3)**2/2
Factor 4/5 - 2/5*b**3 + 8/5*b**2 - 2*b.
-2*(b - 2)*(b - 1)**2/5
Suppose -2*x = 5*p - 2, -5*x = 3*p - 4 - 1. Let i = -6346 - -44425/7. Factor p - 4/7*l**2 + 0*l**3 + 0*l - 1/7*l**5 + i*l**4.
-l**2*(l - 2)**2*(l + 1)/7
Let y(z) be the first derivative of -121*z**4/20 - 176*z**3/15 + 123*z**2/10 - 18*z/5 + 110. Factor y(m).
-(m + 2)*(11*m - 3)**2/5
Let c = -121 + 140. Suppose -c*t = -20*t + 3. Factor 0*d**t + 0 - 3/7*d**4 - 6/7*d + 9/7*d**2.
-3*d*(d - 1)**2*(d + 2)/7
Factor 106/5*l - 1/10*l**2 - 5618/5.
-(l - 106)**2/10
Let z(y) be the second derivative of 81*y**5/4 - 9915*y**4/4 + 6580*y**3/3 - 730*y**2 + 331*y. Suppose z(j) = 0. What is j?
2/9, 73
Factor -272/3*b + 0 + 826/3*b**2 - 10/3*b**5 + 302/3*b**4 - 282*b**3.
-2*b*(b - 1)**3*(5*b - 136)/3
Find h, given that 221*h + 160*h + 4*h**2 - 80 - 385*h = 0.
-4, 5
Let g(m) = -23*m + 33. Let q be g(1). Let t(f) be the third derivative of 1/180*f**5 + q*f**2 - 1/24*f**4 + 0*f + 0 + 1/9*f**3. Factor t(z).
(z - 2)*(z - 1)/3
Let z = -69 + 91. Determine l, given that z*l**5 + 76*l**4 - 31*l**3 - l**3 - 16*l**2 - 50*l**5 = 0.
-2/7, 0, 1, 2
Suppose -18*x**2 + 3/2*x + 3/2 = 0. Calculate x.
-1/4, 1/3
Let c(m) be the first derivative of m**3/6 - 2*m + 409. Determine y so that c(y) = 0.
-2, 2
Let k(v) be the third derivative of -v**9/15120 + 11*v**5/30 - 2*v**2. Let i(g) be the third derivative of k(g). Suppose i(b) = 0. Calculate b.
0
Let d be (-1)/((-6)/10*30/(-2046)). Let v = d + 115. Factor -v + k**2 + 4/3*k - 4/3*k**3 + 1/3*k**4.
(k - 2)**2*(k - 1)*(k + 1)/3
Let l(z) be the first derivative of 0*z - 4*z**2 + 0*z**3 - 7/12*z**5 + 7 - 5/12*z**4 + 1/6*z**6. Let t(h) be the second derivative of l(h). Factor t(q).
5*q*(q - 2)*(4*q + 1)
Let w be (-688)/129 + 8*1. Determine f, given that 2/3*f - 2/3*f**3 - 8/3*f**2 + w*f**4 + 0 = 0.
-1, 0, 1/4, 1
Determine y so that -405/4*y**4 - 45/4*y + 205/2*y**2 - 5/4 + 675/4*y**5 - 315/2*y**3 = 0.
-1, -1/15, 1/3, 1
Let g be 1 + 1/((-9)/(-15)). Let s be (-1)/(36/(-90)*(-10)/(-8)). Determine z, given that -16*z - g - 70/3*z**s = 0.
-2/5, -2/7
Suppose 3*f + 5*i + 410 = 407, 0 = -5*f - 2*i + 14. Determine x so that -1/5*x**3 + 1/5*x**f + 1/5*x - 1/5*x**2 + 0 = 0.
-1, 0, 1
Let c be -1*(-6)/(-8)*(418 + -419). Factor -3/4*w**4 + 3/4*w + 3/4*w**2 - c*w**3 + 0.
-3*w*(w - 1)*(w + 1)**2/4
Let t(p) be the third derivative of p**7/126 - p**6/72 - p**5/6 