 be the second derivative of -k**5/40 - k**4/6 - 5*k**3/12 - k**2/2 + 83*k + 1. Factor d(t).
-(t + 1)**2*(t + 2)/2
Let y(b) be the third derivative of b**5/300 + 22*b**4/15 + 3872*b**3/15 - 43*b**2 - 2*b. What is d in y(d) = 0?
-88
Let f(w) = -w**3 + 2*w**2 + 2*w - 1. Let x be f(2). Let l be (-20)/(-4) + -3 + -2. Factor l*z + 4/7*z**2 - 2/7*z**x + 0.
-2*z**2*(z - 2)/7
Let u be 4652/8480 + (-10)/25. Let q = 12/53 + u. Let -9/8*i - q*i**3 + 0 + 3/8*i**4 - 15/8*i**2 = 0. Calculate i.
-1, 0, 3
Let p(q) be the third derivative of -15/4*q**4 - 1/12*q**5 + 0*q - 135/2*q**3 + 0 + 14*q**2. Factor p(y).
-5*(y + 9)**2
Let k(x) = x**4 - x**3 + x**2 - x - 2. Let o(p) = -3*p**4 + 5*p**3 - 5*p**2 + 3*p + 8. Let n(h) = -4*k(h) - o(h). Factor n(a).
-a*(a - 1)*(a + 1)**2
Suppose -5*f + 5*j + 45 = 0, -f - 11 - 4 = 3*j. Solve -12/13*k**2 - 50/13*k**f + 16/13 + 18/13*k**4 + 72/13*k = 0 for k.
-1, -2/9, 2
Let q be ((-15)/(-18) - 395/(-474))*6/20. Factor -5/4*h**2 + 1/4*h**3 + 3/4*h**4 - 1/4*h + q.
(h - 1)*(h + 1)**2*(3*h - 2)/4
What is s in -565/4*s**3 + 909/4*s**2 - 1 + 111*s = 0?
-2/5, 1/113, 2
Let q = -58 + 62. Let w(v) be the third derivative of -5*v**2 + 0*v + 0 - 1/20*v**5 + 0*v**q + 0*v**3. Factor w(z).
-3*z**2
Let n(a) be the third derivative of a**6/1020 + a**5/255 - a**4/68 + 2*a**2 - 3. Suppose n(m) = 0. Calculate m.
-3, 0, 1
Let s(w) be the third derivative of w**5/60 + 13*w**4/3 + 1352*w**3/3 + w**2 + 189. What is y in s(y) = 0?
-52
Factor -14*t**2 + 10*t**2 - 3*t - 7*t + 9*t**2.
5*t*(t - 2)
Let u = 67 + -66. Let f(v) = v - 1. Let t(b) = -3*b**3 + 6*b**2 - 5*b + 2. Let d(j) = u*t(j) + 2*f(j). Factor d(l).
-3*l*(l - 1)**2
Let d(i) be the second derivative of -1/315*i**6 + 0 + 0*i**3 - 4/105*i**5 - 8/63*i**4 + 31*i + 0*i**2. Find b, given that d(b) = 0.
-4, 0
Let z(n) be the third derivative of 0*n**3 - 1/30*n**6 + 0 + 1/15*n**5 - 11*n**2 + 0*n + 1/3*n**4. Factor z(q).
-4*q*(q - 2)*(q + 1)
Let l = 55 - 28. Suppose 2*q = -7*q + l. Let -1/2*z**5 + 3/2*z**4 + 2 + 1/2*z**q + 0*z - 7/2*z**2 = 0. Calculate z.
-1, 1, 2
Factor -4*s + 17*s + s**2 - 5*s**2 + 23*s.
-4*s*(s - 9)
Let n be (-1)/(-2)*-1*6/(-3)*3. Factor -1/5*d**4 + 0 + 1/5*d**n + 1/5*d**2 - 1/5*d.
-d*(d - 1)**2*(d + 1)/5
Let l(r) be the third derivative of r**5/510 - 13*r**4/102 + 169*r**3/51 + 2*r**2 - 66. Determine s so that l(s) = 0.
13
Suppose -z = 2*z - 6. Let g be (15 - 18)*(1 - z). Factor -63 + q - g*q**2 + 15 + 23*q.
-3*(q - 4)**2
Let b be (-40)/(-2) - (-11 + 6 + 1). Determine p so that 16*p**3 + 19*p - 196*p**2 + 85*p - 58*p + b = 0.
-1/4, 1/2, 12
Let j be ((-261)/(-54))/29 + (-46)/(-12). Factor 2/5*i**5 + 0*i + 2/5*i**2 + 6/5*i**j + 0 + 6/5*i**3.
2*i**2*(i + 1)**3/5
Let x(u) be the second derivative of u**4/4 - 11*u**3/2 - 39*u**2 - 252*u. Determine k so that x(k) = 0.
-2, 13
Let d be 5/(-10) + (-15)/(-10). Let r = 1 + d. Factor -10*l**3 + 22*l**3 + 3*l**r - 9*l**3.
3*l**2*(l + 1)
Let g be (-20)/(-2)*(-72)/(-1980)*11. Let 10/3*x**3 + 0 - 10/3*x + 2/3*x**g - 2/3*x**2 = 0. What is x?
-5, -1, 0, 1
Let c = 1707 + -1702. Factor 0 + 0*y - 10/9*y**4 - 4/9*y**3 + 0*y**2 - 4/9*y**c.
-2*y**3*(y + 2)*(2*y + 1)/9
Let l(h) be the first derivative of -5*h**3/12 - 75*h**2/4 - 1125*h/4 - 57. Determine d, given that l(d) = 0.
-15
Let a = 137 + -137. Let i be 3/(-9) + (2/6 - a). Factor -p**2 - 7/2*p**3 + 0*p - 5/2*p**4 + i.
-p**2*(p + 1)*(5*p + 2)/2
Let d(y) be the third derivative of y**8/5040 - y**7/1260 - y**6/270 + y**5/45 + 8*y**3/3 - 8*y**2. Let l(s) be the first derivative of d(s). Factor l(q).
q*(q - 2)**2*(q + 2)/3
Let h(k) = 23*k + 5 - 7*k - 5*k**2 - 8*k**2. Let j(l) = -19*l**2 + 24*l + 7. Let r(z) = 7*h(z) - 5*j(z). Factor r(d).
4*d*(d - 2)
Let l = 41 - 39. Let z(w) be the second derivative of -2/21*w**4 + 0 - 4*w + 0*w**l + 1/70*w**5 + 4/21*w**3. Suppose z(o) = 0. What is o?
0, 2
Let t(q) be the second derivative of -q**4/18 - 41*q**3/27 + 14*q**2/9 + q + 138. Suppose t(b) = 0. Calculate b.
-14, 1/3
Let s = -259 - -243. Let w = s - -18. Find l, given that 3/4*l**w + 3/4*l - 3/2 = 0.
-2, 1
Let o be 2/(-5) - 301/35. Let g(w) = w**2 + 2*w - 5. Let c be g(o). Factor -36*s**3 + 88*s**3 - 6*s**5 - 1 - 47*s**2 + 12*s + 48*s**4 - c*s**5.
-(s - 1)*(s + 1)*(4*s - 1)**3
Let c(o) be the third derivative of -o**5/12 - 85*o**4/4 - 4335*o**3/2 + 103*o**2 + 2*o. Let c(j) = 0. Calculate j.
-51
Let u = -4439/8 + 556. Let c(f) be the first derivative of -u*f**2 - 1/4*f**3 + 3*f - 5. Let c(o) = 0. What is o?
-4, 1
Suppose 3*b - b = -5*n, 3*n - 7*b - 41 = 0. Factor 4/5*q**n - 8/5 - 4/5*q.
4*(q - 2)*(q + 1)/5
Let y(p) = p**2 - 7*p + 6. Let g be y(6). Suppose -58*z + 54*z = g. Determine b so that -2/7*b - 4/7*b**2 + z - 2/7*b**3 = 0.
-1, 0
Solve 88*j**2 - 13*j + 52*j - 27*j**5 - 12*j**3 + 6 - 12*j**4 - 34*j**2 - 48*j**4 = 0.
-1, -2/9, 1
Let 80/3*o - 32/3*o**2 - 50/3 = 0. What is o?
5/4
Let x(k) be the third derivative of 4*k**7/525 - 3*k**6/100 - 7*k**5/75 + 3*k**4/5 - 8*k**3/15 - 6*k**2 - 10*k. Let x(a) = 0. What is a?
-2, 1/4, 2
Solve 25*i**4 - 113*i**3 - 96194 + 60*i + 8*i**3 + 96210 + 4*i**2 = 0.
-2/5, 1, 4
Let v be (-270)/(-63) + (-4)/14. Suppose 5*u - 18 = -w, -6 = u + w + v*w. Factor -2*a + 0*a**3 + 0*a - 2*a**3 + u*a**3.
2*a*(a - 1)*(a + 1)
Suppose 59*c = -5*c + 256. Let l(i) be the third derivative of -2/525*i**7 + 2/15*i**c + 0*i + 0*i**3 - 9*i**2 + 4/75*i**5 + 0 - 1/150*i**6. Factor l(x).
-4*x*(x - 2)*(x + 1)*(x + 2)/5
Let t(n) = 32 + 12*n**3 - 12 + 8*n**2 - 33*n**4 + 57*n**4. Let m(y) = -y**4 - y**3 - y**2 - 1. Let u(z) = 20*m(z) + t(z). Find w, given that u(w) = 0.
-1, 0, 3
Let t = -630 - -1261/2. What is a in -t*a**2 + 0 - 1/2*a = 0?
-1, 0
Let y = -134 + 146. Suppose y = 233*w - 230*w. Solve -7*m**2 - 3/2*m**w + 2*m - 13/2*m**3 + 4 = 0 for m.
-2, -1, 2/3
Factor 0 + 2/7*h**3 + 0*h + 8/7*h**2.
2*h**2*(h + 4)/7
Let w(c) be the second derivative of -c**6/360 - c**5/40 - c**4/12 + c**3/3 - 4*c. Let q(h) be the second derivative of w(h). What is x in q(x) = 0?
-2, -1
Let h(t) be the third derivative of -t**8/448 + t**7/280 + 7*t**6/160 - t**5/80 - 3*t**4/16 - t**2 - 7. Find p, given that h(p) = 0.
-2, -1, 0, 1, 3
Let z be 2/140*7 - (-1)/10. Let g(h) be the first derivative of 2/15*h**3 - 2 - z*h**2 + 0*h. Factor g(r).
2*r*(r - 1)/5
What is z in -56*z**2 - 78*z**5 + 8/3*z + 226/3*z**3 + 56*z**4 + 0 = 0?
-1, 0, 2/39, 2/3, 1
Let z = -18 - -11. Let t be (-1 - -1)/(8/(-56)*z). Find k, given that 1/5*k**5 - 2/5*k**4 + t*k**2 + 1/5*k**3 + 0 + 0*k = 0.
0, 1
Let 15/8*z**2 + 0 - 9/4*z + 3/8*z**3 = 0. What is z?
-6, 0, 1
Factor 4/11*j + 0*j**3 + 0 + 6/11*j**2 - 2/11*j**4.
-2*j*(j - 2)*(j + 1)**2/11
Let j be (-91)/(-52)*34/119. Solve 4 - 9/2*g + j*g**2 = 0 for g.
1, 8
Let l = 31/85 + 3/85. Let h(r) be the second derivative of 1/4*r**5 + 0 + 1/12*r**4 + 8*r + l*r**2 - 8/15*r**3. Determine n so that h(n) = 0.
-1, 2/5
Let i be (-12)/(-8) - (-2)/4. Suppose 11 = 3*w + 5. Let 2*d**i + 9 - 9 + w*d = 0. What is d?
-1, 0
Let l(u) be the third derivative of -2*u**7/315 + 17*u**6/90 - 22*u**5/15 - 16*u**4/9 + 704*u**3/9 - 460*u**2. Let l(n) = 0. Calculate n.
-2, 4, 11
Let l(i) be the second derivative of -9/2*i**2 - i**3 + 10*i - 1/12*i**4 + 0. Factor l(b).
-(b + 3)**2
Let s(j) = 10*j**2 - 7*j - 10. Suppose -5*p - o = 2*o + 114, 2*o - 99 = 5*p. Let v(i) = 3*i**2 - 2*i - 3. Let c(y) = p*v(y) + 6*s(y). Factor c(l).
-3*(l - 1)*(l + 1)
Let u(m) = -m**3 + 3*m**2 + 27*m + 246. Let g be u(9). Determine v, given that -4/17 + 2/17*v**g - 6/17*v + 0*v**2 = 0.
-1, 2
Let x(h) = 129*h - 1157. Let t be x(9). Let a(i) be the second derivative of 1/3*i**t + 5*i - 2*i**3 + 3/5*i**5 - 4*i**2 + 0 + 2/15*i**6. Factor a(w).
4*(w - 1)*(w + 1)**2*(w + 2)
Let c(x) be the second derivative of -x**4/48 + 5*x**3/24 - 3*x**2/4 + 21*x. Determine f, given that c(f) = 0.
2, 3
Let c = 7892 - 7890. Factor 0 - u**4 - c*u - 9/2*u**3 - 6*u**2.
-u*(u + 2)**2*(2*u + 1)/2
Let a be 3 + -16 + 9 - 57/(-14). Let n(j) be the first derivative of -a*j**6 - 12/35*j**5 + 0*j**2 + 0*j + 7 - 15/28*j**4 - 2/7*j**3. Factor n(v).
-3*v**2*(v + 1)**2*(v + 2)/7
Let u(m) be the second derivative of -m**4/3 - 10*m**3/3 - 5*m - 3. Let u(j) = 0. Calculate j.
-5, 0
Let u(w) be the second derivative of w**5/160 + w**4/48 - w**3/16 + 11*w + 2. Factor u(h).
h*(h - 1)*(h + 3)/8
Let x(g) be the 