2*c**4 + 90*c**3 - 120*c**2 + 75*c - 20. Let w(b) = z*j(b) - 2*t(b). Factor w(f).
3*(f - 6)*(f - 1)**4
Let t = -6036 - -6039. Suppose 6/7 - 2/7*z + 2/7*z**t - 6/7*z**2 = 0. Calculate z.
-1, 1, 3
Let j(f) be the second derivative of 4*f**5/5 - 16*f**4/3 - 6*f**3 - 427*f. Factor j(r).
4*r*(2*r - 9)*(2*r + 1)
Let j = -36177 + 36180. Suppose -5/3*c - c**2 + 8/3*c**j + 2/3 + 4/3*c**4 = 0. What is c?
-2, -1, 1/2
Let c(f) be the first derivative of -f**6/3 + 12*f**5/5 + f**4/2 - 4*f**3 + 57. Solve c(y) = 0.
-1, 0, 1, 6
Suppose 3*f + 2*n = 13, 0 = -6*f + 2*f - 2*n + 18. Suppose 6 = 4*a - 0*a - 3*j, a - f*j + 7 = 0. Factor -3/7*i**a + 3/7*i + 1/7*i**4 - 2/7 + 1/7*i**2.
(i - 2)*(i - 1)**2*(i + 1)/7
Let c = -48424/5 + 9685. Factor c*l**3 - 6/5 + 2/5*l**2 - l.
(l - 2)*(l + 1)*(l + 3)/5
Suppose 2*t - 10*t + 448 = 0. Factor -16*h - 53*h**3 + t*h**2 + 34*h**4 - 24*h**4 + 9*h**3.
2*h*(h - 2)**2*(5*h - 2)
Let i(k) be the first derivative of 5 - k**4 + 2*k**2 + 4*k - 4/3*k**3. Factor i(b).
-4*(b - 1)*(b + 1)**2
Suppose 67 = 25*p - 83. Let a(j) be the first derivative of 4 - 735/4*j**4 - 40*j**p - 696/5*j**5 - 75/2*j**2 - 116*j**3 - 6*j. Let a(u) = 0. Calculate u.
-1, -2/5, -1/4
Let w(c) be the first derivative of -3*c**4/4 + 5*c**3 - 12*c**2 + 12*c - 11. Solve w(d) = 0 for d.
1, 2
Let r be 1 - 1 - 8/(-22). Let d be -13 + 6 - (-1 + (-2 - (-8)/(-2))). Determine x so that 0*x**3 - 2/11*x**5 + r*x**2 + d - 4/11*x**4 + 2/11*x = 0.
-1, 0, 1
Let x be (-996)/(-24) + (-2)/(-4). Find f such that -15*f**3 + 85*f**2 - 15*f**2 - x*f + 7*f - 20 = 0.
-1/3, 1, 4
Let t be ((-15)/(-20))/((-3)/(-8)). Factor -21*b**3 - 32*b**3 - 32*b**t - 4*b**5 + b**3 - 24*b**4 + 4*b**3.
-4*b**2*(b + 2)**3
Let o be (-79)/(-11) - 6/33. Factor o*k**5 + 25*k + 10*k**4 - 30*k - k**5 - 10*k**2 - k**5.
5*k*(k - 1)*(k + 1)**3
Let m = -337/494 - -15/26. Let a = 11/76 - m. Solve 1/4*s**2 + a*s - 1/2 = 0.
-2, 1
Let a(q) = -5*q**3 - 58*q**2 - 24*q + 99. Let l be a(-11). Factor l - 2/9*o**2 + 22/9*o.
-2*o*(o - 11)/9
Suppose 50/17*z + 24/17*z**2 + 12/17 - 14/17*z**3 = 0. Calculate z.
-1, -2/7, 3
Let y(l) = l**2 + 2*l - 4. Let f(w) be the first derivative of -5 + w - 1/2*w**2. Let h(t) = 4*f(t) + y(t). Suppose h(j) = 0. Calculate j.
0, 2
Let q(w) be the second derivative of -4*w + 0 + 1/6*w**6 - 1/3*w**4 + 1/14*w**7 + 0*w**2 - 1/5*w**5 + 0*w**3. Solve q(j) = 0.
-2, -2/3, 0, 1
Let c(x) be the first derivative of 0*x**2 + 0*x + 0*x**4 - 2/45*x**3 + 53 + 2/75*x**5. Factor c(h).
2*h**2*(h - 1)*(h + 1)/15
Factor 1/3*x**3 + 0 + 0*x - 2/3*x**2 + 1/3*x**4.
x**2*(x - 1)*(x + 2)/3
Let y(i) be the first derivative of -10 + 6*i**2 - 2*i**4 - 2/3*i**6 + 8/3*i**3 - 12/5*i**5 + 4*i. Let y(d) = 0. What is d?
-1, 1
Let w be 4 + -8 + (6 - 7)*-6. Let y(o) be the first derivative of -1/28*o**4 + 2/7*o - 1 + 3/14*o**w + 0*o**3. Find x such that y(x) = 0.
-1, 2
Factor -1/5*h**2 - 32/5*h + 0.
-h*(h + 32)/5
Let d(a) be the second derivative of 5/3*a**3 - 4*a**2 + 17/4*a**4 + 7/30*a**6 + 0 + a + 2*a**5. Suppose d(i) = 0. What is i?
-4, -1, 2/7
Factor 10/3*p - 4/15 - 22/5*p**2.
-2*(3*p - 2)*(11*p - 1)/15
Solve 2*n**3 + 27*n**3 - 8*n**5 - 12*n**4 + 10*n**3 - 12*n**2 - 7*n**3 = 0 for n.
-3, 0, 1/2, 1
Let v = 74 - 50. Let g(n) = -28*n**2 + 28*n. Let w(l) = l**2 - l. Let h(z) = v*w(z) + g(z). Let h(b) = 0. Calculate b.
0, 1
Let f(o) be the third derivative of -2*o**7/105 + 13*o**6/30 - 8*o**5/3 + 6*o**4 - 3*o**2 + 47. Find v, given that f(v) = 0.
0, 2, 9
Let z(k) be the second derivative of -k**5/55 + 23*k**4/66 + 4*k**3/11 - 126*k. Factor z(a).
-2*a*(a - 12)*(2*a + 1)/11
Let o = -6 + 11. Factor -3*v**o - 44*v**3 - 27 - 14*v + 36*v**2 + 29 - 3*v**5 + 26*v**4.
-2*(v - 1)**4*(3*v - 1)
Let b(n) be the second derivative of 0 - 4/15*n**3 + 0*n**2 + 7/60*n**4 - 5*n + 1/100*n**5. Factor b(y).
y*(y - 1)*(y + 8)/5
Suppose -111*y + 2 = -110*y. Let d(c) be the first derivative of -1/6*c**y + 0*c + 1/12*c**4 + 3 + 0*c**3. Let d(s) = 0. What is s?
-1, 0, 1
Let g(o) be the second derivative of -1/5*o**5 + 4*o**4 + 29*o + 0 + 128*o**2 - 32*o**3. Factor g(a).
-4*(a - 4)**3
Let y(r) be the third derivative of -r**6/16 - 19*r**5/5 - 1185*r**4/16 - 225*r**3/2 + 12*r**2 + 5*r. Let y(b) = 0. Calculate b.
-15, -2/5
Suppose -602*n + 911 = -293. Suppose 64/7 + 32/7*r + 4/7*r**n = 0. Calculate r.
-4
Let q = 4/24329 + 48638/121645. Factor -2/5*s**2 + 2/5*s + 2/5*s**4 + 0 - q*s**3.
2*s*(s - 1)**2*(s + 1)/5
Factor -k**3 - 287*k - 32*k**2 + 91*k - 60*k.
-k*(k + 16)**2
Let s(t) be the third derivative of 1/144*t**4 + 0*t + 1/90*t**5 - 1/720*t**6 + 7*t**2 - 1/9*t**3 + 0. Suppose s(p) = 0. Calculate p.
-1, 1, 4
Let s(a) be the second derivative of a**6/1620 - a**5/180 - 3*a**3/2 + 14*a. Let h(b) be the second derivative of s(b). Factor h(g).
2*g*(g - 3)/9
Let b = 131/650 + -1/650. Let l(g) be the second derivative of 2/3*g**3 + b*g**5 + 0 - 1/30*g**6 - 1/2*g**2 - 1/2*g**4 - 6*g. Suppose l(f) = 0. What is f?
1
Let o be (43/4)/((-9)/(-12)) + (-5)/5. Find z such that o*z + 16/3 + 11*z**2 + 1/3*z**4 + 10/3*z**3 = 0.
-4, -1
Let c(x) be the third derivative of 3*x**7/490 - 11*x**6/40 + 601*x**5/140 - 1243*x**4/56 - 242*x**3/7 + 443*x**2. What is h in c(h) = 0?
-1/3, 4, 11
Let u(g) be the second derivative of g**7/168 + g**6/20 + 9*g**5/80 + g**4/12 - 268*g. Suppose u(h) = 0. What is h?
-4, -1, 0
Factor s**2 + 31*s**3 - 6*s**3 + 2*s**2 - 22*s**3.
3*s**2*(s + 1)
Let j(a) = 10*a**2 - 58*a + 144. Let h(z) = 2*z**2 - 2*z. Let m(r) = -3*h(r) + j(r). Solve m(t) = 0 for t.
4, 9
Let y(w) be the second derivative of -6*w**5/5 - 19*w**4/6 + 4*w**3 + 4*w**2 + 189*w. Factor y(k).
-2*(k + 2)*(3*k - 2)*(4*k + 1)
Let t(n) be the first derivative of -2*n**3/33 + 20*n**2/11 - 200*n/11 - 231. Suppose t(w) = 0. Calculate w.
10
Let f(m) be the first derivative of -m**5 + 15*m**4/2 + 125*m**3/3 + 45*m**2 - 96. Factor f(d).
-5*d*(d - 9)*(d + 1)*(d + 2)
Factor 0*s**2 - 9*s + 1/3*s**3 + 18.
(s - 3)**2*(s + 6)/3
Let 3*s + 3 - 3/2*s**3 + 3/4*s**4 - 9/4*s**2 = 0. Calculate s.
-1, 2
Let l(v) = -906*v - 8151. Let a be l(-9). Determine w so that 3/5*w**5 + 6*w**3 + 6*w**2 + a*w + 3*w**4 + 3/5 = 0.
-1
Let p be (-36)/(-378) - 3/((-252)/328). Let a(n) be the first derivative of 2/3*n**3 + 0*n + n**p - 3 - 2/5*n**5 - 2*n**2. Factor a(c).
-2*c*(c - 2)*(c - 1)*(c + 1)
Let n(h) be the third derivative of h**7/210 - h**6/45 - h**5/30 + h**4/3 - 11*h**3/2 + 29*h**2. Let s(j) be the first derivative of n(j). Factor s(t).
4*(t - 2)*(t - 1)*(t + 1)
Let a(o) be the third derivative of -o**8/80640 - o**7/10080 - o**6/2880 + 7*o**5/60 - 3*o**2. Let p(l) be the third derivative of a(l). Factor p(m).
-(m + 1)**2/4
Let j(y) be the second derivative of -y**3/6 - y**2 - 2*y. Let q be j(-4). Suppose q*o**3 - 3*o + 2 + 5*o + 4*o + 6*o**2 = 0. Calculate o.
-1
Let y(b) be the third derivative of -b**8/1344 + b**7/420 + 7*b**6/480 + b**5/60 - 36*b**2. Factor y(d).
-d**2*(d - 4)*(d + 1)**2/4
Factor -z**3 - 137 + z + 67 + 68 + 2*z**2.
-(z - 2)*(z - 1)*(z + 1)
Let l be (-29541)/(-41220) - 1/(-13 + 1). Factor -n**2 + 1/5*n**3 - l + 8/5*n.
(n - 2)**2*(n - 1)/5
Factor -24 + 2/3*t**2 - 10/3*t.
2*(t - 9)*(t + 4)/3
Let h(b) be the second derivative of 19*b - 1/42*b**7 + 0 - 1/6*b**4 + 1/30*b**6 + 1/10*b**5 + 1/2*b**2 - 1/6*b**3. Solve h(i) = 0.
-1, 1
Suppose 28*u + 3 = 29*u. Let -i + 1 + i**3 + i**3 - 2*i + 3*i**2 - u*i**3 = 0. Calculate i.
1
Let a be (5 + 95/(-20))/((-1)/(-1)). Suppose -d + 5 = 3. Find q such that 1/4*q**d - a*q + 0 = 0.
0, 1
Let p = 538 - 538. Let n(g) be the third derivative of -1/60*g**6 + 1/15*g**5 + 0 - 6*g**2 - 1/2*g**3 + 1/12*g**4 - 1/210*g**7 + p*g. Factor n(t).
-(t - 1)**2*(t + 1)*(t + 3)
Let f(x) = 10*x + 77. Let y be f(-5). Let t be (-6)/(-4) + 13/((-234)/y). Factor -2/3*r**2 - 5/3*r**4 + t + 0*r + 7/3*r**3.
-r**2*(r - 1)*(5*r - 2)/3
Let 75*b**2 - 17*b**2 - 11*b**2 - 129*b - 18 - 2*b**2 = 0. Calculate b.
-2/15, 3
Let x = 6 + -2. Let o = -30 + 32. Factor -7*z**x - 8*z**o + 7*z**5 + 15*z**4 - 4*z - 3*z**5.
4*z*(z - 1)*(z + 1)**3
Let f(s) = -s. Let p(l) = -2*l**5 - 4*l**4 - 2*l**3 + 9*l. Let t be (14/(-4) - 1)/((-3)/(-12)). Let a(v) = t*f(v) - 2*p(v). Factor a(n).
4*n**3*(n + 1)**2
Let b be 36/2505*2110/9. Let z = b - 6/167. Factor -4 + z*a**2 - 26/3*a.
2*(a - 3)*(5*a + 2)/3
Let g = 812 + -8922/11. Let u(w) = 