
1/2, 1
Let q(l) = -81*l**3 + 66*l**2 - 24*l - 6. Let i(k) = -80*k**3 + 65*k**2 - 22*k - 5. Let b(g) = -6*i(g) + 5*q(g). Let b(p) = 0. Calculate p.
0, 2/5
Let w(i) be the third derivative of i**7/1050 + i**6/120 + i**5/75 - 610*i**2. Factor w(q).
q**2*(q + 1)*(q + 4)/5
Let f(t) be the first derivative of t**6/90 - t**5/60 - t**4/36 + t**3/18 + 6*t - 13. Let r(n) be the first derivative of f(n). Factor r(g).
g*(g - 1)**2*(g + 1)/3
Let r(v) be the first derivative of -2*v**5/95 - 5*v**4/19 - 22*v**3/19 - 36*v**2/19 - 90. Solve r(b) = 0.
-4, -3, 0
Let b(y) be the third derivative of -y**8/112 - y**7/35 - 13*y**2 + y. Determine h so that b(h) = 0.
-2, 0
Let m(t) = -t**2 + 1. Let d be 16/(-4) - (-4 + 2). Let b(o) = -o**2 + 1. Let s(a) = d*b(a) + 3*m(a). Factor s(k).
-(k - 1)*(k + 1)
Let h(o) be the third derivative of -o**5/100 - 153*o**4/20 - 23409*o**3/10 - 3*o**2 + 177*o. Factor h(w).
-3*(w + 153)**2/5
Suppose 5*z - 4 = -2*q + 3*z, 0 = 2*q + z - 6. Suppose -3*l - 4*w = -22, -q*l + w = -1 - 3. Factor l - 2 + 2 + 4*g - 3*g**2 + 5*g**2.
2*(g + 1)**2
Factor 232/3*v**2 - 26912/3*v + 3121792/9 - 2/9*v**3.
-2*(v - 116)**3/9
Suppose -3*d + 47 = 5*y, -4*y - 3*d + 37 = -0*d. Let w(f) = f - 8. Let x be w(y). Factor 10*l - l**2 + 5*l**5 + 7*l**3 - 4*l**x - 2*l**4 - 22*l**3 + 7*l**4.
5*l*(l - 1)**2*(l + 1)*(l + 2)
Let z(v) be the third derivative of -v**6/30 + 8*v**5/5 - 65*v**4/6 + 28*v**3 + 167*v**2. Factor z(y).
-4*(y - 21)*(y - 2)*(y - 1)
Let a = 17/195 - -16/65. Let o(f) be the second derivative of 1/18*f**4 + 1/45*f**6 + 0 - 1/10*f**5 + a*f**3 - 2/3*f**2 + 6*f. Find z, given that o(z) = 0.
-1, 1, 2
Let i be 4*(-1 + 0) - (-522)/108. Factor -d + i + 1/6*d**2.
(d - 5)*(d - 1)/6
Let b(c) be the second derivative of 2*c**7/21 + 8*c**6/15 - c**5/5 - 4*c**4/3 + 51*c + 2. Factor b(t).
4*t**2*(t - 1)*(t + 1)*(t + 4)
Let n(k) = 5*k**2 - 48*k - 741. Let g(s) = -s**2 - s + 2. Let v(t) = -6*g(t) - n(t). Solve v(c) = 0.
-27
Suppose -r + 5 = -i, -5*r + 4*i = -19 - 5. Solve -3*t**4 + 157*t**2 - 192*t + 7*t**r + 83*t**2 - t**4 - 51*t**3 = 0 for t.
0, 1, 8
Factor -12*m**2 - 5*m**4 + 40 - 755*m**3 + 740*m**3 + 22*m**2 + 60*m.
-5*(m - 2)*(m + 1)*(m + 2)**2
Let f(l) be the second derivative of -l**4/22 - 4*l**3/11 - 9*l**2/11 + 708*l. Determine n so that f(n) = 0.
-3, -1
Let h(w) be the second derivative of 27*w**5/5 + 27*w**4/4 + 3*w**3 + w**2/2 - 63*w. Factor h(v).
(3*v + 1)**2*(12*v + 1)
Find u such that -1364*u + 678*u + 2*u**2 - 48 + 676*u = 0.
-3, 8
Let a(i) be the first derivative of i**6/6 - 9*i**5/5 + 13*i**4/2 - 34*i**3/3 + 21*i**2/2 - 5*i - 50. Factor a(r).
(r - 5)*(r - 1)**4
Let i = -3556 - -3558. Suppose -2/9*o**3 + 4*o**i - 24*o + 48 = 0. Calculate o.
6
Let p(g) be the first derivative of -3/14*g**4 - 6/7*g + 22/21*g**3 - 10 - 5/7*g**2. Factor p(a).
-2*(a - 3)*(a - 1)*(3*a + 1)/7
Let u = -243109/13 - -18701. Factor -10/13*b**2 - 4/13*b**3 - u*b + 0.
-2*b*(b + 2)*(2*b + 1)/13
Let a(x) be the third derivative of 675*x**6/4 - 135*x**5/4 + 45*x**4/16 - x**3/8 + 43*x**2 - 2. Factor a(u).
3*(30*u - 1)**3/4
Let a(l) be the second derivative of -l**4/114 - 9*l**3/19 + 92*l. Let a(w) = 0. What is w?
-27, 0
Let u(b) be the second derivative of b**3 - 1/4*b**4 - 6 + 0*b**2 + 5*b. Let u(f) = 0. What is f?
0, 2
Suppose -449*y - 14 = -456*y. Let b(x) be the third derivative of 1/6*x**4 - x**y + 0 + 4/3*x**3 + 0*x + 1/120*x**5. Factor b(w).
(w + 4)**2/2
Let m(x) be the first derivative of 11*x**6/135 - 7*x**5/30 + x**4/6 + x**3/27 - 21*x + 26. Let f(v) be the first derivative of m(v). Factor f(z).
2*z*(z - 1)**2*(11*z + 1)/9
Suppose 3*r - 4 = r. Let v be (-1)/r*-8 + 0. Factor f**5 + f**5 - 2*f**2 + 3*f**4 - 2*f**3 + 3*f**4 - v*f**4.
2*f**2*(f - 1)*(f + 1)**2
Suppose -3*i + 2*y + 5 = 0, 3*y + 1 = -2. Let h(d) be the first derivative of 0*d**3 + 1/24*d**6 - i + 0*d**5 - 1/16*d**4 + 0*d**2 + 0*d. Factor h(c).
c**3*(c - 1)*(c + 1)/4
Let g be (-6)/(-5)*10/6. Factor o + 4*o**3 + 3*o - 55*o**2 + 49*o**2 - g*o.
2*o*(o - 1)*(2*o - 1)
Let y be ((-2)/4)/((-2)/12). Factor 48*j - 32 + 19*j**2 + 5*j**3 - 3*j**y - 37*j**2.
2*(j - 4)**2*(j - 1)
Let m(v) = -19*v**2 + 26*v - 1. Let d be -3 - ((-4)/2 - -2). Let p(h) = -58*h**2 + 78*h - 4. Let c(u) = d*p(u) + 8*m(u). Determine l so that c(l) = 0.
2/11, 1
Suppose -2*g + 98 = 92. Let n be (-72)/(-2)*(-2)/(-4). Factor 2*k**4 + g*k**4 + n*k**3 - 3*k**3 + 2*k**2 + 8*k**2.
5*k**2*(k + 1)*(k + 2)
Let o(j) = 121 - 29*j**2 - 71*j - j**3 + 2*j**2 - 18*j**2. Let r(z) = 45*z**2 + 70*z - 120. Let q(p) = -5*o(p) - 4*r(p). Factor q(a).
5*(a - 1)*(a + 5)**2
Factor -m**4 + 416*m + 272 - 13*m**4 + 10*m**4 + 12*m**2 - 136*m**3.
-4*(m - 2)*(m + 1)**2*(m + 34)
Let b = -1811 + 1816. Factor 0*k**2 + 0 + 0*k + k**4 - k**3 - 1/4*k**b.
-k**3*(k - 2)**2/4
Let g be 5/(-189)*(-13 + -8)/(-7). Let p = 2/9 + g. Factor 0*i**2 + p*i**4 + 0 - 2/7*i**3 + 1/7*i**5 + 0*i.
i**3*(i - 1)*(i + 2)/7
Let g = -1338 + 1342. Let o(l) be the first derivative of 4/7*l**2 + 0*l - 6 + 4/21*l**3 - 1/7*l**g. Factor o(k).
-4*k*(k - 2)*(k + 1)/7
Let s(j) be the second derivative of -j**7/630 - j**6/45 - 2*j**5/15 - 5*j**4/2 + 5*j. Let a(n) be the third derivative of s(n). Factor a(k).
-4*(k + 2)**2
Let r be 4/(-18 + (-504)/(-18)). Suppose -1/10*w**5 + 2/5*w - 2/5*w**2 + 0 + r*w**4 - 3/10*w**3 = 0. Calculate w.
-1, 0, 1, 2
Let w(d) be the third derivative of 4*d**5/75 - 11*d**4/60 + d**3/5 + 79*d**2. Factor w(x).
2*(x - 1)*(8*x - 3)/5
Let r(u) be the third derivative of -u**8/280 + 43*u**7/1575 + u**6/90 + 105*u**2 + 3. Factor r(a).
-2*a**3*(a - 5)*(9*a + 2)/15
Suppose -2*j = -17*j - 13*j. Let s(o) be the second derivative of j + 7/36*o**4 - 1/9*o**3 - 4*o + 0*o**2. Determine b so that s(b) = 0.
0, 2/7
Let o be 352/56 - 6 - 2/7. Factor -2*m**2 - 6*m**4 + 19*m**4 - 3*m**3 - 14*m**4 + o*m**2.
-m**2*(m + 1)*(m + 2)
Let f be -1 - (5*(-8)/120)/(30/110). Find r such that f*r**4 + 0 + 14/9*r**2 + 10/9*r**3 + 2/3*r = 0.
-3, -1, 0
Let x(c) = -c**3 - 8*c**2 - 8*c - 1. Let l be x(-7). Suppose -l = 3*a - 15. Solve -4/3*p + 2*p**a + 0 - 2/3*p**2 = 0 for p.
-2/3, 0, 1
Let s(k) = 38*k + 3. Let o be s(-3). Let b be (-6)/36 - o/18. Solve 12*v - b*v - 2*v**2 - 2*v**3 - 6*v = 0 for v.
-1, 0
Let o(a) be the second derivative of 4*a + 0 + 0*a**3 - 1/6*a**4 + 0*a**2 + 1/50*a**5. Suppose o(k) = 0. Calculate k.
0, 5
Factor 4*o**3 - 111*o**4 - 53*o**3 + 236*o**4 - 23*o**3 + 68*o**2 - 121*o**4.
4*o**2*(o - 17)*(o - 1)
Suppose 0*i - 2*i = -5*w + 1576, w + i - 311 = 0. Let b = w + -2194/7. Find s such that 0*s**2 + 2/7 - 4/7*s + b*s**3 - 2/7*s**4 = 0.
-1, 1
Let t be (-348)/(-22) - 4/(-22). Suppose 5*b = b + t. Factor 1/7*q**b - 1/7*q**2 + 0*q**3 + 0 + 0*q.
q**2*(q - 1)*(q + 1)/7
Suppose -h + 5*m - 1 = -4, -5*m = 2*h - 6. Determine c so that 6*c + 4*c**2 - 2*c**2 + c**2 + 6*c**2 - h*c**4 = 0.
-1, 0, 2
Suppose -5*p - 97 + 112 = 0. Suppose 10 = 3*m - 5. Solve -9*z - z**m - 11*z**4 - 16*z**2 + 1 + 5*z**4 - 3 - 14*z**p = 0 for z.
-2, -1
Let s be ((-8)/5)/(26/(-65)). Suppose -s*h - 6 = -7*h. Factor 1/3*g - 1/3 + g**3 + 5/3*g**h.
(g + 1)**2*(3*g - 1)/3
Let w(n) be the first derivative of -n**3 + 1/10*n**5 - 1/8*n**4 + 5 + 0*n**2 + 0*n. Solve w(p) = 0.
-2, 0, 3
Let u(d) be the second derivative of -1/42*d**4 + 0 + 1/7*d**3 - 2/7*d**2 - 9*d. Factor u(z).
-2*(z - 2)*(z - 1)/7
Let b be ((-86)/(-473))/((-46)/(-44) + -1). Solve 0*u**2 + 1/4*u**3 + 0*u**b - 1/4*u**5 + 0 + 0*u = 0 for u.
-1, 0, 1
Let q be (4 - 1)/(1377/102). Let -4/9*g + 2/9*g**5 + 2/3*g**2 + q*g**3 + 0 - 2/3*g**4 = 0. Calculate g.
-1, 0, 1, 2
Let b be (28/(-10))/(7 - (-108)/(-15)). Factor -23*q**4 + b*q**2 + 3*q + 5*q + 18*q**2 + 10*q**3 - 27*q**4.
-2*q*(q - 1)*(5*q + 2)**2
Let d = 60 + -59. Let q(s) = 7*s**4 + 7*s**3 - 15*s**2 - s + 5. Let i(x) = -x**4 - x**3 + x**2 - x + 1. Let v(j) = d*q(j) + 3*i(j). Factor v(g).
4*(g - 1)**2*(g + 1)*(g + 2)
Let b(m) be the third derivative of -m**8/147 - 6*m**7/245 + m**6/105 + 3*m**5/35 + m**4/21 + 3*m**2 + 18*m. Suppose b(x) = 0. Calculate x.
-2, -1, -1/4, 0, 1
Factor 60 + 10*x - 36*x + 81*x + 8*x**2 - 13*x**2.
-5*(x - 12)*(x + 1)
Let k(y) be the second derivative of -y**4/6 + 152*y**3/3 - 151*y**2 + 335*y. Determine m so that k(m) = 0.
1, 151
Factor -1089/2 + 12*r**2 + 33/4*r - 3/4*r**3.
-3*(r - 11)**2*(r + 6)/4
Factor -26/17*y