t j(f) be the first derivative of f**5/70 + f**4/84 - 2*f**3/21 - 31*f**2/2 + 24. Let s(g) be the second derivative of j(g). Factor s(o).
2*(o + 1)*(3*o - 2)/7
Let r(u) be the second derivative of 0*u**2 - 29*u - 9/50*u**5 + 1/25*u**6 + 0*u**3 + 4/105*u**7 + 0 + 1/15*u**4. Find a, given that r(a) = 0.
-2, 0, 1/4, 1
Let t(o) be the third derivative of -o**5/20 + 5*o**4/8 + 3*o**3 + 9*o**2 + 6. Factor t(d).
-3*(d - 6)*(d + 1)
Let d = 63/2 + -755/24. Let f(j) be the third derivative of 0*j - 5*j**2 + 0 + 1/60*j**5 - 1/3*j**3 - d*j**4. Factor f(b).
(b - 2)*(b + 1)
Factor -10/3*l**2 + 0 + 10/3*l**4 + 5/3*l**5 + 0*l**3 - 5/3*l.
5*l*(l - 1)*(l + 1)**3/3
Let i(a) be the second derivative of -2*a**7/21 + 3*a**5/5 - 2*a**4/3 + 106*a. Let i(l) = 0. What is l?
-2, 0, 1
Suppose 4 = 4*c - o, 12 = -5*c - 2*o - o. Let 18 + 8*f**2 - 27*f**3 + 55*f**2 - 57*f + 3*f**4 + c = 0. Calculate f.
1, 6
Let -73*l**2 + 74*l**2 + 32*l - 4*l**4 - 9*l**2 - 20*l**3 = 0. What is l?
-4, -2, 0, 1
Let t(v) be the third derivative of -v**9/18900 + v**8/2100 - v**7/630 + v**6/450 + 43*v**4/24 + 5*v**2. Let n(q) be the second derivative of t(q). Factor n(f).
-4*f*(f - 2)*(f - 1)**2/5
Let l = 406/303 - 2/303. Suppose -8*g + 568 - 536 = 0. Solve g*o + l + 8/3*o**2 - 4*o**4 - 4/3*o**5 - 8/3*o**3 = 0 for o.
-1, 1
Let t be (-4)/(-6)*(-24)/4. Let u be 1/t*-4*5. What is n in -2*n - 192*n**u + 188*n**5 + 8*n**3 - 2*n = 0?
-1, 0, 1
Solve 294 - 21*r + 3/8*r**2 = 0 for r.
28
Let t(i) = 35*i**2 + 65*i + 60. Let s(v) = 0*v**2 + 1 + 14 + 9*v**2 + 16*v. Let p(j) = 15*s(j) - 4*t(j). Suppose p(w) = 0. What is w?
-3, -1
Suppose 3*y - 5*s - 18 = -s, -5*y = 3*s - 1. Suppose 0*x = -2*x - y*i + 16, 0 = 2*x - 2*i. Factor -3*g**3 + 3*g**4 - 3*g**5 - 5*g**4 - 4*g**x.
-3*g**3*(g + 1)**2
Let v = 347/258 - 1/86. Factor -8/3*m**3 + 0*m - 4/3*m**4 - v*m**2 + 0.
-4*m**2*(m + 1)**2/3
Let -319*q**2 - 18 + 327*q**2 + 4*q - 22*q = 0. What is q?
-3/4, 3
Solve -21*t - 3*t**5 + 18*t**2 - 1040*t**3 - 18 - 1035*t**3 + 2099*t**3 = 0 for t.
-2, -1, 1, 3
Let b(i) be the third derivative of 1/10*i**6 + 1/2*i**4 + 0 + 0*i + 1/70*i**7 + 2*i**2 + 1/2*i**3 + 3/10*i**5. Factor b(j).
3*(j + 1)**4
Let y(f) = -f**4 + f**3 + f + 1. Let m(q) = -104*q**4 + 98*q**3 + 92*q**2 - 62*q + 12. Let v(o) = -2*m(o) + 36*y(o). Determine k, given that v(k) = 0.
-1, -3/43, 1
Let m(t) = -6*t**3 + 2*t**2 - 2*t + 2. Let q(b) = -19*b**3 + 5*b**2 - 7*b + 7. Let l = 12 + -10. Let y(o) = l*q(o) - 7*m(o). Factor y(s).
4*s**2*(s - 1)
Let r(z) = -z**4 - z**3 - z**2. Let p(u) = u**4 + 33*u**3 - 24*u**2 + 8*u. Let x(g) = p(g) + 6*r(g). Solve x(y) = 0.
0, 2/5, 1, 4
Let r(t) be the second derivative of t**7/280 + t**6/120 - t**5/20 + 31*t**3/6 - 10*t. Let f(g) be the second derivative of r(g). Determine m so that f(m) = 0.
-2, 0, 1
Suppose 160*s**2 - 405*s**3 + 767*s**2 - 74842*s + 402*s**3 - 20639*s + 3278181 = 0. Calculate s.
103
Let x(q) be the first derivative of 2*q**3/3 - 2*q**2 - 126*q + 230. Factor x(n).
2*(n - 9)*(n + 7)
Let w(t) = -t**3 + 5*t + 1. Let p(x) = -4*x**3 - 4*x**2 + 26*x + 2. Let v(k) = p(k) - 2*w(k). Factor v(m).
-2*m*(m - 2)*(m + 4)
Let t(b) = 2*b + 2. Let n = 29 - 30. Let a be t(n). Factor 0*i + a - 3/5*i**2.
-3*i**2/5
Let z be (-10)/(-95) + (-14)/133. Let p(a) be the second derivative of 1/28*a**4 + z - 1/7*a**3 + 7*a + 3/140*a**5 + 0*a**2. Factor p(o).
3*o*(o - 1)*(o + 2)/7
Suppose r + 0*r + 5*n = -18, 3*n = 4*r - 20. Suppose -r*i = 2*d - 6*d - 4, 0 = -3*d. Find s such that 4 - 2*s**2 + 3*s + 12*s**i + 13*s - 2*s = 0.
-1, -2/5
Suppose 3*d = 4*p + 7, -2*p = -7*d + 8*d - 9. Let a(i) be the first derivative of 1/18*i**4 + 0*i**3 + 0*i + 4 + 0*i**5 + 0*i**p - 1/27*i**6. Factor a(u).
-2*u**3*(u - 1)*(u + 1)/9
Let a be 16/(-672)*-14 - (-10)/6. Find m, given that 1/2*m + 0 - 1/2*m**4 + 1/2*m**a - 1/2*m**3 = 0.
-1, 0, 1
Let z(j) be the second derivative of -j**4/84 - 5*j**3/21 - 58*j. Factor z(g).
-g*(g + 10)/7
Let r(o) be the second derivative of o**5/20 - o**4/6 + o**3/3 + 9*o. Let g(k) = -k**3 + k**2 - 2*k. Let a(t) = -5*g(t) - 4*r(t). Let a(j) = 0. Calculate j.
-2, -1, 0
Find g, given that -80*g + 30 + 135*g - 3*g**2 + 33*g**2 + 5*g**3 = 0.
-3, -2, -1
Let l be (1 - 1) + (-330)/(-11). Factor -30 + 8*v**2 - 2*v - 4*v**3 - 2*v + l.
-4*v*(v - 1)**2
Let m = 49977/91564 - 3/8324. Suppose 0 - 40/11*r**2 + 24/11*r + m*r**3 = 0. What is r?
0, 2/3, 6
Let x(r) be the second derivative of -5*r**4/24 - 35*r**3/12 - 15*r**2/2 - r - 37. Factor x(m).
-5*(m + 1)*(m + 6)/2
Let y(u) be the second derivative of -u**6/120 + 3*u**5/16 - 13*u**4/16 + 37*u**3/24 - 3*u**2/2 + 16*u + 1. Factor y(j).
-(j - 12)*(j - 1)**3/4
Factor -64/7*c**2 - 8/7 - 36/7*c - 8*c**3 - 4/7*c**5 - 24/7*c**4.
-4*(c + 1)**4*(c + 2)/7
Let s(d) = -29*d**2 - 40*d**2 + 79*d**2 + 47 + d**3 + 5*d + 9*d. Let p be s(-9). Factor 0*v + 0 + 1/5*v**p + 1/5*v**3.
v**2*(v + 1)/5
Let b(k) be the first derivative of -11 + 1/9*k**6 + 0*k**4 + 4/15*k**5 + 0*k - 1/3*k**2 - 4/9*k**3. Determine d so that b(d) = 0.
-1, 0, 1
Let k(h) be the third derivative of h**5/30 + 4*h**4/3 - 194*h**2. Factor k(p).
2*p*(p + 16)
Let r(y) = -5*y**4 + 3*y**3 + y**2 - 3*y + 4. Let q(m) = m**4 + m**2 - 2. Let o(v) = 2*q(v) + r(v). Factor o(n).
-3*n*(n - 1)**2*(n + 1)
Let l be -10*(1 + 6/(-12)). Let j(y) = -y**2 - y - 2. Let a(s) = -3*s**2 - 3*s - 5. Let t = -4 + 6. Let p(w) = l*j(w) + t*a(w). Factor p(f).
-f*(f + 1)
Let d be (3/4)/(-9 - 1089/(-88)). Let f = 232/99 + -16/11. Factor -f*o + 8/9 + d*o**2.
2*(o - 2)**2/9
Let x(m) be the first derivative of -m**3/12 - m**2/8 + m/2 + 92. Factor x(p).
-(p - 1)*(p + 2)/4
Let q(y) be the third derivative of y**6/120 + 4*y**5/5 + 32*y**4 + 2048*y**3/3 + 250*y**2. Factor q(d).
(d + 16)**3
Let b = -11 + 16. Let m = -184/3 - -926/15. Determine x, given that 0*x + 4/5*x**4 + 0 + 2/5*x**b + 0*x**2 + m*x**3 = 0.
-1, 0
Let 0 - 121/9*l**2 - 1/9*l**4 - 22/9*l**3 + 0*l = 0. Calculate l.
-11, 0
Let u(s) be the third derivative of -s**5/60 - s**4/24 + s**3 - 701*s**2. Let u(n) = 0. What is n?
-3, 2
Let a be (-3 - (1 + 1))*-10. Let -4 - a*w + 0 - 125*w**2 - 1 = 0. What is w?
-1/5
Let b(k) be the third derivative of 0*k + 1/20*k**5 + 0 + 25*k**2 + 0*k**3 - 1/896*k**8 + 1/80*k**6 - 1/280*k**7 + 0*k**4. Factor b(j).
-3*j**2*(j - 2)*(j + 2)**2/8
Let x = 30 + -26. Let w(n) = 3*n**2 - 11*n - 1. Let p be w(x). Solve -j**p - 2*j - 6*j**2 + 6*j**2 + 3*j**2 = 0 for j.
0, 1, 2
Factor 1189 - 5*r**4 - 15769 + 210*r**3 + 9069*r + 2271*r - 2745*r**2.
-5*(r - 18)**2*(r - 3)**2
Let s(a) = -46*a + 38*a**2 - 4*a**2 + 8 - 3 - 1. Let y(o) = 11*o**2 - 15*o + 1. Let n(k) = -3*s(k) + 8*y(k). Factor n(p).
-2*(p - 1)*(7*p - 2)
Let i(m) be the third derivative of m**8/672 + m**7/105 + m**6/120 - m**5/30 - m**4/16 + 7*m**2 - 11. Factor i(b).
b*(b - 1)*(b + 1)**2*(b + 3)/2
Let d be (1/3)/(1/21). Let a be (-3)/5 + 345/75. Factor d*s**2 + s**2 - 12*s - a*s**2.
4*s*(s - 3)
Factor -94*s + 18*s**2 + 371 - 171 - 26*s.
2*(3*s - 10)**2
Let h(a) be the second derivative of a**4/54 + 4*a**3/9 - 28*a**2/9 + 352*a. Factor h(l).
2*(l - 2)*(l + 14)/9
Factor -112*i**2 + 244/3*i**3 + 4/3*i**5 - 56/3*i**4 + 0 + 48*i.
4*i*(i - 6)**2*(i - 1)**2/3
Let d(b) be the second derivative of 169*b**4/3 - 208*b**3/3 + 32*b**2 + 6*b. Factor d(n).
4*(13*n - 4)**2
Let p = -93 - -261. Find h, given that 76*h**4 - 33*h + 12 - h**5 + 57*h**2 - 43*h + 111*h**2 - p*h**3 - 11*h**5 = 0.
1/3, 1, 3
Let f be ((-44)/5 + 9)*(3 - 1). Determine i so that f*i + 0 + 0*i**2 - 2/5*i**3 = 0.
-1, 0, 1
Let b(r) be the third derivative of -3*r**4/8 - 23*r**3/6 + 45*r**2. Let u be b(-3). Determine n so that -3/7*n**2 + 6/7 - 3/7*n**u + 9/7*n - 9/7*n**3 = 0.
-2, -1, 1
Suppose 7*r - 1 = 13. Suppose m**2 - 9 - 2*m**r - 112*m + 122*m = 0. Calculate m.
1, 9
Let r(z) be the third derivative of -5*z**7/231 - 166*z**6/33 - 55772*z**5/165 - 664*z**4 - 528*z**3 + 107*z**2 - 2. What is s in r(s) = 0?
-66, -2/5
Let c = -23854 - -141685/6. Let j = c + 240. Solve 1/6*i - 1/6*i**3 - 1/6*i**4 + j*i**2 + 0 = 0.
-1, 0, 1
Factor 2/13*m**5 - 46/13*m**4 + 0*m + 86/13*m**3 - 42/13*m**2 + 0.
2*m**2*(m - 21)*(m - 1)**2/13
Let p(k) be the first derivative of 1/4*k**4 - 9*k + 3/2*k**2 - 12 + 5/3*k**3. Factor p(j).
(j - 1)*(j + 3)**2
Let t(o) be the first derivative of 3 - 1/2*o + 3/8*o**2 - 1/12*o**3. Fact