, 0
Let c(v) be the second derivative of v**5/10 + 7*v**4/6 + 5*v**3 + 9*v**2 - 19*v. Factor c(i).
2*(i + 1)*(i + 3)**2
Let n(s) be the second derivative of 6*s**7/49 - 26*s**6/35 + 67*s**5/35 - 19*s**4/7 + 16*s**3/7 - 8*s**2/7 + s + 8. Solve n(z) = 0.
2/3, 1
Let y(p) = p**3 + 2*p**2 - 5*p - 4. Let d be y(-3). Let k be (-1)/(1*d/(-4)). Suppose -1/4*b + 0 - 1/4*b**k = 0. Calculate b.
-1, 0
Let -7/4*a**2 - 1/4*a**3 + 1/4*a**5 + 0*a + 1 + 3/4*a**4 = 0. What is a?
-2, -1, 1
Suppose -h + 3*n = -8, -5*h = -3*h + 5*n - 5. Let -4/7*r**2 + 4/7*r**4 + 0 - 2/7*r + 2/7*r**h + 0*r**3 = 0. What is r?
-1, 0, 1
Let f = -18 + 45. Let y be -3*(-39)/f - 3. Factor y*a - 2/3 - 2/3*a**2.
-2*(a - 1)**2/3
Let h = 5 - 2. Let q(u) = u**3 + 6*u**2 - u - 4. Let t be q(-6). What is g in -1/2*g**4 + 0*g**h + 0 + 0*g**t + 0*g + 1/2*g**5 = 0?
0, 1
Let h(p) = -3 - 9*p**2 - 3*p - 3*p**3 + 25*p**2 + 8. Let u(t) = t**3 - 8*t**2 + t - 3. Let x(z) = -3*h(z) - 5*u(z). Factor x(j).
4*j*(j - 1)**2
Let g(i) = 2*i**2 - 15*i + 9. Let y be g(7). Let v(x) be the first derivative of -1/2*x**2 + y + 0*x + 5/6*x**3. Suppose v(t) = 0. Calculate t.
0, 2/5
Let p be 185/11 + (-8)/(-44). Suppose -15 + p = w. Find f, given that 0*f**w + 3/5*f**3 - 9/5*f - 6/5 = 0.
-1, 2
Let s = 2101/20 + -105. Let b(q) be the second derivative of 1/100*q**5 + 1/10*q**2 + 0 - q + s*q**4 + 1/10*q**3. Factor b(t).
(t + 1)**3/5
Let d = 118/81 - -8/81. Factor d*y**3 + 4/9*y + 0 + 2*y**2.
2*y*(y + 1)*(7*y + 2)/9
Let v be (-1)/2 - 10/(-4). Let h = 10 - 8. Find i such that i**2 + 3*i**2 - 8*i**v + 4 + h*i - 2*i**3 = 0.
-2, -1, 1
Let q be ((-32)/24)/((-2)/3). Factor -1 + 0*j**2 - 4*j + 5*j**q - 6*j**2 + 2*j.
-(j + 1)**2
Let t = 21 - 16. Let -4*j**4 - 2*j**3 - 3*j**t + 0*j**5 - 3*j**5 + 4*j**5 = 0. What is j?
-1, 0
Let r(m) = -m**3 - 22*m**2 + 40*m - 20. Let t(l) = 6*l**3 + 153*l**2 - 279*l + 141. Let y(g) = 27*r(g) + 4*t(g). Determine p, given that y(p) = 0.
2
Let l(o) = -o**3 + 22*o**2 - 56*o - 16. Let q be l(19). What is t in -8/9*t - 34/9*t**q + 32/9*t**2 + 0 + 10/9*t**4 = 0?
0, 2/5, 1, 2
Let c(y) = y**3 - y**2 + y + 1. Let z(b) = -4*b**3 + 9*b**2 - 3. Let j(x) = x**2 - 8*x - 4. Let m be j(9). Let n(w) = m*c(w) + z(w). Factor n(l).
(l + 1)**2*(l + 2)
Suppose 4*g + a = -g + 1, 2*g + 2 = 2*a. Let r(v) be the first derivative of 5/3*v**3 + g*v - v**2 + 7/4*v**4 - 2. Find k such that r(k) = 0.
-1, 0, 2/7
Let z(u) be the second derivative of u**6/120 + u**5/40 - u**4/4 - u**3 - 2*u. Let n(c) be the second derivative of z(c). Suppose n(y) = 0. Calculate y.
-2, 1
Let c(d) be the third derivative of -d**8/196 - 9*d**7/490 - 3*d**6/140 - d**5/140 - 9*d**2. Factor c(h).
-3*h**2*(h + 1)**2*(4*h + 1)/7
Let s(z) be the second derivative of -z**7/42 + z**6/30 + 3*z**5/20 - 5*z**4/12 + z**3/3 - 9*z. Factor s(p).
-p*(p - 1)**3*(p + 2)
Let r = -5 + 37/7. Let m be 65/13 + 1*-5. Determine w, given that m + r*w**2 + 2/7*w = 0.
-1, 0
Factor -1/4*c**4 - 1 + c - 1/2*c**3 + 3/4*c**2.
-(c - 1)**2*(c + 2)**2/4
Let x(n) be the second derivative of 1/10*n**5 + 1/3*n**3 + 0 + 3*n + 1/3*n**4 + 0*n**2. Factor x(j).
2*j*(j + 1)**2
Let p(z) be the third derivative of z**8/11520 + z**7/2240 + z**6/1440 + z**5/60 + 4*z**2. Let q(t) be the third derivative of p(t). Solve q(x) = 0 for x.
-1, -2/7
Suppose -o = -62 - 12. Let d = o - 369/5. Factor 1/5*y + 3/5*y**2 + d*y**4 + 3/5*y**3 + 0.
y*(y + 1)**3/5
Let g(z) be the third derivative of 5*z**8/84 - 5*z**6/8 - 5*z**5/12 + 25*z**4/8 + 15*z**3/2 + 7*z**2 - z. Factor g(p).
5*(p + 1)**3*(2*p - 3)**2
Factor 8/5*q**3 + 16/5 - 28/5*q**2 + 16/5*q.
4*(q - 2)**2*(2*q + 1)/5
Let g(p) be the second derivative of -3*p**4/8 + 2*p**3 - 3*p**2 - 2*p + 43. Suppose g(x) = 0. What is x?
2/3, 2
Suppose -5*q + 14 = -21. Let r(n) be the second derivative of -1/10*n**5 + 0 + 1/42*n**q + 3*n + 0*n**2 + 0*n**4 + 0*n**6 + 1/6*n**3. Let r(k) = 0. Calculate k.
-1, 0, 1
Let f(l) be the first derivative of 1/4*l**2 + 9 + 1/2*l**3 - 1/8*l**4 - 1/5*l**5 - 1/2*l. Determine g, given that f(g) = 0.
-1, 1/2, 1
Factor 144*q + 108*q**4 + 528*q**2 + 54*q**4 - 154 + 21*q**5 + 456*q**3 + 58.
3*(q + 2)**4*(7*q - 2)
Let m be 6/(-15) + 244/10. Suppose -5*x + 3*k = -m, 0 = -4*x + 3*k + 11 + 10. Factor 2*q + 9*q**2 + 3*q**x + 0*q + 4*q**3.
q*(q + 1)*(7*q + 2)
Let v be ((-4)/10)/(6/(-30)). Find t such that -t - 15*t**2 + 3*t**3 + 4 - 7*t**v + 18*t**4 + 11*t**3 - 13*t = 0.
-1, 2/9, 1
Let 34*o**2 - 15*o**2 - 8*o**2 - 4*o - 6 - 9*o**2 = 0. What is o?
-1, 3
Let o(c) be the third derivative of c**8/672 + c**7/420 - c**6/320 - c**5/240 + c**4/192 + 13*c**2. Suppose o(d) = 0. What is d?
-1, 0, 1/2
Let f be 3 - ((-1)/(-2) - 6/(-60)). Factor -26/5*r**2 - 24/5*r - f*r**3 - 8/5 - 2/5*r**4.
-2*(r + 1)**2*(r + 2)**2/5
Factor -r + 8*r**4 - 6*r**3 - 6*r - 18*r**2 + 3*r.
2*r*(r - 2)*(r + 1)*(4*r + 1)
Let t(n) be the second derivative of -n**6/120 + n**5/30 - n**4/24 + 5*n**2/2 + 4*n. Let u(s) be the first derivative of t(s). Factor u(q).
-q*(q - 1)**2
Let y = -5437/880 + 99/16. Let g(k) be the third derivative of y*k**5 + 1/660*k**6 + 3*k**2 + 0*k**3 + 0*k + 1/66*k**4 + 0. Factor g(n).
2*n*(n + 1)*(n + 2)/11
Let y(t) = 6*t. Let a be y(1). Let l be (-13)/(-52) + a/40. Factor 2/5*g**2 - l*g - 4/5.
2*(g - 2)*(g + 1)/5
Suppose -8*c + 91 = 5*c. Let p(k) be the third derivative of -1/80*k**6 + 0*k**3 + k**2 + 0 + 0*k + 1/21*k**c - 1/60*k**5 + 0*k**4. Factor p(f).
f**2*(4*f + 1)*(5*f - 2)/2
Let h(y) be the first derivative of -4*y**5/25 - y**4/5 + 4*y**3/5 + 2*y**2/5 - 8*y/5 + 1. Suppose h(m) = 0. What is m?
-2, -1, 1
Let u be (2/(-7))/(9/(-21)). Let i(t) be the first derivative of 0*t - u*t**3 + 0*t**2 + 2. Solve i(w) = 0.
0
Let n(s) = s - 1. Let r be n(1). Solve r - 2/7*k**3 + 0*k - 2/7*k**2 = 0 for k.
-1, 0
Let l(w) = -2*w**5 + 10*w**4 - 22*w**3 + 14*w**2 - 8*w + 4. Let d(j) = 2*j**5 - 10*j**4 + 21*j**3 - 14*j**2 + 7*j - 3. Let q(s) = -4*d(s) - 3*l(s). Factor q(f).
-2*f*(f - 2)*(f - 1)**3
Let x(m) be the third derivative of m**7/840 + m**6/160 - m**5/240 - m**4/32 + 10*m**2. Let x(r) = 0. What is r?
-3, -1, 0, 1
Let t(x) be the first derivative of x**5/10 + x**4/8 - x**3/2 - x**2/4 + x + 7. Determine l so that t(l) = 0.
-2, -1, 1
Let m = 181 - 5791/32. Let d(t) be the third derivative of -1/48*t**5 + 2*t**2 + 1/12*t**3 + m*t**4 + 0 + 0*t. Factor d(l).
-(l - 1)*(5*l + 2)/4
Let n(t) be the first derivative of 1/6*t**3 - 1/2*t**2 + 0*t - 2. Solve n(b) = 0 for b.
0, 2
Let c(g) = g**2 + 9*g + 12. Suppose -2*h - 2*h + 3*m = 32, 40 = -5*h - 4*m. Let f be c(h). Solve 5*o**5 + f*o - o - 7*o**3 + 3*o**4 - o - 3*o**2 = 0.
-1, 0, 2/5, 1
Let t(j) be the second derivative of 0 - 3*j - 1/6*j**4 + 1/3*j**3 + 0*j**2. Factor t(c).
-2*c*(c - 1)
Let p(b) be the second derivative of -1/54*b**4 + 0*b**3 - 5*b + 1/9*b**2 + 0. Factor p(h).
-2*(h - 1)*(h + 1)/9
Let k = -33715/24 + 1405. Let a(b) be the second derivative of k*b**3 - 1/12*b**4 + 1/60*b**6 - 2*b - 1/8*b**5 + 1/4*b**2 + 0 + 5/168*b**7. Solve a(f) = 0.
-1, -2/5, 1
Let x be (-12)/(-26)*832/96. Factor 0*w**2 + 0 + 0*w - 2/13*w**5 - 4/13*w**3 - 6/13*w**x.
-2*w**3*(w + 1)*(w + 2)/13
Let l be -1 + ((-3)/1 - -7). Let g(y) be the first derivative of 0*y**2 - 1/3*y**l - 1 + 0*y. Factor g(h).
-h**2
Let y(j) be the third derivative of -j**6/280 + j**4/56 + 2*j**2. Factor y(z).
-3*z*(z - 1)*(z + 1)/7
Let v be (-2 + 0)/1 + 4. Factor -3*k - v - 3*k**2 + 7 - 5.
-3*k*(k + 1)
Let k(r) be the third derivative of -27*r**8/28 - 186*r**7/35 - 71*r**6/6 - 67*r**5/5 - 8*r**4 - 8*r**3/3 + 3*r**2. Suppose k(m) = 0. Calculate m.
-1, -2/9
Suppose -c**2 + 1/3*c**3 + 0*c + 4/3 = 0. Calculate c.
-1, 2
Suppose -3*r + 8*r = 15. Let f(c) be the first derivative of 1/4*c**4 + 0*c**2 + r + 0*c**3 + 0*c. What is s in f(s) = 0?
0
Let k(q) be the second derivative of q**6/60 - q**4/24 - 3*q. Solve k(y) = 0 for y.
-1, 0, 1
Let i(a) be the third derivative of a**5/80 - a**3/2 - 16*a**2. Factor i(r).
3*(r - 2)*(r + 2)/4
Suppose 0 - 4/11*y + 6/11*y**2 - 2/11*y**3 = 0. Calculate y.
0, 1, 2
Let x = -259/9 - -29. Let b = 0 - -2. Factor 0 + 2/9*p - x*p**5 - 4/9*p**b + 0*p**3 + 4/9*p**4.
-2*p*(p - 1)**3*(p + 1)/9
Let w be 3 - (3 + (-56)/20)*13. Find n such that -w*n**2 + 2/5*n**3 + 2/5 - 2/5*n = 0.
-1, 1
Let w(m) be the third derivative of m**5/90 - m**4/9 + 4*m**3/9 + 2*m**2.