t v(h) be the third derivative of -h**5/20 + h**4/8 - 5*h**2. Find r such that v(r) = 0.
0, 1
Let t = -14 - -18. Suppose 2*j = 3*j + 2*u - 13, -5*u = -t*j - 13. Determine q, given that 2/3*q**j + 0 - 2/3*q + 0*q**2 = 0.
-1, 0, 1
Let v(s) be the second derivative of -s**6/6 + 2*s**5 - 35*s**4/12 + 27*s. Let v(i) = 0. Calculate i.
0, 1, 7
Suppose v + 2*v + 4*a + 6 = 0, 0 = 4*v - 3*a - 17. Determine f, given that -12/7 + 8/7*f + 4/7*f**v = 0.
-3, 1
Let q(t) = -t**3 - t**2 + t. Let p(m) = -17*m**3 + 7*m + 5*m + 5*m**3 + 2 - 18*m**2 + 1. Let k(y) = -p(y) + 15*q(y). Determine i so that k(i) = 0.
-1, 1
Let a(b) be the second derivative of b**7/42 + 2*b**6/15 + 3*b**5/20 - b**4/3 - 2*b**3/3 - 4*b. Factor a(u).
u*(u - 1)*(u + 1)*(u + 2)**2
Let n(l) = l**2 - l + 2. Let g(x) = 5*x**2 - 5*x + 11. Let y(t) = t - 11. Let j be y(0). Suppose r + 2 = 2*r. Let v(s) = j*n(s) + r*g(s). Factor v(w).
-w*(w - 1)
Let y be 4*(56/(-144) - 16/(-36)). What is c in 2/9*c**5 + y*c**3 + 0*c**2 + 4/9*c**4 + 0*c + 0 = 0?
-1, 0
Let h(j) be the first derivative of -j**3 + 0*j**2 - 3/4*j**4 + 0*j - 6. What is v in h(v) = 0?
-1, 0
Factor 3*c + 3*c + 13*c - 15*c**2 - 7*c + 3*c**3.
3*c*(c - 4)*(c - 1)
Let o(a) be the second derivative of 1/6*a**4 - 1/45*a**6 + 0 + 2/3*a**2 - 1/30*a**5 + 9*a + 5/9*a**3. Factor o(q).
-2*(q - 2)*(q + 1)**3/3
Let v(a) = a**3 - 13*a**2 - 6*a + 4. Let j(h) = -2*h**3 + 14*h**2 + 6*h - 5. Let t(g) = 4*j(g) + 5*v(g). Find p such that t(p) = 0.
-2, -1, 0
Let c(k) be the first derivative of k**4/16 + k**3/4 + 3*k**2/8 + 10*k + 2. Let w(g) be the first derivative of c(g). Factor w(y).
3*(y + 1)**2/4
Suppose 5*s = 2*f - 4*f, 3*s = -3*f. Let r(y) be the first derivative of -1/3*y**2 - 2/3*y**3 + f*y - 1/2*y**4 - 2/15*y**5 + 1. Factor r(a).
-2*a*(a + 1)**3/3
Let h(u) = 5*u**2 + 32*u + 45. Let o(g) = 15*g**2 + 97*g + 135. Let d(f) = 7*h(f) - 2*o(f). Determine b, given that d(b) = 0.
-3
Let p(c) be the first derivative of -98/33*c**3 - 14/11*c**2 - 2 - 2/11*c. Factor p(y).
-2*(7*y + 1)**2/11
Let v = 5 - 3. Let c = v + 3. Solve -5*l**4 - 2*l**3 - 6*l**5 + 2*l**c + l**5 = 0.
-1, -2/3, 0
Let l(o) = -14*o**2 + 26*o - 10. Let j(t) = 2*t**2 - t + 1. Let v(r) = -15*j(r) - 3*l(r). Factor v(z).
3*(z - 5)*(4*z - 1)
Let m(g) be the third derivative of -1/60*g**5 + 1/24*g**4 + 0*g**3 + 0 + 0*g - g**2 - 1/120*g**6 + 1/210*g**7. Suppose m(u) = 0. Calculate u.
-1, 0, 1
Let n = 856/3 - 278. Let q = n - 7. Factor 2/3*h - q*h**2 - 1/3.
-(h - 1)**2/3
Let t(k) be the first derivative of 2*k**5/5 - k**4 + 2*k**2 - 2*k + 4. Factor t(o).
2*(o - 1)**3*(o + 1)
Let b(g) be the first derivative of 7*g**6/2 - 69*g**5/5 + 81*g**4/4 - 13*g**3 + 3*g**2 - 1. Let b(h) = 0. Calculate h.
0, 2/7, 1
Suppose 4*m - 6 = -2*b + 32, -2*b + 23 = m. What is u in 8 + 3*u**2 + 0*u - 2 - b*u = 0?
1, 2
Let h be 12/206*(-2)/88. Let w = h - -10303/2266. Factor -48/11*i - 90/11*i**2 - 8/11 - w*i**3.
-2*(i + 1)*(5*i + 2)**2/11
Factor 2*q**3 - 162*q + 159*q - 3*q**5 + 4*q**3.
-3*q*(q - 1)**2*(q + 1)**2
Suppose 0 = 2*d + 7 + 1. Let r(o) = 4*o**4 + o**2 + 2*o**2 + 2*o + 0*o**4 - 5*o**4. Let i(x) = -x**4 + 3*x**2 + 2*x. Let a(w) = d*i(w) + 5*r(w). Factor a(b).
-b*(b - 2)*(b + 1)**2
Let n(f) be the third derivative of -f**7/240 + f**6/80 - f**5/160 - f**4/96 + 2*f**2 + 10*f. Factor n(s).
-s*(s - 1)**2*(7*s + 2)/8
Suppose 6 + 3 = 3*v. Let d(k) = k**3 - 6*k**2 - 7*k. Let h be d(7). Factor 4/7*w**v + h*w + 0 - 2/7*w**2 - 2/7*w**4.
-2*w**2*(w - 1)**2/7
Let l(k) be the first derivative of -k**5/20 - k**4/16 + k**3/12 + k**2/8 + 8. Factor l(d).
-d*(d - 1)*(d + 1)**2/4
Factor 0*t**3 + 0 + 0*t - 8/23*t**2 + 2/23*t**4.
2*t**2*(t - 2)*(t + 2)/23
Let a be (1 + 5)/(-1*2). Let b be 34/8 + a - 1. Factor 1/2*u**2 - b*u + 0 - 1/4*u**3.
-u*(u - 1)**2/4
Let n = -1 - -4. Let -j**4 - 8*j**3 - 8 - 2*j**2 + 8*j**2 + n*j**4 + 8*j = 0. What is j?
-1, 1, 2
Let a be (-1 + 2)/(5/10). Let y = a + 0. Determine s so that -1/2*s + 1 - 1/2*s**y = 0.
-2, 1
Let k(l) be the third derivative of -l**7/840 + l**6/160 - l**5/80 + l**4/96 + 3*l**2. Suppose k(s) = 0. What is s?
0, 1
Let w(l) be the third derivative of -l**8/672 + l**6/80 - l**5/60 + 7*l**2. Factor w(d).
-d**2*(d - 1)**2*(d + 2)/2
Suppose 3*f - 22 = -4. Suppose 2*n = 5*n - f. Determine c, given that -1/4*c**3 + 0 - 1/4*c + 1/2*c**n = 0.
0, 1
Suppose -3*h + 17 = -r, 4*h - 41 = 7*r - 2*r. Let d = 6 - h. Factor 1/4*s**d + 0*s - 1/4.
(s - 1)*(s + 1)/4
Suppose -3*r = -2*v - 3, -4*r + 4 = -5*v + 8*v. Factor 0*t - 1/6*t**2 + v*t**3 + 1/6*t**4 + 0.
t**2*(t - 1)*(t + 1)/6
Suppose -7*v + 25*v = 36. Let y(p) be the first derivative of -1/3*p**3 + p + v + 0*p**2. Factor y(h).
-(h - 1)*(h + 1)
Let h(m) be the second derivative of 1/60*m**6 + 1/40*m**5 - 1/12*m**3 - 1/24*m**4 + 0 - 5*m + 0*m**2. Factor h(c).
c*(c - 1)*(c + 1)**2/2
Factor -y - 20*y**3 + 16*y**2 - 10*y**5 + 35*y**4 + y - 36*y**2.
-5*y**2*(y - 2)**2*(2*y + 1)
Factor -1 + 9*t + 3*t**2 + 4 - 3*t.
3*(t + 1)**2
Let h(b) be the second derivative of b**4/6 - b**3/3 - 8*b. Factor h(t).
2*t*(t - 1)
Let v = 27941/4140 + 1/1035. Suppose 0 = -m + 3*b - 15, 0 = 2*b - 2 - 8. Factor -3/2*y + v*y**2 + m - 21/4*y**3.
-3*y*(y - 1)*(7*y - 2)/4
Let a be (-14 + 15)*3*1. Factor -5 - a - m + 5*m + m**2 + 11.
(m + 1)*(m + 3)
Suppose -2*b + 24 = 3*m, 3*m - 2*m - 3*b = -3. Let a be (m - 0)*2/3. Factor -a*u - 14*u**2 - 3*u**3 - 5*u**3 + 2 + 0*u**3.
-2*(u + 1)**2*(4*u - 1)
Let g(n) be the third derivative of n**7/630 + n**6/360 - n**5/60 - n**4/72 + n**3/9 - 5*n**2. Factor g(s).
(s - 1)**2*(s + 1)*(s + 2)/3
Let g = -143099/206028 - -2/17169. Let j = 1/18 - g. Let -j*z + 3/2 - 9/4*z**2 = 0. Calculate z.
-1, 2/3
Let t(x) be the third derivative of x**5/30 - x**4/4 + 2*x**3/3 - 16*x**2. Factor t(z).
2*(z - 2)*(z - 1)
Let k be (-6)/15 - 27/(-30). Factor 1/2*i - k*i**2 + 1.
-(i - 2)*(i + 1)/2
Let r(q) be the third derivative of 0*q - 1/336*q**8 + 0*q**5 + 0 + 0*q**4 + 0*q**3 + q**2 + 0*q**7 + 1/120*q**6. Factor r(i).
-i**3*(i - 1)*(i + 1)
Let c(u) = u**2 - 27*u + 126. Let v be c(6). Suppose -3/5*x - 3/5*x**3 + 6/5*x**2 + v = 0. Calculate x.
0, 1
Suppose 0 = -2*o + 5 - 1. Let -2*d**2 + d**3 + 0*d**2 - 2*d**o + d + 6*d**2 = 0. What is d?
-1, 0
Let l(w) be the second derivative of w**7/189 - 2*w**6/135 + w**4/27 - w**3/27 - 36*w. Factor l(o).
2*o*(o - 1)**3*(o + 1)/9
Let b(s) = -s**2 + 6*s + 9. Let x be b(7). Suppose -x*j = -2*n + 2, 1 + 2 = 3*n. Let -2/7*a - 8/7*a**2 + j = 0. Calculate a.
-1/4, 0
What is t in 0 + 8/11*t**2 - 8/11*t + 6/11*t**3 = 0?
-2, 0, 2/3
Let d(v) be the first derivative of -3*v**5/5 + 3*v**3/2 + 3*v**2/2 - 2*v - 1. Let b(o) be the first derivative of d(o). Factor b(i).
-3*(i - 1)*(2*i + 1)**2
Let v(a) be the third derivative of a**9/17280 + a**8/4480 + a**7/5040 - a**5/30 - a**2. Let m(x) be the third derivative of v(x). Solve m(l) = 0.
-1, -2/7, 0
Suppose -2*n = 2*u - 14, 13 = -u - 0*n + 3*n. Let -11*y**u - y**5 - 6*y**3 - y + 7*y**2 - y**4 - 3*y**4 = 0. Calculate y.
-1, 0
Let n(j) be the second derivative of -1/55*j**5 + 5/66*j**4 + 0 + 0*j**2 + 2/33*j**3 - 1/33*j**6 - j. Suppose n(u) = 0. Calculate u.
-1, -2/5, 0, 1
Let c(o) be the third derivative of -o**6/300 + o**5/150 + o**2. What is h in c(h) = 0?
0, 1
Let m**4 + 66*m**3 + 3*m**4 + 4*m**2 - 58*m**3 = 0. What is m?
-1, 0
Let x(d) = d + 5. Let s be x(-5). Suppose s = 5*q - 10 - 0. Factor -2*o**q + 2*o**4 + o - 3*o**3 + 3*o**3 - o**5.
-o*(o - 1)**3*(o + 1)
Factor -4 + 7*l**5 - 7*l**3 + 4 + 0*l**3 - 2*l**2 + 2*l**4.
l**2*(l - 1)*(l + 1)*(7*l + 2)
Let l(u) be the first derivative of 2/9*u**3 + u + 2 - 5/6*u**2. Determine z so that l(z) = 0.
1, 3/2
Let l be 3/(9/6) - 0. Suppose -i + 5*a + 8 = i, -a - 8 = -l*i. Factor -6*h**4 + 2*h + 0*h**2 - 8*h**3 + h**i - h**2.
-h*(h + 1)**2*(5*h - 2)
Factor 3*y**2 - 5*y**3 - 5*y**4 + 5*y + y**4 + 0*y**2 + 1.
-(y - 1)*(y + 1)**2*(4*y + 1)
Suppose -4*l - 32 = -3*z, -5*z + 2*l = -l - 35. Suppose 0 = -3*w - 3*r + 6, -z*w + 5*r + 13 = 5. Let 0*i + 0*i**3 - 1/3*i**w + 1/3*i**4 + 0 = 0. Calculate i.
-1, 0, 1
Let c(d) = d**2 + d - 1. Suppose -2*r + 6 = 4*y - 14, y - 32 = -5*r. Let b(x) = 17 - 20*x**2 - r*x - x - 3 + x. Let k(w) = -b(w) - 12*c(w). Factor k(i).
2*(i - 1)*(4*i + 1)
Let r(l) = -3*l + 26. Let n be r(8). Let c(g) be the second derivative of 1/12*g**3 + 1/24*g**