 + -56. Factor y*i**5 - 203*i**3 + i + 2*i - 12*i**4 + 221*i**3 - 12*i**2.
3*i*(i - 1)**4
Let r(k) be the second derivative of -19*k + 1/63*k**7 + 1/10*k**5 + 1/15*k**6 + 0*k**3 + 1/18*k**4 + 0*k**2 + 0. Factor r(n).
2*n**2*(n + 1)**3/3
Let d = 12908 - 12906. Factor 0 + 3*p**d - 6/7*p - 15/7*p**3.
-3*p*(p - 1)*(5*p - 2)/7
Let w(f) be the third derivative of -f**5/60 - 41*f**4/24 - 3*f**2 + 61. Find c, given that w(c) = 0.
-41, 0
Suppose -7 = -2*a - r, 0*r + r = 4*a - 17. Factor 32*o**2 + o**4 + 3*o**4 - 6 + 20*o**3 + 28*o + 14 + a*o**2.
4*(o + 1)**3*(o + 2)
Let c be -1*2*45/(-30). Factor 4 + z + 7*z**c - 9*z**3 + 5*z.
-2*(z - 2)*(z + 1)**2
Factor -23*z - 13*z + 7*z**2 + 12*z**2 - 22*z**2 + 7*z**2.
4*z*(z - 9)
Suppose 0 = -4*m + 11 - 3. Let v = 29/102 - 2/17. Let 1/6*q**m - v*q**3 + 0 + 0*q = 0. Calculate q.
0, 1
Let h(t) be the first derivative of -1/15*t**2 + 19 - 1/45*t**6 + 2/75*t**5 - 4/45*t**3 + 1/15*t**4 + 2/15*t. Factor h(x).
-2*(x - 1)**3*(x + 1)**2/15
Let o(i) = i**4 + i**3 + i**2 + 2*i - 1. Let h(n) = -9*n**4 - 6*n**3 - 9*n**2 - 22*n + 11. Let j(b) = 4*h(b) + 44*o(b). Factor j(m).
4*m**2*(m + 2)*(2*m + 1)
Let r(x) be the third derivative of -605*x**8/336 - 143*x**7/21 - 23*x**6/6 - 2*x**5/3 + 190*x**2. Suppose r(n) = 0. Calculate n.
-2, -2/11, 0
Let l = 8141 - 8138. Factor 2*u**2 - 1/2*u**4 + 0 + u**l - 1/4*u**5 + 0*u.
-u**2*(u - 2)*(u + 2)**2/4
Let i(d) be the second derivative of d**5/130 - 7*d**4/39 + 25*d**3/39 - 12*d**2/13 + 441*d. Factor i(f).
2*(f - 12)*(f - 1)**2/13
Suppose -6*d + 36 - 159/4*d**2 + 27/4*d**3 + 15/4*d**4 - 3/4*d**5 = 0. Calculate d.
-3, -1, 1, 4
Let k(g) = 3*g - 12. Let a be k(5). Let b(x) = 2*x**2 - 2*x + 2. Let p be b(1). Factor a - 15 - p*v + 2*v + 3*v**2.
3*(v - 2)*(v + 2)
Let w(d) be the second derivative of d**6/75 - d**4/30 + d - 27. Factor w(p).
2*p**2*(p - 1)*(p + 1)/5
Let o(j) be the third derivative of 1/18*j**3 + 0 + 1/180*j**5 - 20*j**2 + 0*j - 1/36*j**4. Factor o(z).
(z - 1)**2/3
Let h(k) be the second derivative of -k**4/3 + 4*k**3/3 + 48*k**2 - 110*k. Determine t so that h(t) = 0.
-4, 6
Let l(b) = -6*b**3 + 8*b**2 - 3*b - 4. Suppose t - 6 + 2 = 0. Let s = -3 - 2. Let c(j) = -5*j**3 + 7*j**2 - 3*j - 3. Let q(h) = s*c(h) + t*l(h). Factor q(r).
(r - 1)**3
Find g such that -13/5*g**4 - 68/5*g**3 + 12/5*g**5 + 16/5 + 16*g + 48/5*g**2 = 0.
-2, -2/3, -1/4, 2
Suppose -28 = -3*c - c - 4*l, -4*l = 5*c - 40. Factor -h**4 + c*h**3 - 27*h**3 + h**2 + h + 14*h**3.
-h*(h - 1)*(h + 1)**2
Let c(v) be the first derivative of 0*v**4 + 1/2*v**2 + 6 - 1/6*v**6 + 2/5*v**5 - 2/3*v**3 + 0*v. Factor c(r).
-r*(r - 1)**3*(r + 1)
Let f(k) be the second derivative of -k**6/10 + 3*k**5/5 - 8*k**3 + 24*k**2 + 174*k. Find z, given that f(z) = 0.
-2, 2
Let k(w) be the third derivative of w**5/210 - 2*w**4/7 + 48*w**3/7 - 2*w**2 - 14. Determine q so that k(q) = 0.
12
Let p(z) = z**3 - 2*z**2 - 6*z - 13. Let k(f) = f**3 - 3*f**2 - 7*f - 15. Let c(b) = -5*k(b) + 6*p(b). Find i, given that c(i) = 0.
-3, -1, 1
Let o(w) be the first derivative of -3*w**4/4 - 5*w**3 + 33*w**2 - 48*w + 208. Determine j, given that o(j) = 0.
-8, 1, 2
Suppose -a = -5*k - 42, 5*a + 0*k = 3*k + 144. Let x(u) be the first derivative of -2*u**3 + 6*u**2 - 1 + u - 21*u**2 + a*u**3 + 2*u. Factor x(l).
3*(5*l - 1)**2
Let j(t) = -30*t**2 - 45*t - 245. Let p(s) = -s**2 + s. Let z(a) = j(a) - 25*p(a). Factor z(m).
-5*(m + 7)**2
Let i(q) be the first derivative of 4*q**6/45 + 22*q**5/75 + q**4/30 - 26*q**3/45 - q**2/3 + 4*q/15 - 92. Solve i(g) = 0.
-2, -1, 1/4, 1
Let a(h) be the second derivative of -h**6/45 - 2*h**5/15 + h**4/18 + 4*h**3/9 + 24*h + 1. Solve a(w) = 0 for w.
-4, -1, 0, 1
Let d(i) be the second derivative of i**9/3024 + i**8/560 + i**7/420 - 3*i**3/2 - 30*i. Let q(z) be the second derivative of d(z). Solve q(w) = 0.
-2, -1, 0
Let r = -222 + 228. Let d(q) be the third derivative of 0*q - 1/20*q**5 - r*q**2 + 0 - 2*q**3 - 1/2*q**4. Factor d(n).
-3*(n + 2)**2
Suppose r + 2 = -2. Let l be (3 + r/16)*4. Factor -9*v**3 - l*v**2 + 0*v - 6*v + v**2 - 5*v**2.
-3*v*(v + 1)*(3*v + 2)
Find x such that -3/2*x**2 + 33*x - 144 = 0.
6, 16
Let g(q) be the first derivative of -3*q**6/2 + 147*q**5/5 - 156*q**4 + 64*q**3 - 127. Factor g(n).
-3*n**2*(n - 8)**2*(3*n - 1)
Let m(a) be the first derivative of -a**4/16 - a**3/4 - 22. Factor m(x).
-x**2*(x + 3)/4
Let i(m) = m**3 - 92*m**2 - 179*m - 86. Let j(f) = 3*f**3 - 185*f**2 - 359*f - 171. Let t(z) = 5*i(z) - 2*j(z). Determine r, given that t(r) = 0.
-88, -1
Suppose -3*o - 2*o = 5. Let y be (o - 3)/(4 - 5). Find i such that -5*i + 10*i**2 + 4*i**3 + y*i - 3*i - 4*i**2 = 0.
-2, 0, 1/2
Let h(c) be the third derivative of 1/105*c**5 + 1/84*c**4 - 1/420*c**6 - 2/21*c**3 - 34*c**2 + 0 + 0*c. Determine f so that h(f) = 0.
-1, 1, 2
Let i = -233 + 233. Let b(f) be the third derivative of -5*f**2 + 0*f + 1/1050*f**7 + i + 1/75*f**5 + 0*f**4 + 1/150*f**6 + 0*f**3. Factor b(v).
v**2*(v + 2)**2/5
Let v(x) be the third derivative of x**8/312 + x**7/21 + 37*x**6/390 + 8*x**5/195 - 127*x**2. Let v(q) = 0. Calculate q.
-8, -1, -2/7, 0
Suppose 88390 - 1620*f + 59678 - 16848 + 5*f**2 = 0. Calculate f.
162
Let k be ((-10)/4)/(5/8*-2). Let b be ((-8)/(-10))/(1/40). Find x such that 24*x**k + 11*x + 37*x + 6*x**3 + b - 2*x**3 = 0.
-2
Let m(b) be the third derivative of 3*b**5/50 + 2*b**4/5 + 4*b**3/5 + 255*b**2. Factor m(f).
6*(f + 2)*(3*f + 2)/5
Find k such that -32/5 + 1/5*k**4 - 12*k - 3/5*k**3 - 32/5*k**2 = 0.
-2, -1, 8
Suppose 0 = -16*i - 5378 + 706. Let n = 3798/13 + i. Let 2/13*l**4 + n*l**3 + 0*l**2 + 0 + 0*l = 0. What is l?
-1, 0
Let -4/15 - 8/15*u**3 + 2/3*u**5 - 16/15*u**4 - 2/15*u + 4/3*u**2 = 0. Calculate u.
-1, -2/5, 1
Let z(s) = 2*s + 21. Let t be z(7). Let w be (2/45)/(7/t). What is v in -8/9*v + w*v**2 + 8/9 = 0?
2
Let 29/7*o - 99/7*o**2 - 2/7 = 0. What is o?
1/9, 2/11
Let l(r) be the second derivative of 0 + 5/12*r**4 + 5/2*r**3 + 13*r + 5*r**2. What is u in l(u) = 0?
-2, -1
Let n(w) be the third derivative of -w**7/70 + 3*w**6/20 + w**5 - 3*w**4 - 32*w**3 + 987*w**2. Determine g, given that n(g) = 0.
-2, 2, 8
Find i, given that -512/11 - 25/11*i**3 - 64*i - 216/11*i**2 - 1/11*i**4 = 0.
-8, -1
Let q(m) be the third derivative of 10*m**2 - 1/168*m**8 + 0*m**3 - 1/10*m**5 - 7/60*m**6 - 1/21*m**7 + 0*m**4 + 0*m + 0. Factor q(r).
-2*r**2*(r + 1)**2*(r + 3)
Factor -96/11 + 98/11*m - 2/11*m**2.
-2*(m - 48)*(m - 1)/11
Let m be (-8)/(-28) + 6/(-21). Suppose 1 = 3*q - 5, 5*v + 5*q - 30 = m. Determine j, given that -v*j**5 + j**4 - 3*j**4 + 0*j**4 = 0.
-1/2, 0
Determine s, given that 2/3*s**4 + 2/3*s**2 - 4/3 - 2*s**3 + 2*s = 0.
-1, 1, 2
Let x(g) = 3*g**2. Let m be x(1). Suppose 2*y - 4*y - m*o + 18 = 0, 0 = -3*y + 4*o + 27. Factor 15*l**2 - 4*l**3 - 4*l - 6*l**2 + y*l + 1 - 11*l.
-(l - 1)**2*(4*l - 1)
Let p(o) be the second derivative of o**4/4 - 3*o**3 + 27*o**2/2 + 45*o. Let p(z) = 0. What is z?
3
Let s(v) be the second derivative of 0*v**2 + v - 1/285*v**6 - 2/57*v**4 - 11 + 0*v**3 - 1/38*v**5. Determine t so that s(t) = 0.
-4, -1, 0
Determine n so that -64/3*n + 2*n**3 - 8 + 26/3*n**2 = 0.
-6, -1/3, 2
Let c(k) be the third derivative of k**6/20 + 32*k**5/15 + 319*k**4/12 - 242*k**3/3 - 80*k**2. Factor c(d).
2*(d + 11)**2*(3*d - 2)
Let b(t) = 4*t**3 + 0*t**3 - 9 - 3*t**3 + 8. Let v(u) = u**4 - 2*u**3 - u**2 - 3*u + 5. Let s(f) = -15*b(f) - 3*v(f). Factor s(o).
-3*o*(o - 1)*(o + 1)*(o + 3)
Let b(x) = -5*x**5 + 200*x**4 - 479*x**3 + x**2 + 451*x - 256. Let m(v) = -3*v**5 + 99*v**4 - 240*v**3 + 225*v - 129. Let p(u) = -6*b(u) + 11*m(u). Factor p(a).
-3*(a - 1)**3*(a + 1)*(a + 39)
Suppose -16*y + 7*y = 8*y. Factor 9/4*t**5 + y - 3/4*t**3 + 0*t - 3*t**4 + 3/2*t**2.
3*t**2*(t - 1)**2*(3*t + 2)/4
Let q(x) be the second derivative of x**3/6 + 2*x**2 - 3*x. Let f be q(5). Factor f*n + 4*n**2 + 8*n - 5*n.
4*n*(n + 3)
Suppose -13*p - 67 + 158 = 0. Let f(i) be the second derivative of 1/18*i**5 + 0 - 1/6*i**4 - p*i - 1/135*i**6 - 2/9*i**2 + 7/27*i**3. Factor f(y).
-2*(y - 2)*(y - 1)**3/9
Let r = 24 + -20. Factor -32*z + r*z**2 + 17 + 3*z**2 - 1 + 5*z**2.
4*(z - 2)*(3*z - 2)
Let v(w) be the third derivative of -w**8/112 + 2*w**7/35 - 3*w**6/20 + w**5/5 - w**4/8 + w**2 - 34. Let v(p) = 0. What is p?
0, 1
Let z(p) be the first derivative 