11*c**2 - 28*c + 86. Let y(o) = -6*q(o) - 25*s(o). Factor y(i).
-5*(i - 4)**2
Let m(c) be the third derivative of -c**8/21 + 12*c**7/35 - 97*c**6/120 + 3*c**5/5 - c**4/6 + 2*c**2 - 21. Factor m(h).
-h*(h - 2)**2*(4*h - 1)**2
Let d(s) be the third derivative of -s**7/735 - 3*s**6/280 + s**5/105 + 3*s**4/14 + 8*s**3/21 + 6*s**2 - 2. Let d(m) = 0. Calculate m.
-4, -2, -1/2, 2
Suppose -2*b + t = -1 - 0, -5 = -5*b + 5*t. Suppose -14 = -7*f - b*f. Determine i, given that 2/5*i + 0*i**f - 2/5*i**3 + 0 = 0.
-1, 0, 1
Let t(h) be the second derivative of -h**7/21 - 11*h**6/15 - 9*h**5/10 + 11*h**4/6 + 10*h**3/3 - 41*h - 2. Determine x so that t(x) = 0.
-10, -1, 0, 1
Let u(h) = -7*h**4 + 3*h**3 - h**2 + 3*h - 4. Let l(m) = m**4 - m**3 + 1. Let f(k) = 6*l(k) + u(k). Factor f(q).
-(q - 1)*(q + 1)**2*(q + 2)
Let d(m) be the first derivative of m**5/150 - m**3/15 + 3*m**2 - 3. Let r(t) be the second derivative of d(t). Factor r(n).
2*(n - 1)*(n + 1)/5
Let z(n) be the third derivative of 5/336*n**8 + 0*n - 1/24*n**6 - 1/21*n**7 + 1/6*n**5 + 0*n**3 + 0*n**4 + 0 + 3*n**2. Factor z(w).
5*w**2*(w - 2)*(w - 1)*(w + 1)
Suppose -101 = -18*j + 7. Let v(q) be the second derivative of 0*q**5 - 1/3*q**3 - 1/30*q**6 - j*q + 0 + 1/4*q**4 + 0*q**2. Determine l, given that v(l) = 0.
-2, 0, 1
Let d(v) = -v**2 + 10*v + 5. Let r be d(10). Factor 5 - 39*o**2 - 18*o**3 - r - 8 - 4 - 36*o - 3*o**4.
-3*(o + 1)**2*(o + 2)**2
Let j(n) be the second derivative of n**5/20 + n**4/4 + n**3/3 + 18*n + 1. Factor j(d).
d*(d + 1)*(d + 2)
Let p(i) be the first derivative of -1/10*i**2 + 0*i + 15 + 1/15*i**3. Factor p(n).
n*(n - 1)/5
Let f(b) be the first derivative of -35*b**4/16 - 25*b**3/6 - 15*b**2/8 + 124. Factor f(s).
-5*s*(s + 1)*(7*s + 3)/4
Suppose 45*x - 252 = -18*x. Find o such that 0*o**2 - 3/2*o**3 + 0 + 0*o + 3*o**x - 3/2*o**5 = 0.
0, 1
Let r(u) = -25*u**5 + 260*u**4 - 640*u**3 + 315*u**2 + 5. Let g(m) = -12*m**5 + 130*m**4 - 320*m**3 + 157*m**2 + 3. Let d(h) = -5*g(h) + 3*r(h). Factor d(z).
-5*z**2*(z - 4)**2*(3*z - 2)
Let r = 289 - 67. Factor -17*b**3 - r*b + 6*b**2 + 222*b + 5*b**4.
b**2*(b - 3)*(5*b - 2)
Let c(s) be the first derivative of -s**4/2 - 32*s**3/3 - 45*s**2 + 324*s + 72. Suppose c(z) = 0. What is z?
-9, 2
Let v(f) be the first derivative of -10 + 0*f - 2/33*f**3 + 1/11*f**2. Factor v(h).
-2*h*(h - 1)/11
Let c(b) be the third derivative of -b**8/1848 - b**7/165 + b**6/660 + 7*b**5/330 + 6*b**2 - 6. What is u in c(u) = 0?
-7, -1, 0, 1
Let w = 1274 + -1271. Factor -15*o**2 - 57/4*o - 9/2 - 9/2*o**w + 3/4*o**5 + 3/2*o**4.
3*(o - 3)*(o + 1)**3*(o + 2)/4
Let w be 2/((-4)/(-24)*-2). Let g be ((-4)/w)/((-2)/(-6)). Suppose l + 0*l - 6*l**g - 2 + 2*l**3 + 5*l = 0. Calculate l.
1
Let j(s) be the third derivative of -s**8/1848 - s**7/231 + s**6/30 - 8*s**5/165 - 391*s**2. Suppose j(n) = 0. What is n?
-8, 0, 1, 2
Let a(d) be the third derivative of 49/4*d**3 + 0*d + 0 + 1/40*d**5 - 20*d**2 - 7/8*d**4. Factor a(c).
3*(c - 7)**2/2
Factor 107*u + 14*u - 7010 + 165 + 29*u + 220*u - 5*u**2.
-5*(u - 37)**2
Let p(m) be the first derivative of 7*m**5/30 + 25*m**4/12 + 37*m**3/6 + 25*m**2/3 + 16*m/3 + 862. Let p(w) = 0. Calculate w.
-4, -8/7, -1
Let t(s) be the second derivative of -s**6/120 + s**5/20 - s**4/8 + 3*s**3 - 13*s. Let y(b) be the second derivative of t(b). Factor y(o).
-3*(o - 1)**2
Suppose -166 + 199 = 11*z. Solve 88/3*l**2 - 46/3*l**z - 4/3 - 38/3*l = 0 for l.
-2/23, 1
Let k be (6 - 6) + 2 + (8/30 - 2). Factor 0 - 2/3*t**2 + k*t + 2/5*t**3.
2*t*(t - 1)*(3*t - 2)/15
Let s be (14/77)/(80/22). Let g(v) be the second derivative of 1/36*v**4 + 0 + s*v**5 + 1/30*v**6 + 0*v**2 + 0*v**3 + 1/126*v**7 - 3*v. Factor g(p).
p**2*(p + 1)**3/3
Let q = -30 + 33. Factor -1 - 2*m + m + m**2 + 5*m**q - 4*m**3.
(m - 1)*(m + 1)**2
Let p(q) = -63*q + 14. Let t be p(2). Let h = 115 + t. What is i in -h*i + 3/2 + 3/2*i**2 = 0?
1
Let n be (-21)/(-9)*(-2)/(-7). Let h = 3965 - 3965. Determine k so that n*k + h - 2/3*k**2 = 0.
0, 1
Suppose 5*q - 20 = -0*q. Factor 2*t**4 - 5*t**3 + t**5 - 3*t**5 + q*t**3 + t**5.
-t**3*(t - 1)**2
Let c be (1 + (-2)/8)/((-15)/240). Let x be (-7 - (-366)/60)*10/c. Factor 3/4*l**2 + x*l + 1/4 + 1/4*l**3.
(l + 1)**3/4
Let j(f) be the third derivative of f**6/720 - 7*f**4/144 - f**3/6 + 3*f**2 + 6*f. Factor j(q).
(q - 3)*(q + 1)*(q + 2)/6
Let s be 9/((-81)/(-15))*(-78)/(-325). Find m, given that 17/5*m + 2/5*m**2 - 17/5*m**3 - s = 0.
-1, 2/17, 1
Let g(z) be the third derivative of 0*z**4 + 24*z**2 + 0*z**3 + 1/40*z**5 + 1/160*z**6 + 27/448*z**8 - 3/28*z**7 + 0*z + 0. Suppose g(u) = 0. Calculate u.
-2/9, 0, 1/3, 1
Let p be 0 + 3/6*20. Let b = p + -8. Solve 17*z**b - 3*z + z - 20*z**2 = 0 for z.
-2/3, 0
Let o = -13849/84 - -559/21. Let u = o + 139. Factor -1/4 - 3/4*q - 1/4*q**3 - u*q**2.
-(q + 1)**3/4
Let w(s) be the third derivative of -s**6/90 + s**5/45 + 5*s**4/18 + 2*s**3/3 - 4*s**2 - 32. Factor w(h).
-4*(h - 3)*(h + 1)**2/3
Let p(n) be the first derivative of -n**6/21 + 4*n**5/105 + n**4/6 + 4*n**3/63 + 172. Suppose p(t) = 0. What is t?
-1, -1/3, 0, 2
Let a be (-14 + 0)/(17/119). Let d = a + 884/9. Let -2/9*p**3 + d*p + 4/9 - 4/9*p**2 = 0. What is p?
-2, -1, 1
Let b(l) = l**3 - 15*l**2 - 32*l + 258. Let w be b(16). Determine o, given that 8/3*o**w + 0 + 0*o - 4*o**3 = 0.
0, 2/3
Suppose -98 = -14*o - 70. Let x(q) be the third derivative of 0 + 1/48*q**4 + 0*q - q**o + 0*q**3 + 1/240*q**5. Solve x(b) = 0.
-2, 0
Let a(j) be the second derivative of j**4/3 - 140*j**3/3 + 2450*j**2 - 18*j + 4. Suppose a(i) = 0. Calculate i.
35
Factor -1822 - 1788 + 180*v**2 - 745*v + 5*v**3 + 973*v + 1197*v.
5*(v - 2)*(v + 19)**2
Let t(r) = r**3 - 4*r**2 - r. Let y be t(4). Let u be (-8 + 3)/(3 + y). What is j in 8*j**4 + 6*j**3 - 8*j - 15*j**2 - 3*j**u + 6*j**2 + 5*j**5 + j**2 = 0?
-2, -1, 0, 1
Suppose -84*q = -5*s - 85*q + 12, -4*q = -2*s + 18. Suppose 6*v - 2*v - 5*n = 18, 0 = -3*v + 3*n + 12. Factor -1/2*x + 1/2*x**4 - 1/2*x**v + 0 + 1/2*x**s.
x*(x - 1)*(x + 1)**2/2
Let n(x) be the first derivative of -3/7*x**3 - 6/7*x**2 + 34 + 0*x. Factor n(r).
-3*r*(3*r + 4)/7
Let d(u) = -17*u + 167. Let v be d(23). Let q be (v/12)/7*3/(-4). Factor 0 + 4/9*t**3 - 2/9*t**q - 2/9*t.
2*t*(t - 1)*(2*t + 1)/9
What is j in -127 + 4*j**2 - 79 + 242 + 24*j = 0?
-3
Factor 94*f + 14*f**2 + 2 - 2 - 25*f**2 + 10*f**2.
-f*(f - 94)
Suppose 4*j + 13*j**3 + 40/3*j**2 + 5*j**4 + 2/3*j**5 + 0 = 0. What is j?
-3, -2, -1/2, 0
Let o be ((-4)/(-40))/((0 - -3)/504). Let d(s) = s**3 - 5*s**2 + 5*s - 23. Let w be d(5). Factor -o*u**w + 3/5*u + 6/5.
-3*(4*u + 1)*(7*u - 2)/5
Let u(c) be the first derivative of c**3/2 + 105*c**2/4 + 51*c + 10. Factor u(v).
3*(v + 1)*(v + 34)/2
Let s be (((-7)/2)/7)/(-3 + 2). Factor -1/2*i + 1/2*i**3 + 1/2*i**2 - s.
(i - 1)*(i + 1)**2/2
Let o = 1086 - 1086. Let g(q) be the third derivative of 1/240*q**5 + 0*q + 12*q**2 + o*q**4 + 0 - 1/24*q**3. Factor g(r).
(r - 1)*(r + 1)/4
Let f = 4554 + -22764/5. Suppose -f + 17/5*z**3 - 31/5*z**2 + 23/5*z - 3/5*z**4 = 0. Calculate z.
2/3, 1, 3
Let u(c) be the second derivative of -1/200*c**6 + 0*c**2 + 1/6*c**3 + 1/50*c**5 + 0 - 2*c + 1/10*c**4. Let m(s) be the second derivative of u(s). Factor m(n).
-3*(n - 2)*(3*n + 2)/5
Let i(u) be the third derivative of u**5/75 + 23*u**4/30 - 5*u**2 + 5. Find y such that i(y) = 0.
-23, 0
Let z be -9*(24/(-27))/4. Let t be 1/z + (-1511)/(-2). Factor -1274*p**3 + 146*p**4 - 188*p - t*p**2 + 4*p - 832*p**4 - 16.
-2*(p + 1)*(7*p + 2)**3
Let s(f) = f**3 - f. Let m be (-18)/(-4) + 3/(-6). Let r(l) = -2*l**3 + 2*l. Suppose 5*n - 3*n - 14 = 0. Let x(v) = m*r(v) + n*s(v). Factor x(b).
-b*(b - 1)*(b + 1)
Let d(w) be the third derivative of 0*w + 3/20*w**6 + 0*w**3 - 7*w**2 - 1/70*w**7 - 9/20*w**5 + 0*w**4 + 0. Find v, given that d(v) = 0.
0, 3
Let p = -58 + 106. Let x be 4/((-16)/12) + 5. Solve -32*d**2 - 2*d**2 - 64*d**x + p*d + 8*d - 8 = 0.
2/7
Let p(a) = -14*a - 126. Let h(x) = 9*x + 84. Let o(n) = 8*h(n) + 5*p(n). Let t be o(-20). Solve 8/3*m**3 + 4*m**2 + t*m**5 - 16/3*m**4 + 4/3 - 14/3*m = 0 for m.
-1, 2/3, 1
Let a(u) = u**3 + 2*u**2 - 2*u - 3. Let v be a(-1). Let t(n) be the first derivative of -4 + 1/2*n**4 + v*n**2 + 0*n + 2/5*n**5 + 0*n**3. Factor t(g).
2*g**3*(g + 1)
Let w(p) = -3*p**3 - p - 4. Suppose 3*x - 10 =