) + 5*p(x). Factor d(f).
3*(f - 3)*(31*f - 2)
Let h(i) be the third derivative of -2*i**7/105 - 7*i**6/30 - 2*i**5/5 - 29*i**2. Suppose h(w) = 0. Calculate w.
-6, -1, 0
Let d(q) be the first derivative of 2*q**3/21 - 2*q**2/7 + 2*q/7 - 309. Factor d(f).
2*(f - 1)**2/7
Factor 325 - 6*c**3 + c**3 - 75 - 225*c - 20*c**2 + 80*c**2.
-5*(c - 5)**2*(c - 2)
Let f(s) be the third derivative of s**8/168 - 4*s**7/105 + 3*s**6/80 + 11*s**5/120 - 5*s**4/48 - s**3/4 - 576*s**2. Determine p, given that f(p) = 0.
-1/2, 1, 3
Suppose 0 = -2*q - 4*t - 16, 2*q - 4*t - 2 + 10 = 0. Let a be q/(-8)*(-2)/(3 - 4). Factor 9/2*m - a*m**3 + 0*m**2 + 3.
-3*(m - 2)*(m + 1)**2/2
Suppose 8/5 - 8/5*q**2 + 2/15*q**3 - 2/15*q = 0. Calculate q.
-1, 1, 12
Let i(q) = -4*q**3 + q + 1. Let l be i(-1). Suppose 0 = -4*c - h + 6*h, 0 = l*c - 2*h. Factor -2/13*f**2 + 2/13*f + c.
-2*f*(f - 1)/13
Let o(t) be the first derivative of 14/57*t**3 + 2/95*t**5 + 3/19*t**2 + 14 + 5/38*t**4 + 0*t. Determine n so that o(n) = 0.
-3, -1, 0
Suppose -135 = -5*p - 4*p. Determine z so that -55*z - p + 3*z**2 - 4*z**2 - 20*z**4 + 55*z**3 + 36*z**2 = 0.
-1, -1/4, 1, 3
Suppose 2*g - 2 + 0 = 0, 4*m + 3*g = 7. Let t(q) be the first derivative of -m - 17*q**2 + 48*q + 3*q**3 + 29*q**2 - 2*q**3. Factor t(u).
3*(u + 4)**2
Let w(q) = -2*q**2 + 38*q + 927. Let h be w(-14). Find k, given that -1/8*k**4 - 1/2*k**h + 3/8*k**2 + 7/4*k + 1 = 0.
-4, -1, 2
Let y(w) be the first derivative of -21 - 1/15*w**3 + 0*w + 1/25*w**5 + 0*w**4 + 0*w**2. Factor y(j).
j**2*(j - 1)*(j + 1)/5
Let y be 2 - -5 - 3 - 1. Let i(k) = -5*k. Let d be i(0). Find n, given that d + 1/2*n**3 + 9/2*n + y*n**2 = 0.
-3, 0
Let v be (-6)/(-15) + (-12)/(-45). Suppose 64*k = 66*k. Factor 0 - v*h**3 + k*h**2 + 2/3*h.
-2*h*(h - 1)*(h + 1)/3
Let x be (-3 + 21/7)/(-2). Let f(d) be the third derivative of 0 + 1/20*d**5 - 1/16*d**6 + x*d**3 + 0*d**4 + 0*d + 6*d**2 + 3/140*d**7. Factor f(n).
3*n**2*(n - 1)*(3*n - 2)/2
Let y be 728/1995 + 10/285. Let 4/5 + y*i - 2/5*i**2 = 0. Calculate i.
-1, 2
Factor -72*a + 97 + 15 + 36 - 74*a - 2*a**2.
-2*(a - 1)*(a + 74)
Suppose 3*g - g - 8 = 0. Let w be 57/(1*3/g). Factor 76*y - w*y + 9*y**3 + 3*y**2 + 3*y**5 + 9*y**4.
3*y**2*(y + 1)**3
Let j(l) be the first derivative of -2*l**4/3 - 100*l**3/9 + 88*l**2/3 + 112*l/3 - 227. Find m such that j(m) = 0.
-14, -1/2, 2
Factor -10/3 - 20/3*r**2 - 25/3*r - 5/3*r**3.
-5*(r + 1)**2*(r + 2)/3
Let b = -2 - -7. Let d = 516 - 512. Solve -3*p**5 + 0*p**d + 10*p**3 + 4*p**5 - 1 + b*p - 10*p**2 - 5*p**4 = 0 for p.
1
Let y(b) = b**2 + 25*b + 64. Let c(n) = 3*n**2 + 77*n + 190. Let l(o) = 6*c(o) - 21*y(o). Factor l(s).
-3*(s + 4)*(s + 17)
Suppose -3*y + 13 = 2*t - 88, y = 5. Let f = -40 + t. Factor 18/5*o**2 - 4/5*o + 0 - 14/5*o**f.
-2*o*(o - 1)*(7*o - 2)/5
Let f(m) be the first derivative of -3*m**5/5 - 15*m**4/4 - 3*m**3 + 15*m**2/2 + 12*m + 84. Factor f(c).
-3*(c - 1)*(c + 1)**2*(c + 4)
Let k(p) = -121*p + 121. Let n be k(1). Let l(v) = -v**3 + 9*v**2 - 10*v + 20. Let c be l(8). Factor 0*o**3 + 3/4 + n*o + 3/4*o**c - 3/2*o**2.
3*(o - 1)**2*(o + 1)**2/4
Let n(y) be the first derivative of 0*y**2 - 28/5*y**4 - 9 + 16/15*y**3 + 196/25*y**5 + 0*y. Factor n(u).
4*u**2*(7*u - 2)**2/5
Suppose 108/11*h + 18/11*h**2 - 54/11 - 112/11*h**3 + 32/11*h**4 = 0. What is h?
-1, 3/4, 3
Let h(u) be the first derivative of -10*u**5 + 245*u**4/2 - 368*u**3/3 + 36*u**2 + 378. Factor h(b).
-2*b*(b - 9)*(5*b - 2)**2
Let o(i) = i**3 - 6*i**2 + 24*i - 35. Let x(v) = 4*v**2 - 24*v + 34. Let j(q) = 2*o(q) + 3*x(q). Factor j(k).
2*(k - 2)**2*(k + 4)
Suppose 6*b = 49 - 31. Let t(q) = 3*q - 21. Let l be t(7). Determine k so that -1/4*k**b - 1/2*k**2 + l - 1/4*k = 0.
-1, 0
Let x be (42/12 + 7)*18/63. Let 72/7*f - 30/7*f**4 + 132/7*f**2 - 48/7 - 18/7*f**x = 0. Calculate f.
-2, -1, 2/5, 2
Let a(z) be the first derivative of -2*z**5/35 - 5*z**4/14 - 10*z**3/21 + 5*z**2/7 + 12*z/7 - 110. Suppose a(k) = 0. What is k?
-3, -2, -1, 1
Factor 43*j - 3*j**2 + 37*j + 42*j - 110*j + 36.
-3*(j - 6)*(j + 2)
Suppose -3*d + d + 16 = 0. Let c(p) = -p**3 + 3*p**2 + p. Let v be c(3). Factor 4 + s**4 + 6*s - s**2 - 4 + 2*s**v - d*s.
s*(s - 1)*(s + 1)*(s + 2)
Factor -3*b - 22*b**3 + 85*b**2 - 76*b**2 + 13*b**3 + 3*b**4.
3*b*(b - 1)**3
Let q(z) be the third derivative of -z**5/300 - z**4/120 + z**3/5 - 24*z**2 - 1. Factor q(g).
-(g - 2)*(g + 3)/5
Let j(z) be the third derivative of z**6/360 - 7*z**5/60 + 5*z**4/3 - 50*z**3/9 + z**2 - 7*z. Factor j(c).
(c - 10)**2*(c - 1)/3
Suppose 0 = -192*k + 186*k. Let n(h) = -h - 7. Let q be n(-9). Find x, given that -2/5*x**3 - 4/5 + 6/5*x + k*x**q = 0.
-2, 1
Let t(n) be the first derivative of -1/6*n**3 + 3/2*n - 1/2*n**2 + 11. Solve t(l) = 0.
-3, 1
Let j(p) be the second derivative of p**6/3060 - p**5/255 + p**4/51 + 5*p**3/3 - 5*p + 4. Let k(o) be the second derivative of j(o). Factor k(a).
2*(a - 2)**2/17
Let 1/6*w**2 + 75/2 + 5*w = 0. Calculate w.
-15
Let i = -23 + 25. Solve 0*h**2 + 5*h**2 - 9*h**i - 4*h = 0 for h.
-1, 0
Suppose -2*k + 4 = -5*x, 0 = -15*x + 4*k - 12 + 4. Factor -20*v + 32*v**2 - 64/5*v**3 + x.
-4*v*(4*v - 5)**2/5
Let i = 29 + -26. Factor -2*y**4 - 3*y**2 + 2*y**5 + 7*y**4 + 10*y**i + 3*y**4 + 7*y**2.
2*y**2*(y + 1)**2*(y + 2)
Let g(f) be the third derivative of -4*f**2 + 0*f + 0 + 0*f**4 - 2*f**3 + 1/20*f**5. Suppose g(t) = 0. What is t?
-2, 2
Suppose 0*g - 3*g = -4*o + 97, 3*g + 75 = 3*o. Suppose -4*q + 2 = -o. Solve q + 7*b + 12*b**2 + 4*b**4 - 22 + 9*b - 16*b**3 = 0 for b.
-1, 1, 2
Let h(x) = 18*x + 9. Let a be h(-7). Let o = a + 355/3. What is t in 8/9*t + 2/9*t**4 + o*t**2 + 8/9*t**3 + 2/9 = 0?
-1
Let g = 1913/5 + -13171/35. Let z be 54058/6342 + (-1)/(-3). Solve -25/7*p**5 - z*p**2 + g*p - 8/7 + 10*p**4 - 19/7*p**3 = 0 for p.
-1, 2/5, 1, 2
Let p(z) = 2*z - 8. Let n be p(6). Suppose 7*o**3 + 8*o**2 - 11*o**3 - 4*o**4 + n*o - 4*o**2 = 0. What is o?
-1, 0, 1
Let q(r) = -r**2 + 10*r - 2. Let o be q(9). Let b(s) = -8 + 45*s**2 - o + 30*s - 39*s**2. Let y(z) = -z**2 - z - 1. Let a(f) = -b(f) + 3*y(f). Factor a(x).
-3*(x + 4)*(3*x - 1)
Let v(f) be the first derivative of 3*f**3 + 15/4*f**4 + 18 + 9/20*f**5 + 0*f + 0*f**2. Factor v(t).
3*t**2*(t + 6)*(3*t + 2)/4
Let o(x) be the first derivative of 5*x**2 + 4*x + 1/2*x**4 - 45 + 8/3*x**3. Factor o(r).
2*(r + 1)**2*(r + 2)
Let b(f) = -10*f + 13. Let z be b(1). Solve -3*v**z - 21*v**3 + 44*v**2 + 38*v + 5 - 45 - 10*v = 0.
-1, 5/6, 2
Let q(k) be the first derivative of -2*k**6/3 - 48*k**5/5 - 30*k**4 - 112*k**3/3 - 18*k**2 - 181. Determine t, given that q(t) = 0.
-9, -1, 0
Let a be (29 - (-4872)/(-145)) + (2 - -8). Determine c so that 3/5*c**2 - a*c - 6 = 0.
-1, 10
Factor -2/7*i + 2/7*i**2 + 0.
2*i*(i - 1)/7
Let z be (-15 - -15)*2/(-8). Let n(k) be the second derivative of -2/75*k**6 + k + 0*k**2 + 0 + 0*k**4 + z*k**3 + 2/105*k**7 + 0*k**5. Factor n(j).
4*j**4*(j - 1)/5
Suppose -4*u + 2158 = 2*m, -3*u + 1626 = 4*m - m. Factor -4200*r - 2940*r**2 - 572*r**3 - 1463 - u - 114*r**3.
-2*(7*r + 10)**3
Let h = 2547 - 2545. Solve 0 + 6/7*y - 3*y**h = 0 for y.
0, 2/7
Let w(t) be the third derivative of -5*t**8/504 + 17*t**7/1260 + 11*t**6/144 + t**5/20 + 221*t**2. Determine i, given that w(i) = 0.
-1, -2/5, 0, 9/4
Let s(t) be the third derivative of t**7/1260 - t**6/240 - t**5/120 + 11*t**4/144 - t**3/6 - 2*t**2 - 11. Factor s(p).
(p - 3)*(p - 1)**2*(p + 2)/6
Let f(l) be the third derivative of 0*l**3 + 0 - 1/390*l**5 - 1/156*l**4 + 5*l**2 + 1/780*l**6 + 1/1365*l**7 - 2*l. Factor f(w).
2*w*(w - 1)*(w + 1)**2/13
Let k(b) = -9*b**2 - 321*b + 897. Let f(u) = 34*u + 34*u + u**2 - 114 - 28*u + 2. Let x(g) = 33*f(g) + 4*k(g). What is r in x(r) = 0?
6
Let w be 72/7 - (2 + (-24)/14). Suppose 5*s + w = 30. Let 4/3*c**3 - 2/3*c**s - 8/3 + 2*c**2 - 8/3*c = 0. Calculate c.
-1, 2
Let t(j) be the third derivative of 0*j**7 + 0*j**3 + 1/195*j**6 + 0*j**4 + 0*j + 0 + 0*j**5 - 23*j**2 - 1/2184*j**8. Suppose t(z) = 0. Calculate z.
-2, 0, 2
Let j(l) be the third derivative of -l**8/2520 + 4*l**7/1575 - l**6/150 + 2*l**5/225 - l**4/180 - 6*l**2 + 3. Let j(z) = 0. Calculate z.
0, 1
Let g = 23 + -11. Let c be 3/g + (-45)/(-12). Find t such that 4/5*t**c - 2/5*t - 4/5*t**2 + 2/5*t**5 + 0*t**3 + 0 = 0.
-1, 0, 1
Let w(k) be the first derivative of 0*k + 2/7*k**2 + 34