/7
Factor 1463*w**2 + 57*w + 127*w - 1465*w**2.
-2*w*(w - 92)
Let n(c) be the second derivative of c**7/126 + c**6/30 + c**5/60 - c**4/12 - c**3/9 - 168*c. Factor n(x).
x*(x - 1)*(x + 1)**2*(x + 2)/3
Let z(f) be the first derivative of -1/2*f**2 - 9 + f + 1/12*f**3. Factor z(a).
(a - 2)**2/4
Factor 1/5*o**3 + 51*o - 289/5 + 33/5*o**2.
(o - 1)*(o + 17)**2/5
Factor -19/7*i + 48/7 + 1/7*i**2.
(i - 16)*(i - 3)/7
Let h(c) = 46*c**4 + 18*c**3 - 28*c**2 - 14*c + 30. Let j(f) = -2*f**4 - f**3 + f**2 + f - 1. Let s(u) = 2*h(u) + 44*j(u). Factor s(l).
4*(l - 2)**2*(l + 1)**2
Let d be 8901/483 + (-18 - 0). Factor -d*m**2 - 12/7*m - 9/7.
-3*(m + 1)*(m + 3)/7
Let q(i) be the third derivative of i**5/40 - 27*i**4/16 - 7*i**3 - 88*i**2. Factor q(j).
3*(j - 28)*(j + 1)/2
Suppose -44/13*m**2 + 6/13*m**3 + 0*m + 0 = 0. What is m?
0, 22/3
Let a(y) be the first derivative of 4/21*y**2 + 15/14*y**4 - 8/15*y**5 - 4 - 7/9*y**6 + 0*y + 8/9*y**3. Suppose a(h) = 0. Calculate h.
-1, -2/7, 0, 1
Let i(f) be the third derivative of -1/600*f**6 - 7*f**2 + 1/150*f**5 + 0 + 0*f + 0*f**3 + 0*f**4 + 1/1680*f**8 - 1/525*f**7. Factor i(n).
n**2*(n - 2)*(n - 1)*(n + 1)/5
Factor 212/7*t + 2/7*t**2 + 0.
2*t*(t + 106)/7
Let m(k) = k**2 + k - 1. Let o(g) = 21*g**2 - 21*g - 60. Let i(n) = -18*m(n) + o(n). What is f in i(f) = 0?
-1, 14
Suppose -300*f**2 - 301*f**2 + 59*f + 602*f**2 = 0. Calculate f.
-59, 0
Let c = 1029 + -1027. Let q(b) be the third derivative of 0*b**3 + 0*b**4 - 1/840*b**7 + 0*b**5 + 0 + 0*b + 10*b**c + 0*b**6. Factor q(z).
-z**4/4
Solve 6*h**2 - 873*h + 857*h + 20 - 10*h**2 = 0.
-5, 1
Suppose -1 = 5*p + 29. Let b(y) = y**4 - 2*y**3 - 2*y**2 + 2. Let w(n) = n**4 - 2*n**3 - 3*n**2 + 3. Let m(f) = p*b(f) + 4*w(f). Factor m(v).
-2*v**3*(v - 2)
Let h(r) = -r**3 - 12*r**2 - 19*r - 4. Let o(b) = -6*b**3 - 72*b**2 - 113*b - 21. Let l(d) = 39*h(d) - 6*o(d). Let l(z) = 0. Calculate z.
-10, -1
Let m be 11*((-896)/154 + 6). Suppose 5/4*q**m - 1 + 2*q = 0. What is q?
-2, 2/5
Let w(h) be the third derivative of 14*h**7/75 - 21*h**6/200 - h**5/25 + h**4/30 - 246*h**2. Factor w(a).
a*(4*a + 1)*(7*a - 2)**2/5
Let l(h) be the third derivative of -1/260*h**6 + 0*h**4 + 0*h**5 + 0*h**3 - 10*h**2 + 1/1365*h**7 + 0 + 0*h. Let l(w) = 0. Calculate w.
0, 3
Suppose -11*y = -c - 16*y + 28, 0 = 2*c - 2*y + 4. Solve -1/3*q**2 + 0 - 1/3*q**4 + 0*q - 2/3*q**c = 0 for q.
-1, 0
Let p be 15/6*(-132)/(-30). Suppose 4*b + p*b**2 - 8*b**2 + 8*b**3 + 11*b**2 - 8*b**4 = 0. What is b?
-1/2, 0, 2
Let n(r) be the second derivative of r**8/420 - r**7/70 + r**6/90 + r**5/10 - r**4/3 + 2*r**3 + 5*r. Let z(f) be the second derivative of n(f). Factor z(d).
4*(d - 2)*(d - 1)**2*(d + 1)
Let o = 3097/9 + -344. Let k(r) be the second derivative of 5/9*r**3 - 2/3*r**2 - 2*r - o*r**4 + 0. Suppose k(x) = 0. What is x?
1/2, 2
Let y = -323 + 326. Let q(l) be the second derivative of 0*l**5 + 2/15*l**6 - 2/3*l**4 - 3*l + 2*l**2 + 0*l**y + 0. Suppose q(p) = 0. What is p?
-1, 1
Let d(x) be the first derivative of -x**4/4 - 14*x**3/3 - 30*x**2 - 72*x - 11. Factor d(t).
-(t + 2)*(t + 6)**2
Let q(x) be the second derivative of -x**5/160 + 11*x**4/24 - 121*x**3/12 - 138*x. Let q(a) = 0. What is a?
0, 22
Let q(n) be the second derivative of -2*n**6/45 - n**5/12 + n**4/18 + n**3/6 + 5*n. Solve q(b) = 0.
-1, 0, 3/4
Let t be (-24)/(-144)*(-3)/(-2). Let a = -45 + 181/4. Solve a*q**2 + 0 + 0*q - 1/4*q**5 - t*q**4 + 1/4*q**3 = 0.
-1, 0, 1
Factor 2 - 429*f**3 - 22 - 7*f**2 + 42*f + 431*f**3 - 17*f**2.
2*(f - 10)*(f - 1)**2
Let b(o) be the first derivative of -6/19*o - 3/19*o**4 - 10/19*o**2 - 8/19*o**3 - 8 - 2/95*o**5. Let b(m) = 0. Calculate m.
-3, -1
Let p be 11719/360 - (-3 - (-125)/45). Let h = -159/40 + p. Determine y so that 3*y**4 - 48/5 - 48/5*y**2 - h*y + 36/5*y**3 = 0.
-2, -2/5, 2
Factor -68/5*a - 578/5 - 2/5*a**2.
-2*(a + 17)**2/5
Let p(y) be the second derivative of -9*y**4/2 - 2*y**3/3 - 2*y - 24. Factor p(m).
-2*m*(27*m + 2)
Suppose 0 = 8*z + 70 - 94. Let c(o) be the first derivative of 1/3*o**z + 0*o**2 - 3/4*o**4 + 0*o + 5. Factor c(p).
-p**2*(3*p - 1)
Let l(a) = -14*a - 6. Let x be l(6). Let w = x + 92. Factor 1/5 + 1/5*o**w + 2/5*o.
(o + 1)**2/5
Let k(u) be the third derivative of 0 - 1/160*u**5 + u + 0*u**3 + 1/32*u**4 - 3/320*u**6 + 15*u**2. Factor k(d).
-3*d*(d + 1)*(3*d - 2)/8
Let y(o) = -o**3 + 2*o**2 - 4*o + 2. Let j be y(3). Let t = -16 - j. Factor 4*v**2 + v**4 - v**t - 5*v**2 + v**3.
v**2*(v - 1)*(v + 1)
Let o(q) be the second derivative of 237/85*q**6 - 4/17*q**2 - 108/119*q**7 + 7*q - 43/17*q**5 + 19/102*q**4 + 0 + 28/51*q**3. Determine p, given that o(p) = 0.
-1/4, 2/9, 1
Let c(g) = -9 + g**2 + 11 - 1. Let v(f) = -2*f**2 - f. Let n(r) = 3*c(r) + 2*v(r). Factor n(j).
-(j - 1)*(j + 3)
Let y(u) be the third derivative of -8*u**2 - 1/30*u**5 + 1/120*u**6 - 2/3*u**3 + 1 + 0*u - 7/24*u**4. Factor y(g).
(g - 4)*(g + 1)**2
Let v be ((-18)/69)/((-189)/378). Factor -6/23*q**2 - v - 22/23*q.
-2*(q + 3)*(3*q + 2)/23
Let u = 4124/105 + -808/21. Let -u*g + 1/5*g**3 + 2/5*g**2 - 8/5 = 0. Calculate g.
-2, 2
Suppose w = -0*w - 4*f + 12, f = -3*w + 14. Find l, given that 0*l**2 + 0 + 2/7*l**5 + 4/7*l**w + 0*l + 2/7*l**3 = 0.
-1, 0
Factor -2/5*c**2 + 0 + 2/5*c + 2/5*c**4 - 2/5*c**3.
2*c*(c - 1)**2*(c + 1)/5
Let o(t) be the third derivative of -1/15*t**5 + 0*t - 1/20*t**6 + 0*t**3 + 0 - 1/105*t**7 + 0*t**4 + t**2. Factor o(x).
-2*x**2*(x + 1)*(x + 2)
Suppose -4*q + 3*h + 10 = -21, 2*q = 2*h + 18. Suppose 4*b**2 + 4859 - 4859 - 4*b**3 - 4*b**q + 4*b**5 = 0. What is b?
-1, 0, 1
Let r(c) be the third derivative of c**10/302400 - c**8/40320 - c**5/12 + 13*c**2. Let b(v) be the third derivative of r(v). Find d such that b(d) = 0.
-1, 0, 1
Let j(p) = 35 - 840*p + p**2 + 418*p + 408*p. Let a be j(11). Suppose 15/4*t**a + 3/2 + 21/4*t = 0. Calculate t.
-1, -2/5
Let b(h) = h**3 - h**2 - 1. Let o be b(2). Suppose -y - 1 = g - 3, -2*y + 6 = o*g. Factor -21*w**2 - 12 + 18*w - 54*w**g + 30*w + 12*w.
-3*(5*w - 2)**2
Let n(q) be the second derivative of -11/36*q**4 - 18*q - 13/60*q**5 + 0*q**2 + 0 + 1/9*q**3. Factor n(u).
-u*(u + 1)*(13*u - 2)/3
Solve 0*q - 1/4*q**3 - 15/4*q**2 + 0 = 0.
-15, 0
Let s(d) be the third derivative of -d**8/896 - 3*d**7/560 + d**6/160 + 3*d**5/80 - d**4/64 - 3*d**3/16 - 112*d**2. Solve s(k) = 0 for k.
-3, -1, 1
Let p be (-3)/(-6) - (1 + (-2)/4). Let w(m) be the second derivative of -1/15*m**6 + p*m**4 - 3/20*m**5 - 5*m + 0 + 1/6*m**3 + 0*m**2. Factor w(h).
-h*(h + 1)**2*(2*h - 1)
Let y(i) be the third derivative of -1/112*i**8 + 4/5*i**5 - 7/20*i**6 + 4*i**2 - 9/8*i**4 + 3/35*i**7 + 0*i + 0 + i**3. Factor y(z).
-3*(z - 2)*(z - 1)**4
Let r(q) be the third derivative of 3*q**6/160 + 7*q**5/40 - 7*q**4/32 - 5*q**3/4 - 2*q**2 - 38. Factor r(d).
3*(d - 1)*(d + 5)*(3*d + 2)/4
Let u(n) be the third derivative of -n**6/420 - 2*n**5/105 - n**4/21 - 7*n**2 + 25. Factor u(f).
-2*f*(f + 2)**2/7
Let f = -2 - -95. Factor -11*c**4 - 5*c**5 + 97*c**3 + 3*c**4 + 10*c**2 - 2 + c - f*c**3.
-(c - 1)*(c + 1)**3*(5*c - 2)
Let u(r) be the first derivative of 8*r**3/3 - 3*r**2/2 - 5*r + 3. Let w(j) = 175*j**2 - 65*j - 110. Let f(y) = -45*u(y) + 2*w(y). Factor f(d).
-5*(d - 1)*(2*d + 1)
Let f = -25 + 30. Let k(m) = -4*m**2 - 44*m. Let w be k(-11). Suppose -8/3*g + 8/3*g**2 + w + 2*g**3 - 8/3*g**4 + 2/3*g**f = 0. Calculate g.
-1, 0, 1, 2
Find r, given that -17*r**2 + 1/3*r**3 + 50/3*r + 0 = 0.
0, 1, 50
Factor 12/5*v**2 + 9/5*v**3 - 12/5*v - 6/5*v**4 - 3/5*v**5 + 0.
-3*v*(v - 1)**2*(v + 2)**2/5
Let l(h) be the third derivative of -h**7/120 + 3*h**6/160 + 13*h**5/120 - 3*h**4/8 + h**3/3 + 213*h**2 + 1. Find s, given that l(s) = 0.
-2, 2/7, 1, 2
Let j(t) be the third derivative of -t**6/900 - 2*t**5/225 + 7*t**4/36 + 10*t**3/3 - t**2 + 33*t. Factor j(s).
-2*(s - 6)*(s + 5)**2/15
Suppose 0 = -4*j - 4*b - 2 - 14, -2*j - 5*b - 26 = 0. Solve -2/5*i**j - 4/5*i + 6/5 = 0.
-3, 1
Let c be ((-8)/(-12))/(8/36). Let b(v) = -2*v**4 - 20*v**3 + 8*v**2. Let y(g) = g**4 + 7*g**3 - 3*g**2. Let k(a) = c*b(a) + 8*y(a). Suppose k(d) = 0. What is d?
0, 2
Suppose -2*r = -2*a - 44, a - 8 = -5*r - 18. Let u = a + 129/5. Factor 486/5*j**3 + 81*j**5 + 2/5 + 168/5*j**2 + 702/5*j**4 + u*j.
(3*j + 1)**4*(5*j + 2)/5
Factor 5*u**2 - 17*u**2 - 2 - 2 - 20*u**2 + 2*u**5