q + 1)**2
Let b(x) be the second derivative of -x**6/30 + x**5/5 - x**4/4 - 3*x. Factor b(h).
-h**2*(h - 3)*(h - 1)
Let p(c) be the second derivative of 7*c**7/3 - 28*c**6/15 + 2*c**5/5 - 3*c. Factor p(f).
2*f**3*(7*f - 2)**2
Let x(o) be the third derivative of -1/60*o**5 + 0*o + 1/60*o**6 - 4*o**2 + 1/70*o**7 + 0*o**3 + 0*o**4 + 0. Factor x(j).
j**2*(j + 1)*(3*j - 1)
Let v(y) be the first derivative of 2*y**3/39 + y**2/13 - 2. Let v(g) = 0. Calculate g.
-1, 0
Let t be (16/(0 + 4))/2. Factor 2*z - 8*z**t - 2*z**3 + 8*z**2.
-2*z*(z - 1)*(z + 1)
Let p(a) be the second derivative of -a**6/10 - a**5/20 + 3*a**4/4 - a**3/2 - a**2 + 3*a. Suppose p(x) = 0. Calculate x.
-2, -1/3, 1
Let j(o) = o**4 - o**3 - o - 1. Let g(l) = 20*l**4 - 5*l**3 + 5*l**2 - 15*l - 15. Let y(r) = g(r) - 15*j(r). Factor y(h).
5*h**2*(h + 1)**2
Let q(d) be the first derivative of d**6/24 - 3*d**5/40 - d**4/16 + d**3/6 - d/8 + 9. Find p such that q(p) = 0.
-1, -1/2, 1
Let z = 2860/10059 - -2/1437. What is w in -2/7*w**4 + 0*w - z + 0*w**3 + 4/7*w**2 = 0?
-1, 1
Suppose -24 = -2*z + 5*i, z + 6 = -3*i - 4. Let v(a) be the second derivative of 0*a**z + 1/12*a**4 + 1/6*a**3 - 1/30*a**6 + 0 - 1/20*a**5 - a. Factor v(w).
-w*(w - 1)*(w + 1)**2
Let k(r) be the third derivative of -r**9/151200 - r**8/50400 + r**5/60 + r**2. Let g(o) be the third derivative of k(o). Let g(t) = 0. What is t?
-1, 0
Let p(z) be the second derivative of -z**6/315 - z**5/105 - z**4/126 + 11*z. Factor p(i).
-2*i**2*(i + 1)**2/21
Let q(s) = -3*s**4 + 9*s**3 - 3*s**2 - 3*s. Let i(t) = -t**3 + t. Let d(g) = -3*i(g) - q(g). Factor d(r).
3*r**2*(r - 1)**2
Suppose 6*b + 5 = 5*b, -20 = -5*r + 2*b. Suppose 5*j - 12 = r*j. Factor -j*v**2 + 2 - 4*v**2 + 5*v**2 + v.
-(v - 1)*(3*v + 2)
Determine y, given that 1/4*y + 5/8*y**2 + 0 - 3/8*y**5 - 5/8*y**4 + 1/8*y**3 = 0.
-1, -2/3, 0, 1
Let k(j) = -j**2 + 6*j - 1. Let y(q) = q - 1. Let b(s) = k(s) - 4*y(s). Let b(v) = 0. Calculate v.
-1, 3
Let d be ((-2)/1)/((-2)/4). Let f = 30/7 - d. Let 2/7*j**2 - 4/7*j + f = 0. Calculate j.
1
Suppose w - 3*q = 3*w + 31, -32 = 2*w + 4*q. Let c = w + 16. Suppose -9/5*a + 2/5 + 7/5*a**c = 0. Calculate a.
2/7, 1
Let w be ((-6)/(-8))/((-1)/52). Let c(a) = -6*a**2 - 7*a + 13. Let m(z) = -z**2 - z + 2. Let u(g) = w*m(g) + 6*c(g). Suppose u(o) = 0. What is o?
0, 1
Factor q**5 - 15*q**2 + 18*q + 18 - 7*q**3 - 2*q**4 + 5*q**4 - 18.
q*(q - 2)*(q - 1)*(q + 3)**2
Let t(f) be the first derivative of f**4/8 - 3*f**3 + 27*f**2 - 108*f + 64. Determine j so that t(j) = 0.
6
Let f(j) be the third derivative of -j**6/120 + j**5/60 - 2*j**2. What is z in f(z) = 0?
0, 1
Let f(n) = 2*n - 10. Let x be f(9). Let j be -1 + 0 + -2 + x. Factor 0 + 1/4*m**4 + 0*m**3 + 0*m**2 + 0*m + 1/4*m**j.
m**4*(m + 1)/4
Let p = 57 + -1367/24. Let z(s) be the third derivative of 0 + 1/2*s**4 - p*s**6 - 1/20*s**5 + 0*s + s**2 - 2/3*s**3. Factor z(t).
-(t - 1)*(t + 2)*(5*t - 2)
Let w(l) be the first derivative of -l**3/8 + 3*l**2/4 - 9*l/8 + 7. Factor w(b).
-3*(b - 3)*(b - 1)/8
Let v(c) = -c**2 - 9*c - 18. Let w be v(-4). Determine y so that -3/2*y**3 + 3 + 3/2*y - 3*y**w = 0.
-2, -1, 1
Let a(b) be the second derivative of -b**9/7560 + b**7/630 - b**5/60 + b**4/4 - b. Let z(l) be the third derivative of a(l). Factor z(v).
-2*(v - 1)**2*(v + 1)**2
Let n = 23 - 13. Suppose -n = -0*y - 5*y. Factor 3*o**2 + o**2 - y*o**3 - o - o.
-2*o*(o - 1)**2
Suppose -3*j = 3*j - 72. Factor j*b**3 - 8*b**3 + 8 - 2*b - 2*b - 8*b**2.
4*(b - 2)*(b - 1)*(b + 1)
Let d be (-1)/(-3) - 24/(-9). Find j such that -3*j**3 - 2*j**d + 4*j**3 = 0.
0
Suppose -3*s + 108 = 3*u, -4*s - 5*u - 10 + 158 = 0. Let z be 4/2 - 56/s. Solve -1/2*b - z - 1/4*b**2 = 0.
-1
Let b(s) = s**3 + 2*s**2 + s + 2. Let p(x) = -3*x**2 - 2*x - 1. Let w be p(-1). Let z be b(w). Determine o, given that -o**2 + 3 + z + 2*o - 3 = 0.
0, 2
Suppose 6*c - c = 0. Let r(j) be the second derivative of 3*j - 1/30*j**5 + c + 5/18*j**4 - 8/9*j**3 + 4/3*j**2. Solve r(h) = 0.
1, 2
Let z(p) be the first derivative of p**3 + 3*p**2/2 - 1. Solve z(m) = 0 for m.
-1, 0
Let z(m) be the first derivative of m**8/6720 - m**7/1680 + m**6/1440 - 2*m**3/3 - 2. Let q(c) be the third derivative of z(c). Find n, given that q(n) = 0.
0, 1
Let z(n) be the third derivative of -n**5/30 - n**4/12 - 10*n**2. Determine c so that z(c) = 0.
-1, 0
Let y = 1336/4725 - -2/675. Factor 2/7*k**2 + 0 - y*k.
2*k*(k - 1)/7
Let i = 15 + -10. Let w(s) = 5*s**4 - 10*s**3 + s**2 + 2. Let v(p) = 9*p**4 - 19*p**3 + p**2 - p + 5. Let o(g) = i*w(g) - 2*v(g). Suppose o(a) = 0. Calculate a.
-2/7, 0, 1
Suppose 2*n = 10 - 4. Suppose 7 + n = 5*j. Factor -2/3*p**3 + 0*p**j + 0 + 2/3*p.
-2*p*(p - 1)*(p + 1)/3
Suppose 79*h**2 + h**3 - 59*h**2 - 13*h**3 - 8*h = 0. Calculate h.
0, 2/3, 1
Let t(x) = -4*x**3 + 4*x - 2. Let c(i) = 4*i**3 - 4*i + 3. Let h(a) = 2*c(a) + 3*t(a). Factor h(w).
-4*w*(w - 1)*(w + 1)
Let p(c) be the second derivative of c**6/165 - c**5/22 + 4*c**4/33 - 4*c**3/33 + 10*c. Let p(m) = 0. What is m?
0, 1, 2
Factor -6*d - 27*d**2 - 20*d**4 + 72*d**4 + 6*d**3 - 25*d**4.
3*d*(d - 1)*(d + 1)*(9*d + 2)
Let a(u) = u**3 + 5*u**2 - 8*u - 7. Let f be a(-6). Factor 2*k**f + 4*k**4 - 4*k**2 + 0*k**4 + 2*k**3 + 4*k**2.
2*k**3*(k + 1)**2
Let f(b) be the third derivative of -b**5/75 + b**4/10 - 4*b**3/15 - 4*b**2. Factor f(y).
-4*(y - 2)*(y - 1)/5
Let o(w) be the third derivative of -w**6/480 + w**5/80 + w**4/96 - w**3/8 - 2*w**2. Factor o(y).
-(y - 3)*(y - 1)*(y + 1)/4
Let j(n) = -n**3 - 3*n**2 - n - 1. Let k be j(-3). Let i(s) be the first derivative of 2/3*s**3 - 2*s - k + 0*s**2. Factor i(h).
2*(h - 1)*(h + 1)
Let b = 1 + -4. Let o(i) = i**2 - 4*i - 2. Let h(j) = -j. Let m(t) = b*h(t) + o(t). Factor m(q).
(q - 2)*(q + 1)
Let g(f) be the first derivative of -2 + f - 9/4*f**4 + 1/2*f**2 - 3*f**3. Factor g(w).
-(w + 1)*(3*w - 1)*(3*w + 1)
Solve 3/5*m + 9/5*m**3 - 9/5*m**2 + 0 - 3/5*m**4 = 0.
0, 1
Let m(b) be the second derivative of b**4/78 + 2*b**3/39 + b**2/13 - 4*b. Factor m(w).
2*(w + 1)**2/13
Let a(d) = d**3 + d**2 - d - 5. Let j be a(0). Let n be (-20)/(-12)*(-4)/j. Factor 0*c - n*c**3 + 2/3*c**4 + 2/3*c**2 + 0.
2*c**2*(c - 1)**2/3
Let q = 4/7 + -65/126. Let r(y) be the third derivative of 0*y + 0 + 1/90*y**6 - q*y**4 + 1/315*y**7 + 2*y**2 - 1/9*y**3 + 0*y**5. What is w in r(w) = 0?
-1, 1
Let a = 599/4 - 149. Suppose 0*k + 1/4*k**5 - a*k**4 + 3/4*k**3 - 1/4*k**2 + 0 = 0. Calculate k.
0, 1
Determine b so that -26/7*b**2 + 12/7*b - 2/7*b**4 + 16/7*b**3 + 0 = 0.
0, 1, 6
Let t(s) be the second derivative of 2/7*s**7 + 0*s**2 + 0 - 3*s - 17/60*s**5 + 1/18*s**3 + 7/30*s**6 - 1/36*s**4. Find n, given that t(n) = 0.
-1, -1/4, 0, 1/3
Suppose -3*g - 5*m = 16 + 4, -5 = 2*g - 5*m. Let r = -3 - g. Factor 0*c**2 + 0*c**2 + c**3 - c**r.
c**2*(c - 1)
Let c(z) be the third derivative of 9*z**2 + 0 - 2/15*z**4 + 11/150*z**5 - 4/15*z**3 - 1/100*z**6 + 0*z. Find l, given that c(l) = 0.
-1/3, 2
Let k(f) = f**3 + 3*f**2 - 1. Let p be k(-2). Factor -9*t**3 - 2*t**2 - 5*t - p + 5 + 14*t.
-(t - 1)*(t + 1)*(9*t + 2)
Suppose -1 = -4*v + 19. Let g(z) be the third derivative of 0*z + 0 - 2*z**2 + 0*z**4 + 0*z**3 - 1/30*z**v. Let g(h) = 0. What is h?
0
Let y(u) be the first derivative of 1 - 1/2*u**2 - 1/150*u**5 + 0*u + 0*u**4 + 0*u**3. Let g(j) be the second derivative of y(j). Find s, given that g(s) = 0.
0
Factor -2/7 - 6/7*f - 2/7*f**3 - 6/7*f**2.
-2*(f + 1)**3/7
Let v be 2/8 - (-4 - (-20)/16). Let g(s) be the second derivative of 1/16*s**4 - 3*s + 0 + 1/80*s**5 - 1/24*s**v - 1/40*s**6 + 0*s**2. Factor g(m).
-m*(m - 1)*(m + 1)*(3*m - 1)/4
Let m = 2 - 3. Let t be (-6)/4*(-3 - m). Determine b, given that 2 - b**3 - 2*b**4 + b**2 - b**2 - t*b**3 + 4*b = 0.
-1, 1
Let n(h) be the third derivative of -h**7/5880 - h**6/2520 + h**5/840 + h**4/168 + h**3/3 - 3*h**2. Let j(s) be the first derivative of n(s). Factor j(l).
-(l - 1)*(l + 1)**2/7
Let g(v) be the third derivative of v**5/150 - v**4/20 + v**2. Suppose g(c) = 0. What is c?
0, 3
Let x(r) = 3*r**2 - r - 4. Let l(f) = -16*f**2 + 4*f + 21. Let i(g) = -2*l(g) - 11*x(g). Let k be i(2). Factor -m**2 - 3/2*m - 1/2 + 3/2*m**k + m**3 + 1/2*m**5.
(m - 1)*(m + 1)**4/2
Let v(i) be the first derivative of i**4/12 - 2*i**3/9 - 7*i**2/6 - 4*i/3 + 35. Factor v(m).
(m - 4)*(m + 1)**2/3