 1)/5
Let y be (5 + -1)*2*2. Factor -150 + y*x**3 + 9*x - 24*x**2 + 150.
x*(4*x - 3)**2
Suppose 8*n = 4*n - 16. Let v be 2/4 - (n + 4). Let 0*k + 0 + 0*k**3 + 0*k**2 + 1/2*k**4 - v*k**5 = 0. Calculate k.
0, 1
Factor -4/5*v**3 - 2/5*v**5 - 4/5*v**2 + 6/5*v + 6/5*v**4 - 2/5.
-2*(v - 1)**4*(v + 1)/5
Let m(g) be the second derivative of 0*g**2 - 1/30*g**6 + 0*g**3 - 7*g + 1/6*g**4 + 0 - 1/20*g**5. Factor m(t).
-t**2*(t - 1)*(t + 2)
Let x(j) = -7*j**2 + 2*j - 3. Let g(q) = 15*q**2 - 3*q + 5. Let y(n) = -6*g(n) - 13*x(n). Let i be y(7). Solve -t**i - 2 + 2 - t**3 = 0.
-1, 0
Let w(c) = -4*c**3 - 16*c**2 + 2. Let g(o) = 1. Let q(n) = -2*g(n) + w(n). Suppose q(k) = 0. What is k?
-4, 0
Suppose -2*b - 2*n - n - 14 = 0, -n + 12 = -b. Let i = -10 - b. Factor 2/9*s + 2/3*s**3 + i + 2/3*s**2 + 2/9*s**4.
2*s*(s + 1)**3/9
Let w(g) = -g**3 - 2*g - 1. Let f be w(-3). Factor 2*i**5 + 3*i**5 - i**5 + f*i**2 - 8*i**4 - 12*i**3 - 16*i.
4*i*(i - 2)*(i - 1)**2*(i + 2)
Suppose 16 - 66 = 5*d. Let u be (12/(-15))/(4/d). Factor -22/9*c**u + 0 + 2*c**3 + 4/9*c.
2*c*(c - 1)*(9*c - 2)/9
Suppose 28 = -4*s + 2*a, s - 2*s - 5*a = -4. Let x be 30/25*(-20)/s. Suppose z**2 - 9*z**3 - 5*z**4 + 5*z**2 - 13*z**4 + 3*z**x = 0. Calculate z.
-1, 0, 2/5
Let a(i) = -5*i**2 + 10*i - 10. Let l(t) = -66*t**2 + 129*t - 129. Let f(d) = -27*a(d) + 2*l(d). Solve f(j) = 0 for j.
2
Let g(r) be the second derivative of -3*r**5/20 - 21*r**4/4 - 147*r**3/2 - 1029*r**2/2 - 21*r. What is t in g(t) = 0?
-7
Let w(f) = f**2 + 7*f + 3. Let r be w(-7). Suppose -r*y = -0*y - 18. Determine q, given that 2*q**2 - y*q**2 + 4*q - 10*q**2 = 0.
0, 2/7
Solve -252*x**4 + 123*x**4 + 126*x**4 + 9*x**3 = 0 for x.
0, 3
Factor -12*j**3 - 4*j**5 - 52 - 12*j**4 + 52 - 4*j**2.
-4*j**2*(j + 1)**3
Let j(d) be the third derivative of 5*d**8/336 + 17*d**7/210 + 7*d**6/40 + 11*d**5/60 + d**4/12 + 7*d**2. Factor j(s).
s*(s + 1)**3*(5*s + 2)
Suppose -61 + 7 = -3*q. Let u be ((-1)/4)/((-3)/q). Factor 1/2*j**2 + 0*j + 1/2*j**5 + u*j**4 + 0 + 3/2*j**3.
j**2*(j + 1)**3/2
Let b(g) = g**2 + g - 1. Let o(v) be the second derivative of -v**4/3 - v**3/6 + v**2 + 2*v. Let r(f) = -6*b(f) - 2*o(f). Factor r(w).
2*(w - 1)**2
Let d(u) = 3*u**4 + 10*u**3 + 4*u**2 + 4*u - 4. Let x(n) = 3*n**4 + 11*n**3 + 5*n**2 + 5*n - 5. Let t(c) = 5*d(c) - 4*x(c). Solve t(m) = 0 for m.
-2, 0
Let s(p) be the third derivative of -2*p**7/105 + p**6/15 + p**5/15 - p**4/3 + 6*p**2. Determine c, given that s(c) = 0.
-1, 0, 1, 2
Let o be 36/(-15)*(25 + -27). Factor -o*k**2 + 16/5*k + 0 + 12/5*k**3 - 2/5*k**4.
-2*k*(k - 2)**3/5
Suppose -2*u = -5*k - 14, -5*k - 4 = -3*k. Let m = -14/15 + 128/105. Suppose 4/7*x**u - 2/7*x**3 + 0 - m*x = 0. What is x?
0, 1
Factor 0 + 1/3*d**2 - 1/3*d**4 + 1/9*d**3 + 1/9*d**5 - 2/9*d.
d*(d - 2)*(d - 1)**2*(d + 1)/9
Let p(c) be the second derivative of c**7/189 - 2*c**6/135 - c**5/45 + 4*c**4/27 - 7*c**3/27 + 2*c**2/9 + 23*c. Factor p(k).
2*(k - 1)**4*(k + 2)/9
Let f be 2 - (0 - (5 - 2)). Let a = f - 1. Factor 2*n**4 - 4*n**a + 1 + 2*n + 1 + 2*n - 4*n**3.
-2*(n - 1)*(n + 1)**3
Factor 2 - 4*c - 19/2*c**2 - 7/2*c**3.
-(c + 1)*(c + 2)*(7*c - 2)/2
Let u(n) be the second derivative of 3*n**5/100 + n**4/5 + n**3/2 + 3*n**2/5 - 43*n. Let u(k) = 0. What is k?
-2, -1
Let m(z) be the second derivative of 4*z**7/189 - z**6/15 - z**5/9 + z**4/18 - 52*z + 2. Let m(v) = 0. Calculate v.
-1, 0, 1/4, 3
Factor -8*m - 16 - 2*m + 2*m - m**2.
-(m + 4)**2
Suppose 0 = -5*t + 5*j + 15, 3*t = 7*t + 5*j - 21. Suppose t*v + 3*u - 6 + 4 = 0, v = -4*u - 6. Suppose -4 - s**v - 4*s + 4*s - 4*s = 0. What is s?
-2
Let f = 6 - 4. Let t be ((-16)/(-33))/(f/3). Factor 2/11*o**2 + t - 8/11*o.
2*(o - 2)**2/11
Let q(z) be the third derivative of -z**5/270 + 4*z**3/27 + 13*z**2. Factor q(f).
-2*(f - 2)*(f + 2)/9
Let d(k) be the second derivative of 2*k + 8/15*k**6 + 2/21*k**7 + 4/3*k**4 + 0 + 2/3*k**3 + 0*k**2 + 6/5*k**5. Solve d(p) = 0.
-1, 0
Let c = -9 + 11. Factor -z**3 + z**2 - c - 2*z - 5*z**2 - 3*z.
-(z + 1)**2*(z + 2)
Let y = 5 - 3. Suppose -2*g + s + 0 + 2 = 0, -4*g - y = s. Factor 0 - 1/2*c**2 + g*c.
-c**2/2
Let u = -503/5 - -101. Factor -32/5*s**4 + 48/5*s**3 - u - 12/5*s - 2/5*s**2.
-2*(s - 1)**2*(4*s + 1)**2/5
Solve 3/2*r**3 + 1 - 7/2*r + r**2 = 0 for r.
-2, 1/3, 1
Let k be 4/1 + 4 - 4. Suppose k = -5*u + 14. Find x such that 0 + 0*x**u - 1/5*x + 1/5*x**3 = 0.
-1, 0, 1
Let q(l) be the second derivative of -3*l**5/20 + l**4/2 + l**3/2 - 3*l**2 - 8*l. What is i in q(i) = 0?
-1, 1, 2
Let z(a) be the second derivative of a**10/10080 - a**9/2520 + a**7/420 - a**6/240 - a**4/2 + 2*a. Let j(s) be the third derivative of z(s). Factor j(h).
3*h*(h - 1)**3*(h + 1)
Suppose -d = -6*d + 5*s + 40, d = -4*s - 17. Suppose 2*l - d*l + 2 = 0. Factor 0*n + 0 + 1/4*n**l - 1/4*n**3.
-n**2*(n - 1)/4
Let z be 12/(-30)*((-51)/36 + 1). Let d(i) be the first derivative of -z*i**3 - 1/8*i**4 + 4 + 1/2*i + 1/4*i**2. Factor d(q).
-(q - 1)*(q + 1)**2/2
Let x(w) be the second derivative of -2*w**6/105 + w**4/21 - 12*w. Let x(z) = 0. Calculate z.
-1, 0, 1
Find b such that 3 + 5*b**4 + 5 - 8 - 5*b**2 = 0.
-1, 0, 1
Find u such that -3/8*u**3 - 3/4*u - 9/8*u**2 + 0 = 0.
-2, -1, 0
Let s(p) be the third derivative of -p**5/300 + 7*p**4/120 - 18*p**2 - p. Factor s(x).
-x*(x - 7)/5
Factor -13 - 3*w**2 + 17*w - 5 + 4*w.
-3*(w - 6)*(w - 1)
Let z(d) be the second derivative of -d**6/20 + 3*d**5/20 - d**4/8 - 4*d. Factor z(b).
-3*b**2*(b - 1)**2/2
Let v(y) be the second derivative of y**7/21 - 2*y**6/15 + y**5/10 - 10*y. Suppose v(z) = 0. Calculate z.
0, 1
What is c in 47 + 4*c**3 - 51 + 4*c**4 - 2*c**5 + 0*c**4 + 14*c - 16*c**2 = 0?
-2, 1
Suppose 0 = -2*o + 2*q + 14, -3*o - 2*q - 4 = -0*q. Solve 3/2*w**3 + w**o + 1/4*w**5 + 1/4*w + w**4 + 0 = 0 for w.
-1, 0
Let g = -12 - -16. Factor -g*k - k**2 + 4*k - 2 + 0*k**2 - 3*k.
-(k + 1)*(k + 2)
Let p(s) be the second derivative of -1/10*s**5 - 1/10*s**6 + s + 7/12*s**4 + 0 - 1/3*s**3 + 0*s**2. Solve p(i) = 0 for i.
-2, 0, 1/3, 1
Let m be (-6)/(-12) - (-3)/2. Factor p**m + 6*p**4 - 6*p**4 - p**4.
-p**2*(p - 1)*(p + 1)
Let j(s) be the third derivative of 25*s**8/168 - s**7/7 - 3*s**6/20 - s**5/30 - s**2. Suppose j(k) = 0. What is k?
-1/5, 0, 1
Factor v + 0 - 3/2*v**2 + 1/2*v**4 + 0*v**3.
v*(v - 1)**2*(v + 2)/2
Suppose -3*b - 21*b + 5*b = 0. Factor -1/4*h**3 + b + 1/4*h**2 + 0*h.
-h**2*(h - 1)/4
Let f = 1102/9 - 122. Factor -f*s + 2/9*s**2 + 2/9.
2*(s - 1)**2/9
Let c(v) be the second derivative of -v**7/126 + v**6/15 - v**5/5 + 5*v**4/18 - v**3/6 - 3*v. Solve c(s) = 0.
0, 1, 3
Let r be (8/12)/((-1)/(-6)). Let i(p) be the second derivative of 0*p**2 + 2*p + 0 - 1/48*p**r + 1/24*p**3. Let i(o) = 0. What is o?
0, 1
Let k = -31762/63 + 3568/9. Let t = 108 + k. Factor -t - 2/7*u**2 - 4/7*u.
-2*(u + 1)**2/7
Let t = 11 - 8. Suppose -t*m + 0*m + 6 = 0. Factor -5*h + 9*h**3 - m*h**2 + 6*h**4 - 5*h - 4 + h**3.
2*(h - 1)*(h + 1)**2*(3*h + 2)
Let x(n) be the first derivative of -n**5 - 15*n**4/4 - 5*n**3 - 5*n**2/2 - 11. Factor x(a).
-5*a*(a + 1)**3
Let r(i) be the second derivative of i**5/110 - i**4/33 + 23*i. What is h in r(h) = 0?
0, 2
Let g(p) be the third derivative of -p**7/315 - p**6/90 + p**4/18 + p**3/9 - 5*p**2. Factor g(b).
-2*(b - 1)*(b + 1)**3/3
Let h(v) be the first derivative of -3*v**5/20 + v**4/4 + v**3/2 - 3*v**2/2 - 3*v + 6. Let m(n) be the first derivative of h(n). Factor m(z).
-3*(z - 1)**2*(z + 1)
Let g(d) = d**3 + 4*d**2 + 5. Let a be g(-4). Let b(y) be the third derivative of 0*y**a + 1/28*y**4 + 0 - 1/420*y**6 + 0*y - 2*y**2 + 2/21*y**3. Factor b(v).
-2*(v - 2)*(v + 1)**2/7
Suppose -2*k - 3 = 5*z - 29, -3*z + 5*k = -28. Let m be (0 + 3/z)*4. Factor -1 - 2*w**2 - 3 + 4 + 2*w + 2 - m*w**3.
-2*(w - 1)*(w + 1)**2
Let m = 261 - 1293/5. Factor -m - 3/5*d**2 + 12/5*d.
-3*(d - 2)**2/5
Let z(t) be the third derivative of -t**8/20160 - t**7/5040 - t**5/60 + 10*t**2. Let v(j) be the third derivative of z(j). Let v(p) = 0. Calculate p.
-1, 0
Let b(l) be the first derivative of -l**5/15 - l**4/6 + l**3/9 + l**2/3 + 3. Factor b(p).
-p*(p - 1)*(p + 1)*(p + 2)/3
Let d(w) = -3*w**3 - w**2 + 8*w. Let j(r) = -r**2 - r. Let z(k) = d(k) + 2*j(k). Factor z(x).
-3*x*(x - 1)*(x + 2)
Let t(r) be the first derivative of -1/8*r**2 + 0*r - 2 - 1/12*r**3. Factor t(f).
-f*(f + 1)/