Let l(c) = c**3 - 8*c**2 - 10*c + 13. Let g be l(9). Factor -2*t**3 - 5*t**2 - g*t + t**2 + t**3.
-t*(t + 2)**2
Let f(i) be the second derivative of -i**5/20 - i**4/4 + 2*i**3/3 - 22*i. Factor f(k).
-k*(k - 1)*(k + 4)
Let p(h) be the third derivative of -h**9/113400 + h**7/18900 - 5*h**4/24 + 9*h**2. Let u(i) be the second derivative of p(i). Factor u(l).
-2*l**2*(l - 1)*(l + 1)/15
Suppose 2*y + 4*l = 8, -2*y + 1 = -l - 7. Factor 0*w + 6*w + 4*w**3 - 12*w**2 + y*w**3 - 1.
(2*w - 1)**3
Let g be (-16)/112*3*-7. Suppose 1/4*y**g + 1/4*y**2 - 1/4*y**4 - 1/4*y**5 + 0 + 0*y = 0. What is y?
-1, 0, 1
Let i = 73/840 - 3/56. Let k(a) be the third derivative of 0 - i*a**5 + 0*a - 3*a**2 - 1/3*a**4 - 4/3*a**3. Factor k(c).
-2*(c + 2)**2
Let m(p) = -10*p**2 - 98*p - 588. Let c(a) = -3*a**2 - 32*a - 196. Let t(r) = -7*c(r) + 2*m(r). Factor t(i).
(i + 14)**2
Let g(w) be the third derivative of 1/60*w**4 + 1/150*w**5 + 0*w**3 + w**2 + 0*w + 0. Determine f, given that g(f) = 0.
-1, 0
Let k = 34 - 22. Factor 3*i**2 + 10 - k*i + 3 - 4.
3*(i - 3)*(i - 1)
Suppose 1/2*q - 17/8*q**2 + 1/2*q**3 + 0 = 0. What is q?
0, 1/4, 4
Let m = 123 + -1105/9. Suppose 0*q - 2/9*q**4 + 0*q**3 + m*q**2 + 0 = 0. What is q?
-1, 0, 1
Let g(h) be the third derivative of h**5/210 - h**4/84 + 3*h**2. Factor g(t).
2*t*(t - 1)/7
Let g(x) = -5 + 0*x**2 + x**2 - 2 + 8*x. Let s be g(-9). Factor -1 + s + 4*c + 4*c**3 + 0*c**3 + 6*c**2 - 2*c**4 + 3*c**4.
(c + 1)**4
Let -2/5*m**3 + 14/15*m**4 + 2/3*m**5 + 0 - 14/15*m**2 - 4/15*m = 0. What is m?
-1, -2/5, 0, 1
Let h be (-36)/(-15) + (40/(-25))/4. Solve -1/2 + 3*l + 7/2*l**h = 0.
-1, 1/7
Let b(p) be the first derivative of 3 + 3/2*p**4 - 6/5*p**5 + p**3 - 15/4*p**2 + 3*p + 1/4*p**6. Factor b(i).
3*(i - 2)*(i - 1)**3*(i + 1)/2
Let j = -15 + 13. Let a be (0 + -2)/j*5. Factor 0 + 0*r**3 + 2/3*r**4 - 2/3*r**2 - 1/3*r**a + 1/3*r.
-r*(r - 1)**3*(r + 1)/3
Let 0 - 1/3*v**2 + 0*v**3 + 1/3*v**4 + 0*v = 0. Calculate v.
-1, 0, 1
Let k(u) be the second derivative of u**5/90 - u**4/18 + 2*u**2 - 4*u. Let h(m) be the first derivative of k(m). Find t, given that h(t) = 0.
0, 2
Let q(r) = -9*r**3 - r**2 + 43*r + 1. Let c(i) = -3*i**3 + 15*i. Let f(j) = -17*c(j) + 6*q(j). Factor f(a).
-3*(a - 1)*(a + 1)*(a + 2)
Let c = 179 - 172. Let r(w) be the third derivative of -1/420*w**c + 1/40*w**5 - 3*w**2 - 1/6*w**3 + 0 - 1/48*w**4 + 1/240*w**6 + 0*w. Factor r(a).
-(a - 2)*(a - 1)*(a + 1)**2/2
Suppose 8*g + 16 = 12*g. Let b(r) be the first derivative of -1/12*r**g - 1/15*r**5 - 2/3*r + 1/3*r**3 - 1 + 1/6*r**2. Let b(o) = 0. Calculate o.
-2, -1, 1
Let j = 4 - 3. Let l be (-1 + 2)/j*3. Factor n - n**l - 4*n + 0 + 1 + 3*n**2.
-(n - 1)**3
Factor -8/15*x**4 - 2/5*x**3 + 2/15*x + 8/15*x**5 + 4/15*x**2 + 0.
2*x*(x - 1)**2*(2*x + 1)**2/15
Let z(c) be the third derivative of c**6/660 + 2*c**5/165 + 5*c**4/132 + 2*c**3/33 - 10*c**2. Let z(o) = 0. What is o?
-2, -1
Suppose -2*u + 12 = 2*u. Factor -2*s**3 + 2*s**2 - 3*s + s**u + 2*s.
-s*(s - 1)**2
Suppose 3*p = -0*p. Find v, given that 0*v - 4*v**2 - v**3 + 5*v**3 - v**4 + p*v = 0.
0, 2
Factor 3 - 13*f**2 - 3 - 5*f**5 - 15*f**4 + 33*f**2.
-5*f**2*(f - 1)*(f + 2)**2
Let v(q) be the third derivative of -q**6/2 - 7*q**5/12 + 35*q**4/24 + 5*q**3/3 - 20*q**2. Suppose v(j) = 0. What is j?
-1, -1/4, 2/3
Factor 0 + 0*d + 1/2*d**3 + d**2.
d**2*(d + 2)/2
Let d(m) be the first derivative of -m**3/12 - 5*m**2/8 - m - 6. Factor d(c).
-(c + 1)*(c + 4)/4
Let j(q) be the third derivative of 25*q**8/336 - q**7/6 + q**6/12 + 3*q**2 + q. Determine k, given that j(k) = 0.
0, 2/5, 1
Determine j, given that -20*j**4 + 36*j**3 - 48 + 11*j**5 + 10*j**5 + 6*j**5 + 68*j**2 - 31*j**5 - 32*j = 0.
-6, -1, 1, 2
Let p(m) be the third derivative of m**5/10 - m**4/12 - 2*m**3/3 + 3*m**2. Let y(d) = 4*d**2 - d - 3. Let i(a) = 5*p(a) - 8*y(a). Let i(k) = 0. What is k?
-2, 1
Solve 124*g + 2*g**2 + 120*g - 1 - 244*g - g**4 = 0 for g.
-1, 1
Let h(z) be the first derivative of -z**5/5 - 3*z**4/4 - z**3 - z**2/2 + 5. Determine t, given that h(t) = 0.
-1, 0
Let n be 2/(-6) + 9/9. Determine o so that -2/3*o**3 - 2/3*o**4 + 0 + 2/3*o**5 + n*o**2 + 0*o = 0.
-1, 0, 1
Suppose -4*t - t - 6 = -3*h, 3*t = 0. Find f, given that -8*f**2 + 18*f**h - 9*f**2 - 2*f = 0.
0, 2
Suppose -f = 3*f + 24. Let o = f + 6. Determine x, given that o + 2/3*x**2 + 0*x = 0.
0
Let i(o) be the second derivative of -o**6/60 - o**5/20 - o**4/24 + 4*o. Factor i(m).
-m**2*(m + 1)**2/2
Let z = 0 - 0. Let i(p) = p**2 + 3. Let x be i(z). Suppose -2*l**5 - 3*l**x - 2*l - 6*l**4 + l**2 + 3*l + l**4 = 0. Calculate l.
-1, 0, 1/2
Let n = 5877/4 + -1453. Let j = n - 16. Factor 1/2 + 0*h**2 - j*h**3 + 3/4*h.
-(h - 2)*(h + 1)**2/4
Let w be 1/9 + (-43)/(-18). Factor -5*d**3 - w*d + 1/2 - 1/2*d**5 + 5/2*d**4 + 5*d**2.
-(d - 1)**5/2
Determine d so that 0*d**2 + 0 + 4/3*d**4 + 0*d + 0*d**3 + 2/3*d**5 = 0.
-2, 0
Let m(k) = 2*k**2 - 3*k. Let q be m(2). Solve -15 + 15 + 3*z**q = 0.
0
Let a(o) = o**3 + 6*o**2 - 2*o. Let y be a(-6). Let l be (8/6)/(y/18). Determine t so that 4 - 4 - 4*t - l*t**2 = 0.
-2, 0
Let j(o) be the third derivative of o**7/2520 - o**5/120 + o**4/36 - o**3/3 - o**2. Let d(m) be the first derivative of j(m). Factor d(t).
(t - 1)**2*(t + 2)/3
Let q be 4 + -2 + 10 + 0. Solve -2*z + 22*z**2 - 2*z + q*z**3 - 29*z**3 - 15*z**3 + 14*z**4 = 0 for z.
0, 2/7, 1
Let a(o) be the second derivative of o**2/2 + 3*o. Let z(s) = 2*s**2 + 2. Let t(m) = -10*a(m) + z(m). Factor t(w).
2*(w - 2)*(w + 2)
Let g(x) be the second derivative of -x**6/30 + 3*x**5/20 - x**4/12 - x**3/2 + x**2 - x. Factor g(q).
-(q - 2)*(q - 1)**2*(q + 1)
Let u = -7 + 11. Let z(i) be the first derivative of 0*i - 3 - 1/3*i**3 - 1/3*i**6 - 3/4*i**u + 1/2*i**2 + i**5. Factor z(q).
-q*(q - 1)**3*(2*q + 1)
Let l(c) be the first derivative of 2 - 2*c**3 - 2*c**3 - 3*c + 5*c**3 - 8. Find a, given that l(a) = 0.
-1, 1
Let q(o) be the first derivative of -2*o**3/9 - 13*o**2/15 + 4*o/5 + 1. Factor q(s).
-2*(s + 3)*(5*s - 2)/15
Let g(b) = -2*b**2 + 4. Let v be g(0). Let 10*k**2 + 10*k**3 - 6*k**4 + 14*k + 0 + 8*k**4 + v + 8*k**2 = 0. Calculate k.
-2, -1
Let k(l) be the first derivative of l**8/840 + 2*l**7/525 + l**6/300 + 4*l**2 + 2. Let z(h) be the second derivative of k(h). Factor z(u).
2*u**3*(u + 1)**2/5
Let k be (-7)/(-14) + (-148)/300. Let o(b) be the third derivative of 0*b - k*b**5 + 0*b**3 + 1/300*b**6 + 2*b**2 + 0 + 0*b**4. Let o(p) = 0. What is p?
0, 1
Let h(s) be the third derivative of -s**7/210 - s**6/120 + s**5/60 + s**4/24 + 16*s**2. Suppose h(k) = 0. Calculate k.
-1, 0, 1
Let w(l) be the second derivative of 5/84*l**7 - l**2 + 0*l**3 - 17/40*l**5 - 1/20*l**6 - 2*l + 0 + 19/24*l**4. Factor w(h).
(h - 1)**3*(h + 2)*(5*h + 2)/2
Let f(x) = -x**2 + 16*x + 3. Let t be 1/(-1) - (4 + 0). Let l = 18 + -11. Let o(m) = -m**2 + 11*m + 2. Let c(u) = l*o(u) + t*f(u). Factor c(h).
-(h + 1)*(2*h + 1)
Let p = -92 + 921/10. Let b(x) be the second derivative of -1/6*x**4 + 1/3*x**3 + x**2 + 0 - p*x**5 - x. Solve b(d) = 0.
-1, 1
Let v be 44/8 + 6/(-4). Suppose v - 16 = -4*i. Factor 1/2*r**2 - r**4 + 0*r + 1/4*r**i + 0 - 3/4*r**5.
-r**2*(r + 1)**2*(3*r - 2)/4
Let s(l) be the first derivative of 50/3*l**3 + 18*l + 2 + 30*l**2. What is x in s(x) = 0?
-3/5
Let q(y) be the first derivative of -y**6/180 + y**5/18 - 2*y**4/9 + 4*y**3/9 - y**2 + 5. Let v(o) be the second derivative of q(o). Let v(u) = 0. What is u?
1, 2
Suppose 31*q**2 + 17*q**2 + 3 - 3 + 4*q**3 + 144*q = 0. What is q?
-6, 0
Suppose -3*l = -5*s - 15, 0 = -2*s + 11 - 17. Let o = -7/36 + 5/12. Factor -o*z + l + 2/9*z**2.
2*z*(z - 1)/9
Let u be (-1)/(-3) - 72/(-27). Let y(x) = 2*x - 6. Let g be y(5). Factor 7*o + 2*o**3 - 29*o + 26*o**2 + g - 4*o**u - 6*o**3.
-2*(o - 2)*(o - 1)*(4*o - 1)
Let -3/2 + 2*z - 1/2*z**2 = 0. Calculate z.
1, 3
Suppose 3*y = -0*y + 147. Let n be (-4 - -1) + 175/y. Solve 4/7*w**3 - 2/7*w - 4/7 + 8/7*w**2 - n*w**4 - 2/7*w**5 = 0.
-2, -1, 1
Let u = 155 + -929/6. Solve -1/6*i**3 + 1/6 - 1/6*i**2 + u*i = 0 for i.
-1, 1
Let y(o) be the first derivative of -o**5/5 - 3*o**4/4 - 2*o**3/3 + 9. Find w, given that y(w) = 0.
-2, -1, 0
Let z(d) = d**3 + d**2 + 1. Let n(p) = -8*p**3 - 4*p**2 - 6. Let v(f) = -n(f) - 6*z(f). Suppose v(g) = 0. What is g?
0, 1
Factor 0 - 16/9*u**4 + 14/9*u**3 - 4/9