/2*p - b - 1/4*p**2 = 0. What is p?
1
Suppose -18*r**3 + 225*r**2 + 53*r**3 + 25*r - 3*r**4 - 5 - 270*r**2 - 7*r**4 = 0. Calculate r.
1/2, 1
Let a(g) be the first derivative of -g**7/70 + g**6/40 + g**5/20 - g**4/8 + g**2 - 2. Let s(c) be the second derivative of a(c). Find z such that s(z) = 0.
-1, 0, 1
Let n(r) be the third derivative of -r**6/120 - r**5/5 + 9*r**4/8 - 7*r**3/3 + 44*r**2. Factor n(z).
-(z - 1)**2*(z + 14)
Suppose 2*j - 20 = -3*j. Let k(f) be the third derivative of -1/504*f**8 + 0*f + 0*f**3 - 1/90*f**5 + 0 + 0*f**j + 1/180*f**6 + 1/315*f**7 - f**2. Factor k(m).
-2*m**2*(m - 1)**2*(m + 1)/3
Suppose -2*m + 3*n = 2, -6*n + n + 10 = 0. Factor 2/5*f**m + 4/5*f + 0.
2*f*(f + 2)/5
Let s be (-6)/(-21) - 40/(-7). Let p = 16 + -25/2. Factor 2 - s*x - p*x**2.
-(x + 2)*(7*x - 2)/2
Let a = 240 + -710/3. Find c, given that 2/3*c**2 + 2*c**5 + 0 + 14/3*c**4 + 0*c + a*c**3 = 0.
-1, -1/3, 0
Let c(n) be the third derivative of n**9/20160 + n**8/2240 - n**6/60 - 3*n**5/20 + 5*n**2. Let y(f) be the third derivative of c(f). Factor y(s).
3*(s - 1)*(s + 2)**2
Let c(d) = -16*d**3 - 6*d**2 + 9*d - 20. Let k(t) = 3*t**3 + t**2 - 2*t + 4. Let s(f) = 2*c(f) + 11*k(f). Solve s(o) = 0.
-2, 1, 2
Let x(w) be the second derivative of -w**6/12 - w**5/30 + 19*w**4/72 + w**3/9 - w**2/3 - 20*w. Suppose x(f) = 0. Calculate f.
-1, -2/3, 2/5, 1
Let a(i) be the second derivative of 1/10*i**3 + 0 + 1/5*i**2 - 1/12*i**4 - 3*i. Find p such that a(p) = 0.
-2/5, 1
Find x such that 322*x**3 - 6*x - 327*x**3 + 16*x + 5*x**2 = 0.
-1, 0, 2
Let b(z) be the second derivative of -z**5/110 - z**4/33 - z**3/33 - 3*z. Factor b(m).
-2*m*(m + 1)**2/11
Let v(y) be the second derivative of y**9/1512 - y**8/210 + y**7/84 - y**6/90 - y**3/6 - 2*y. Let k(c) be the second derivative of v(c). Factor k(u).
2*u**2*(u - 2)*(u - 1)**2
Let -6/5*m + 3/5*m**2 + 0 = 0. Calculate m.
0, 2
Let a(r) be the second derivative of -r**4/24 - r**3/12 + r**2/2 - 11*r. Factor a(p).
-(p - 1)*(p + 2)/2
Let a(x) = 4*x. Let l be a(1). Let p = -1 + l. Factor -h**5 - p*h**3 - h + h**3 + 4*h**3.
-h*(h - 1)**2*(h + 1)**2
Let a(q) be the third derivative of -q**8/5376 - q**7/1260 - q**6/2880 + q**5/240 - q**4/8 + 4*q**2. Let f(v) be the second derivative of a(v). Factor f(y).
-(y + 1)**2*(5*y - 2)/4
Let l(g) be the third derivative of -g**6/900 + g**5/100 - g**4/30 + g**3/2 - g**2. Let p(o) be the first derivative of l(o). Factor p(w).
-2*(w - 2)*(w - 1)/5
Suppose -12 = 5*t - 8*t. Let i(w) be the first derivative of 0*w - w**2 + 0*w**3 + 1 + 1/2*w**t. Solve i(g) = 0.
-1, 0, 1
What is q in 22/7*q**2 - 24/7*q - 8/7*q**3 + 1/7*q**4 + 9/7 = 0?
1, 3
Let p(j) be the first derivative of j**8/1008 + j**7/315 + j**6/360 + 3*j**2/2 - 1. Let y(u) be the second derivative of p(u). Factor y(l).
l**3*(l + 1)**2/3
Let g = 6 - 9. Let a be (g/(-2))/(2/4). Factor 1 + 2*b**3 - a - b - b + 2*b**2.
2*(b - 1)*(b + 1)**2
Let k(g) be the second derivative of -3*g**5/20 + 3*g**4/4 + 9*g. Suppose k(u) = 0. What is u?
0, 3
Let z be -9 + -1 + (-265)/(-25). Factor -3/5*x + z*x**4 - 3/5*x**2 + 3/5*x**3 + 0.
3*x*(x - 1)*(x + 1)**2/5
Let y(w) be the second derivative of w**4/24 + w**3/36 - 2*w. Factor y(o).
o*(3*o + 1)/6
Suppose -25 - 5 = -5*v. Suppose -2 = -4*b + v. Factor 4*p**2 - 3*p**b - 2*p**2.
-p**2
Let c(k) = -k**3 - 3*k**2 + 3*k + 1. Let n(m) = -m**3 - 6*m**2 + 6*m + 1. Let z(t) = 5*c(t) - 2*n(t). Factor z(s).
-3*(s - 1)*(s + 1)**2
Suppose 5*b + 0*b - 10 = 0. Suppose -2*k + 3 + 4*k**3 - b*k**5 - 3 = 0. Calculate k.
-1, 0, 1
Let c be 3/(-40)*(-32)/72. Let q(p) be the second derivative of 0 - p + c*p**5 + 0*p**4 + 0*p**2 - 1/9*p**3. Factor q(r).
2*r*(r - 1)*(r + 1)/3
Suppose k - 2 = -4*r, 4*r - r + 8 = 4*k. Factor -i**5 + 0*i**4 - 2*i**5 + 5*i**5 - k*i**4.
2*i**4*(i - 1)
Suppose 14*q - 8*q = 12. Factor 3/4*g**q - 3/4 + 0*g.
3*(g - 1)*(g + 1)/4
Let t(m) be the first derivative of m**6/6 - m**5/5 - m**4/4 - m + 4. Let c(b) = -8*b**5 + 5*b**4 + 8*b**3 + b**2 + 6. Let k(v) = -c(v) - 6*t(v). Factor k(r).
r**2*(r - 1)*(r + 1)*(2*r + 1)
Let a(d) be the first derivative of 2/15*d**5 + 0*d**4 + 0*d + 1 + 2/3*d**2 - 2/3*d**3. Factor a(i).
2*i*(i - 1)**2*(i + 2)/3
Suppose -9 = 3*i - 3*p, p = -4*i - 4*p + 15. Suppose -9 = -b - i*b. Solve 2*h**3 + h**4 - b*h**4 + 0*h**3 = 0.
0, 1/4
Let x = -10 - -12. Factor 51*f**4 + 25*f**2 - 8*f**x + 63*f**3 + 16*f**2 + 15*f**5 + 6*f.
3*f*(f + 1)**3*(5*f + 2)
Let k = -10 - -10. Suppose f - 5 = -k. Determine t so that 3/2*t**3 + 0*t - 3*t**2 + 0 + 18*t**4 + 27/2*t**f = 0.
-1, -2/3, 0, 1/3
Factor -3*d - d**3 + 0*d**3 + 3*d**2 + 0 + 1.
-(d - 1)**3
Factor 5/6*n**3 + 1/6*n**5 + 0*n + 1/3*n**2 + 0 + 2/3*n**4.
n**2*(n + 1)**2*(n + 2)/6
Let f = 68 - 44. Let x be 5/15 - f/(-9). Determine m, given that -1/3*m**x - m + 1/3 + m**2 = 0.
1
Let a(v) = 4*v**4 - 5*v**2 + 5. Let f = -11 - -15. Let y(b) = -13*b**2 + 5*b**2 + 6*b**f + 8 + 0. Let t(x) = -8*a(x) + 5*y(x). Determine q so that t(q) = 0.
0
Let w(y) = y**3 - 7*y**2 + 3. Let d(a) = a**2 + 2*a - 1. Let p be d(-4). Let g be w(p). Let -1/3*j**5 + 2/3*j**4 + 0 + 1/3*j + 0*j**g - 2/3*j**2 = 0. What is j?
-1, 0, 1
Let y = 215 - 212. What is u in 1/2*u**2 + 9/2 + y*u = 0?
-3
Let y(f) be the second derivative of -f**4/9 + 2*f**2/3 + 7*f. Factor y(m).
-4*(m - 1)*(m + 1)/3
Let i(n) be the third derivative of 0*n**3 + 4/35*n**7 + 1/42*n**8 + 1/12*n**4 + 0 + 13/60*n**6 - 2*n**2 + 0*n + 1/5*n**5. Factor i(m).
2*m*(m + 1)**2*(2*m + 1)**2
Factor -4*p + 5*p**5 + 0*p**5 + 5*p**3 + 18*p**4 + 12*p**3.
p*(p + 1)**2*(p + 2)*(5*p - 2)
Suppose 11*g - 6 = 16. Suppose -y**5 + 0*y - 2*y**3 + 2*y**g + 0 - 7/2*y**4 = 0. What is y?
-2, 0, 1/2
Let w be -2 + 2 - 6/(-3). Let b(a) = -2*a + 2*a**3 + 0 + 2 - 4. Let m(y) = -y**2 + y + 1. Let l(f) = w*m(f) + b(f). What is u in l(u) = 0?
0, 1
Let p(i) be the third derivative of -i**8/1344 - i**7/840 + i**6/480 + i**5/240 - 7*i**2. Factor p(l).
-l**2*(l - 1)*(l + 1)**2/4
Let z(b) be the first derivative of -1/2*b**2 + 4/3*b**3 - 2*b + 4 + 3/4*b**4. Let z(d) = 0. What is d?
-1, 2/3
Let m(o) be the third derivative of o**9/22680 - o**7/1890 + o**5/180 + o**4/12 - 3*o**2. Let f(a) be the second derivative of m(a). Factor f(t).
2*(t - 1)**2*(t + 1)**2/3
Suppose -3*q = -12, -3*c + 9 = 5*q - 17. Determine a, given that 1/2 + 0*a - 1/2*a**c = 0.
-1, 1
Let j(q) = q - 20. Let m be j(-12). Let n be (-1 - m/36)*-3. Factor -1/3 + 1/3*d + n*d**2 - 1/3*d**3.
-(d - 1)**2*(d + 1)/3
Let t = -5 + 8. Suppose -21 = -3*n + 3*q, -t*n + 31 = n - 5*q. Factor -2/3 - 4/3*g + 0*g**2 + 2/3*g**n + 4/3*g**3.
2*(g - 1)*(g + 1)**3/3
Let o(k) be the first derivative of 9 + 12*k**2 - 4/3*k**3 - 3/2*k**4 - 16*k + 2/5*k**5. Factor o(p).
2*(p - 2)**2*(p - 1)*(p + 2)
Let n(q) be the second derivative of q**8/504 - 2*q**7/315 + q**5/45 - q**4/36 + q**2/2 - q. Let f(a) be the first derivative of n(a). Factor f(u).
2*u*(u - 1)**3*(u + 1)/3
Let q(s) = 0*s**4 - s + 5 + 7*s**4 - s**2 - s**4 + s**3. Let z(m) = m + 11. Let p be z(-6). Let o(r) = -r**4 - 1. Let i(g) = p*o(g) + q(g). Factor i(b).
b*(b - 1)*(b + 1)**2
Let -8*o**4 - 8*o**3 + 4*o**2 - 3*o**5 - 7*o + o**5 + 4 + 17*o = 0. What is o?
-2, -1, 1
Suppose -2*a + 8 = -3*g - 2, 3*a + 5*g + 4 = 0. Factor -2/7*p**4 + 0 + 0*p**3 + 2/7*p**a + 0*p.
-2*p**2*(p - 1)*(p + 1)/7
Determine o, given that 3*o**4 - 4*o**3 - 2*o**3 + 0*o**4 + 3*o**2 = 0.
0, 1
Let b(f) = -2*f**2 + 42*f + 28. Let w(u) = -u**2 + 28*u + 19. Let x(k) = 5*b(k) - 8*w(k). Factor x(y).
-2*(y + 1)*(y + 6)
Let j = -8 + 14. Let x(m) = m**3 - 6*m**2 + m + 1. Let o be x(j). Factor -o*c - 19/2*c**2 - 2*c**4 - 1/4*c**5 - 25/4*c**3 - 2.
-(c + 1)**2*(c + 2)**3/4
Suppose -2*g - 3*g + 2*d = -65, 4*g + 4*d = 24. Let s = g + -8. Factor -s*i**2 - 3*i**2 + 7*i**2.
i**2
Determine t so that -3*t**3 - 5*t**2 + 179 + 170 - 345 + 4*t = 0.
-2, -2/3, 1
What is g in 6*g + 12 + 4*g**2 - 4*g - 18*g + 0*g**2 = 0?
1, 3
Let s(m) be the first derivative of 4/5*m**2 - 2/5*m - 2/25*m**5 + 2/5*m**4 - 5 - 4/5*m**3. Factor s(h).
-2*(h - 1)**4/5
Let c(i) = -i**3 - 10*i**2 - 10*i - 7. Let z be c(-9). Suppose -12 + 2 = -z*y. Factor -3*f - 3*f**4 + 2 + 2*f**2 - 3 + 2 + 2*f**3 + f**y.
(f - 1)**4*(f + 1)
Let t(c) be the second derivative of 3*c**6/50 - 3*c**5/50 + c**4/40 + c**3/6 + 8*c. Let j(r) be the second derivative of t(r). F