b**5 - k*b - 26/15*b**3 - 12/5*b**2. Factor s(n).
-2*(n + 1)**2*(n + 2)**2/5
Let h = 0 - -4. Let v(x) be the second derivative of x + 2/9*x**3 - 1/18*x**h + 0 - 1/3*x**2. Suppose v(b) = 0. What is b?
1
Let z = -2/103 + 212/309. Determine v so that 2/9 - z*v + 2/3*v**2 - 2/9*v**3 = 0.
1
Suppose 0*l = 2*l - 4*o + 4, -l + o = 0. Let k(v) be the second derivative of v + 0*v**5 + 1/105*v**7 + 0*v**4 + 0*v**l + 1/75*v**6 + 0*v**3 + 0. Factor k(m).
2*m**4*(m + 1)/5
Let 2/7*l**2 - 2/7*l - 4/7 = 0. Calculate l.
-1, 2
Let l(n) be the third derivative of n**10/60480 - n**9/15120 + n**7/2520 - n**6/1440 + n**4/24 - 2*n**2. Let h(j) be the second derivative of l(j). Factor h(p).
p*(p - 1)**3*(p + 1)/2
Let 2*t**4 - 2/3*t**5 - 2*t**3 + 2/3*t**2 + 0*t + 0 = 0. What is t?
0, 1
Solve 15/2*d + 0 - 3/2*d**2 = 0 for d.
0, 5
Let i(w) be the first derivative of w**2 + 2/3*w**3 - 1/2*w**4 + 2 - w. Let f(z) be the first derivative of i(z). Factor f(h).
-2*(h - 1)*(3*h + 1)
Let s(b) be the second derivative of -2*b**6/15 + b**5 - 7*b**4/3 + 2*b**3 + 22*b. Find o such that s(o) = 0.
0, 1, 3
Let y(i) be the second derivative of -i**5/20 + i**3/6 - 4*i. Factor y(z).
-z*(z - 1)*(z + 1)
Let l(z) be the third derivative of -z**8/784 - z**7/490 + z**6/280 + z**5/140 - 16*z**2. Suppose l(r) = 0. Calculate r.
-1, 0, 1
Suppose -7*h + 96 = -h. Solve h*f + 12*f**3 + 0*f**4 - 19*f**2 + 0*f**3 + 2*f**4 + 43*f**2 = 0.
-2, 0
Let q(r) be the first derivative of -r**8/1680 + r**6/180 - r**4/24 - 2*r**3/3 - 1. Let a(z) be the third derivative of q(z). Suppose a(b) = 0. What is b?
-1, 1
Factor 0*c**2 - 6/7*c**3 - 9/7*c**4 - 3/7*c**5 + 0*c + 0.
-3*c**3*(c + 1)*(c + 2)/7
What is f in 0*f - 1/4*f**4 - 1/4*f**2 + 1/2*f**3 + 0 = 0?
0, 1
Let i(h) be the second derivative of -h**7/42 + 3*h**5/10 + 2*h**4/3 + h**3/2 - 5*h - 1. Determine a, given that i(a) = 0.
-1, 0, 3
Let y(m) be the first derivative of -3 + 0*m**2 + 0*m + 1/6*m**4 + 1/9*m**6 + 0*m**3 + 4/15*m**5. Factor y(v).
2*v**3*(v + 1)**2/3
Let t(r) = 2*r**4 - 6*r**2 + 4. Let l(m) = 4*m**3 + 0*m**4 + m**3 - 6*m**3 - m**4 - 1 + m**2. Let j(u) = 4*l(u) + t(u). What is z in j(z) = 0?
-1, 0
Let z = 6 + 2. Let w = z + -8. Suppose 2/3 + w*l - 2/3*l**2 = 0. What is l?
-1, 1
Let o be 4/6*45/48*8. Factor 2/9 - 2/9*h**o - 4/9*h**2 - 2/9*h + 2/9*h**4 + 4/9*h**3.
-2*(h - 1)**3*(h + 1)**2/9
Suppose 0*b + 4*b - 4*z = 0, -z + 2 = 0. Let j(i) be the first derivative of -4/3*i - 2/9*i**3 - i**2 + b. Find v such that j(v) = 0.
-2, -1
Suppose 21 = 2*d - 5*d. Let r be (8/d)/(18/(-28)). What is b in -8/9 + 10/9*b**3 - 2/9*b**2 - r*b - 2/9*b**5 + 2/9*b**4 = 0?
-1, 2
Find g, given that -2*g**3 - g - 8 + 2*g**2 + g**3 + 5*g = 0.
-2, 2
Let v(p) be the first derivative of -7*p**4/5 - 16*p**3/15 + 6*p**2/5 - 2. Factor v(g).
-4*g*(g + 1)*(7*g - 3)/5
Suppose 0 = -2*b + 6 - 2. Let o**2 + 6*o - b*o**2 - 3*o**2 + o**2 = 0. What is o?
0, 2
Solve -2/3 - 2/3*j - 1/6*j**2 = 0.
-2
Suppose -5*z - 21 + 4 = s, 4*s - 3*z = 24. Let f(v) be the first derivative of -1/9*v**3 - s - 1/6*v - 1/4*v**2. Factor f(l).
-(l + 1)*(2*l + 1)/6
Let i be (3 - -4 - 3)/2. Let n = 6 + -6. Suppose n + 0*w + 2/7*w**i = 0. Calculate w.
0
Factor -2/3*f**5 - 26/3*f**3 + 0 - 8/3*f + 4*f**4 + 8*f**2.
-2*f*(f - 2)**2*(f - 1)**2/3
Let t(d) be the first derivative of 9/2*d + 21/4*d**2 - 25/8*d**4 - 4 - 5/6*d**3. Determine r so that t(r) = 0.
-3/5, 1
Factor -9*r**2 - 3*r + 3*r + 2 + 7*r**2.
-2*(r - 1)*(r + 1)
Let j(p) = 16*p**4 + 36*p**3 + 34*p**2 + 7*p. Let z(t) = -11*t**4 - 24*t**3 - 23*t**2 - 5*t. Let x(k) = 5*j(k) + 7*z(k). Factor x(q).
3*q**2*(q + 1)*(q + 3)
Let p = 7 - 3. Let o = 8 - p. Find c, given that -2/3*c - 8/3*c**2 - 4/3*c**o - 10/3*c**3 + 0 = 0.
-1, -1/2, 0
Determine r, given that -6 + 3*r**3 + 0*r + 8*r - 6*r**2 - 6*r**2 + 7*r = 0.
1, 2
Let o = -28148 + 141322/5. Let n = o - 116. Factor n*b**2 + 0*b + 0 - 2/5*b**5 + 2/5*b**3 - 2/5*b**4.
-2*b**2*(b - 1)*(b + 1)**2/5
Let c(i) be the second derivative of -i**6/6 + i**5/4 + 5*i**4/12 - 5*i**3/6 - 7*i. Solve c(j) = 0 for j.
-1, 0, 1
Solve -7/5*f - 2/5 - f**3 - 9/5*f**2 - 1/5*f**4 = 0 for f.
-2, -1
Let x(p) be the second derivative of -3*p**5/70 - p**4/28 - 7*p. Factor x(f).
-3*f**2*(2*f + 1)/7
Let h(a) = -a + 2. Let t be h(-8). Suppose l - 3 = t. Factor 2*w**3 + 2*w**2 + l - 13.
2*w**2*(w + 1)
Let p be (-15)/25 - (-23)/5. Let q = p - 2. Find h such that 2*h**3 + 3*h**2 + 1/2*h**4 + 1/2 + q*h = 0.
-1
Solve -o**3 + 0 - 1/3*o + 1/3*o**4 + o**2 = 0 for o.
0, 1
Let i(q) be the second derivative of -1/2*q**2 - 2/3*q**3 - 1/2*q**4 + 3*q - 1/30*q**6 + 0 - 1/5*q**5. Solve i(f) = 0.
-1
Factor 4/13 + 6/13*c + 2/13*c**2.
2*(c + 1)*(c + 2)/13
Suppose -3/7*k - 15/7*k**2 - 9/7*k**3 + 3/7 = 0. What is k?
-1, 1/3
Suppose -5 = -3*t + 37. Let w be ((-3)/t)/(3/(-144)). Factor -2/7 - 54/7*j**4 - w*j**2 + 20/7*j + 108/7*j**3.
-2*(j - 1)*(3*j - 1)**3/7
Determine d so that -14*d + 2*d + 14*d**3 - 9*d**2 + 12 + 9*d**4 - 2*d**3 - 12*d**4 = 0.
-1, 1, 2
Let d(g) be the first derivative of -4*g**3/9 + 8*g**2/3 + 16*g - 11. Factor d(n).
-4*(n - 6)*(n + 2)/3
Let v(y) = -y**3 - 7*y**2 - y - 4. Let g be v(-7). Factor 2*z**3 + 2*z**2 - 2*z**g + 4*z**4 - 3*z**3 - 3*z**4.
z**2*(z - 2)*(z - 1)
Let s(j) be the second derivative of 1/24*j**4 - 1/80*j**5 - 1/24*j**3 + 5*j + 0*j**2 + 0. Suppose s(q) = 0. What is q?
0, 1
Suppose 5*c - 2*t + 5 = 3*t, -3*t + 3 = -2*c. Suppose f - 5*f + 5*l + 8 = c, -2*l - 4 = -2*f. Factor -f*d**2 - 10 + 10 + 2*d**4.
2*d**2*(d - 1)*(d + 1)
Suppose 4*n = n + 2*x - 21, 0 = -5*n - 4*x - 13. Let z be ((-72)/(-90))/((-14)/n). Factor 0 - 2/7*m**3 + z*m**4 + 0*m**2 + 0*m.
2*m**3*(m - 1)/7
Let g(a) = a**5 - a**2 + a - 1. Let d(t) = -2*t**5 - 14*t**4 + 76*t**3 - 197*t**2 + 253*t - 125. Let q(k) = -d(k) - 3*g(k). Factor q(o).
-(o - 4)**2*(o - 2)**3
Let i(k) be the second derivative of 2/39*k**3 + 1/78*k**4 - 1/130*k**5 + 0*k**2 + 0 + 3*k. Suppose i(n) = 0. What is n?
-1, 0, 2
Let m(p) be the second derivative of 1/12*p**4 + 0*p**2 - 3*p + 0*p**3 + 0. Suppose m(y) = 0. What is y?
0
Suppose 0 = -i + 2*i - 1. Let l(d) = -d**4 + 3*d**3 - d**2 + 1. Let s(j) = j**2 + 1. Let a(p) = i*s(p) - l(p). Factor a(w).
w**2*(w - 2)*(w - 1)
Factor -5*c**3 + 6*c + 1 - 1 - 3*c**2 + 2*c**3.
-3*c*(c - 1)*(c + 2)
Find k, given that 1/3*k**3 - 2*k + 0 + 1/3*k**2 = 0.
-3, 0, 2
Find a, given that 0*a**3 + 1/8*a**4 + 0*a + 0 - 1/2*a**2 = 0.
-2, 0, 2
Let f(v) = v**2 - 13*v - 48. Let a be f(-3). Find z, given that a*z + 2/15*z**2 + 2/15*z**3 + 0 = 0.
-1, 0
Let v be (3 - 2)*12*(-9)/(-48). Let -9/4*y**4 + v*y**2 - 3/4*y + 0 - 3/4*y**3 + 3/2*y**5 = 0. What is y?
-1, 0, 1/2, 1
Let s(z) be the second derivative of z**4/30 + 2*z**3/15 - 3*z**2/5 + 6*z. Factor s(k).
2*(k - 1)*(k + 3)/5
Let l be 0/(-3) - 4/(-2). Suppose -6*w = -5*i - 4*w + 25, l*i + 2*w = -4. Determine v, given that -v**3 + 2*v**4 + 0*v**3 + 3*v**i = 0.
-1, 0
What is x in 12 + 2*x**3 - 5*x**4 + x**4 - 33*x**2 - 2*x**4 + 25*x**3 = 0?
-1/2, 1, 2
Let q = 40 - 36. Let c(n) be the third derivative of 2/3*n**3 + 0*n + 0 + 1/60*n**5 + 2*n**2 - 1/6*n**q. Factor c(f).
(f - 2)**2
Factor -2/11*l**3 + 0 - 24/11*l**2 - 2*l.
-2*l*(l + 1)*(l + 11)/11
Let v(n) be the third derivative of -1/120*n**6 - 1/420*n**7 + 0 - 1/120*n**5 + n**2 + 0*n**4 + 0*n + 0*n**3. Factor v(d).
-d**2*(d + 1)**2/2
Let a be (7 + -2)*(-4)/(-5). Let y(b) = b**2 + 11*b + 2. Let g be y(-11). Let 3 - a*d - 3 + 2*d - 2*d**g = 0. Calculate d.
-1, 0
Factor -2/7*o**4 - 6/7*o**2 - 6/7*o**3 - 2/7*o + 0.
-2*o*(o + 1)**3/7
Let m(o) be the first derivative of 2*o**3/9 + 2*o**2/3 + 2*o/3 - 8. Let m(d) = 0. What is d?
-1
Let x be (4/6)/(2/12). Suppose 10 = -q - 0*r + 3*r, -14 = q - x*r. Factor -3*y**2 - 2*y - 3*y**2 - q*y**3 + 2*y**2.
-2*y*(y + 1)**2
Suppose v + 1 + 2 = 0. Let z be (1 - -1)/((-7)/v). Find f, given that -2/7*f**2 - z*f - 4/7 = 0.
-2, -1
Let s(r) be the second derivative of r**7/63 + 4*r**6/45 + r**5/10 - 2*r**4/9 - 4*r**3/9 + 5*r - 5. Suppose s(i) = 0. What is i?
-2, -1, 0, 1
Let l(j) be the second derivative of 0*j**2 - 1/30*j**5 + 0*j**3 + 0 + 0*j**4 - 3*j + 7/90*j**6. Factor l(w).
w**3*(7*w - 2)/3
Let t be 4 - -5 - (5 - 3). Let l(a) = a**2 - 7*a + 5. Let w be l(t). Solve 10/3*d**3 - 2*d**4 - 2/3*d + 2*d**2 + 0 - 8/3*d**w = 0 for d.
-1, 0, 1/4, 1
Let l(k) be the first deri