- 2/15*c**3 + 0*c + c**2. Solve h(v) = 0 for v.
1, 2
Let q(j) = j**3 - 6*j**2 - 7*j + 42. Let x be q(6). Factor 9*b**3 + x - 6*b**4 + 3/2*b**5 - 6*b**2 + 3/2*b.
3*b*(b - 1)**4/2
Let u(g) be the third derivative of -4/75*g**5 + 0*g + 1/60*g**6 + 0 + 1/60*g**4 + 2/15*g**3 - 3*g**2. Determine k, given that u(k) = 0.
-2/5, 1
Let j(k) be the first derivative of k**4/4 + 7*k**3/3 + 3*k**2 + 2*k - 6. Let s be j(-6). Solve 0 + 1/2*x**4 + 0*x + 0*x**s - 1/2*x**3 = 0.
0, 1
Suppose 2/9*b**5 + 0*b**3 + 0 - 4/9*b**2 + 4/9*b**4 - 2/9*b = 0. What is b?
-1, 0, 1
Let a(d) be the third derivative of -3*d**2 + 0*d**3 + 0*d + 3/112*d**8 - 13/240*d**6 + 2/15*d**5 - 1/28*d**7 + 0 - 1/12*d**4. Find o, given that a(o) = 0.
-1, 0, 1/2, 2/3
Let z(b) be the second derivative of b**6/135 + b**5/30 + b**4/18 + b**3/27 + 5*b. Suppose z(q) = 0. What is q?
-1, 0
Let k(b) be the third derivative of -32/9*b**3 + 4*b**2 + 22/45*b**6 + 0*b - 2/45*b**7 - 32/15*b**5 + 0 + 40/9*b**4. Suppose k(q) = 0. Calculate q.
2/7, 2
Suppose -13*y = -9*y. Let l(s) be the third derivative of -s**2 + 0 - 1/27*s**3 - 1/270*s**5 + y*s - 1/54*s**4. Factor l(w).
-2*(w + 1)**2/9
Factor -12*t**5 + 7*t**5 + 10*t**2 - 10*t**4 - 4*t + 9*t.
-5*t*(t - 1)*(t + 1)**3
Determine k, given that -30/7*k**3 - 16/7 + 120/7*k - 244/7*k**2 + 50*k**4 = 0.
-1, 2/7, 2/5
Let f(s) be the first derivative of -s**5/110 + s**4/66 + s + 2. Let q(g) be the first derivative of f(g). Suppose q(d) = 0. Calculate d.
0, 1
Let w = -4 + 6. Find j such that 2*j**w - 11*j**3 - 15*j**4 - 4*j**2 - 3*j**5 - j**4 - 4*j**5 = 0.
-1, -2/7, 0
Let p(w) = 2*w**2 - w + 5. Let k(q) = -q + 1. Let r(v) = -v**3 - 4*v**2 + 4*v. Let c be r(-5). Let o(y) = c*k(y) - p(y). Find g, given that o(g) = 0.
-2, 0
Let n be (15 + -19 - (-54)/15) + 1. Factor 0 - 12/5*u**2 - n*u**4 + 0*u + 12/5*u**3.
-3*u**2*(u - 2)**2/5
Let l(m) = -3*m + m**2 + 2 - 3*m + 3*m**2 + 0*m. Let o(p) = -p**2 - 1. Let d(t) = l(t) + 6*o(t). Factor d(a).
-2*(a + 1)*(a + 2)
Suppose -5 = -5*j, k + 4*j + j - 167 = 0. Let w be k/14*7/2. Factor w*a**2 + 2 - 18*a.
(9*a - 2)**2/2
Suppose -13 = 2*n - 21. Let c be (126/n)/9 - 2. Factor c*b**2 - 3/2*b**4 + 3/2*b**3 - 3/2*b**5 + 0 + 0*b.
-3*b**2*(b - 1)*(b + 1)**2/2
Let l(o) be the first derivative of -4*o**6/15 - 16*o**5/25 + 11*o**4/10 - 2*o**3/5 + 23. Factor l(b).
-2*b**2*(b + 3)*(2*b - 1)**2/5
Let n(t) be the first derivative of 2*t**5/5 - 2*t**4 + 10*t**3/3 - 2*t**2 - 2. Suppose n(x) = 0. What is x?
0, 1, 2
Suppose 6*a - 7 = 5. Let n(s) be the second derivative of 9/40*s**5 + s + 0 - 1/4*s**a - 5/12*s**3 - 1/8*s**4. Factor n(c).
(c - 1)*(3*c + 1)**2/2
Let m(i) be the first derivative of -1/16*i**4 + 1/24*i**3 + 1/4*i**2 + 2 - i. Let l(b) be the first derivative of m(b). Factor l(y).
-(y - 1)*(3*y + 2)/4
Let h(y) be the first derivative of -2*y**3/3 - 5*y**2/2 + 7*y - 3. Let g(l) = -l**2 - 3*l + 4. Let t(o) = 5*g(o) - 3*h(o). Solve t(c) = 0 for c.
-1, 1
Let g(c) be the first derivative of c**6/40 + 3*c**5/40 + c**4/16 + 7*c - 6. Let z(y) be the first derivative of g(y). Factor z(u).
3*u**2*(u + 1)**2/4
Let w(v) = v**3 - 8*v**2 - 2*v - 2. Let h be w(9). Solve h*n - n**3 - 63*n + 3*n**3 = 0 for n.
-1, 0, 1
Suppose -2*j = -3*b - 21, 5*b + 15 = -2*j - 4. Determine o, given that 29*o**j - 26*o**3 - 3*o**5 + 0*o**5 = 0.
-1, 0, 1
Determine l so that -54/5*l + 18/5*l**2 + 54/5 - 2/5*l**3 = 0.
3
Let q(m) be the first derivative of -m**6/90 + m**5/15 - m**4/6 - 2*m**3/3 - 2. Let v(c) be the third derivative of q(c). What is o in v(o) = 0?
1
Let i(p) = p**2 + 3*p. Suppose 1 = -2*n + 3. Let h(z) = z. Let v(g) = n*i(g) - 2*h(g). Factor v(r).
r*(r + 1)
Let w(i) be the first derivative of 2*i**6/33 - 2*i**5/11 + i**4/11 + 8*i**3/33 - 4*i**2/11 + 2*i/11 + 22. Find f, given that w(f) = 0.
-1, 1/2, 1
Let k(f) be the third derivative of 0*f + 1/6*f**3 - 1/48*f**4 - 1/120*f**5 + 2*f**2 + 0. What is u in k(u) = 0?
-2, 1
Let q be 6/(-210)*1/(-10 + 1). Let j(p) be the third derivative of 5*p**2 - 1/9*p**3 + 0 - 1/45*p**6 - q*p**7 + 0*p - 1/9*p**4 - 1/15*p**5. Factor j(a).
-2*(a + 1)**4/3
Factor -8/5*r + 0 - 2/5*r**3 + 1/5*r**5 - 12/5*r**2 + 3/5*r**4.
r*(r - 2)*(r + 1)*(r + 2)**2/5
Let y be (-3)/(-4) - (-153)/36. Suppose -r = 4*a + a + 3, 3*r = -y*a + 1. Factor 2*s**r - 2*s + 2*s - 2.
2*(s - 1)*(s + 1)
Suppose -4*y - 20 = 0, -7*f + 4*y = -2*f - 50. Factor -6*n + 0*n**3 + 12*n**3 + 8*n**2 + f*n + 8*n**4 + 2*n**5 + 2*n.
2*n*(n + 1)**4
Let t = -205/3 - -69. Let b(q) be the first derivative of -2*q**2 + t*q**3 + 2*q - 3. Factor b(c).
2*(c - 1)**2
Suppose -10/9*b**5 + 4/9*b**3 + 0*b + 0*b**2 - 2/3*b**4 + 0 = 0. What is b?
-1, 0, 2/5
Suppose 5*p = 26*p. Factor -1/3*a + 1/3*a**2 + p.
a*(a - 1)/3
Let b(t) = t**2 - 4*t. Let y be b(2). Let f be 1/y - 51/(-12). Factor -2*m**2 - 3*m**5 + 2*m**3 + f*m**5 + 2*m**4 - 3*m**5.
-2*m**2*(m - 1)**2*(m + 1)
Let u be (-1 - -6) + 9 + -12. Let g(o) be the third derivative of 0*o + 0*o**3 + 0 + o**u + 0*o**4 + 1/120*o**6 + 0*o**5. What is c in g(c) = 0?
0
Suppose 0*h + 3*a = 5*h, -5*a + 19 = -2*h. Factor 4*p + 0 - 8 + 4*p**h - 4*p - 4*p + 8*p**2.
4*(p - 1)*(p + 1)*(p + 2)
Suppose 0 = -2*p - 22 - 30. Let q be (p/325)/((-1)/5). Factor -q*u**2 - 2/5*u + 0.
-2*u*(u + 1)/5
Let g(x) be the third derivative of x**7/5040 - x**6/1440 - x**4/6 + x**2. Let y(n) be the second derivative of g(n). Factor y(a).
a*(a - 1)/2
Let k(z) = z**2 + 12*z - 9. Let g(l) = 0*l - 24*l + 13 + 5 - 3*l**2. Let r(x) = -4*g(x) - 9*k(x). Let r(s) = 0. Calculate s.
1, 3
Suppose 5*x = -2*i + 35, -3*i + 30 = 2*x + i. Let a(m) be the second derivative of 1/3*m**3 - 1/10*m**x + 0 - m**2 - m + 1/6*m**4. Factor a(g).
-2*(g - 1)**2*(g + 1)
Let f(t) be the first derivative of -t**2/2 - 2*t - 2. Let z be f(-5). Suppose 6*q + 1 + 5*q**3 + 3 + 6*q**2 - z*q**3 - 2 = 0. What is q?
-1
Let n(g) = g**3 - g + 3. Let u be n(0). What is w in 3*w**3 - w**3 - w**u = 0?
0
Let k(c) be the first derivative of c**4/2 + 2*c**3 - 5*c**2/2 - 9*c + 7. Let t(f) = -f**3 - 3*f**2 + 3*f + 5. Let w(j) = 6*k(j) + 11*t(j). Factor w(x).
(x + 1)**3
Let q(f) = f + 1. Suppose 4*b - 13 = -5. Let a(p) = 3*p**2 - 2*p - 2. Let t(s) = b*a(s) - 4*q(s). Find g such that t(g) = 0.
-2/3, 2
Factor -3/2*f + 0 + 3/2*f**2.
3*f*(f - 1)/2
What is h in 740/9*h**2 + 124/9*h**3 + 416/9*h + 64/9 + 4*h**5 - 76/3*h**4 = 0?
-1, -1/3, 4
Suppose -4*a + 23 = v, 4*v = 6*a - 3*a - 3. Factor 2 - 2*o - 2*o**2 - 2*o**v - o**5 - 3 + 3*o**4 + 5*o + 0*o**3.
-(o - 1)**4*(o + 1)
Let r(j) be the first derivative of j**6/480 + j**5/48 + j**4/32 - 3*j**3/8 + j**2/2 + 8. Let d(q) be the second derivative of r(q). Let d(s) = 0. Calculate s.
-3, 1
Factor 1/3*h - 1/6*h**2 + 0.
-h*(h - 2)/6
Let 32*t + 4*t**3 - 36 + 16*t**2 + 28*t - 44*t**2 = 0. What is t?
1, 3
Factor 4 + 6 - w**3 + 4*w - 10.
-w*(w - 2)*(w + 2)
Suppose 0*l + 0 - 2/3*l**3 + 0*l**2 = 0. What is l?
0
Let t(o) be the second derivative of -o**2 - 2*o - 1/15*o**5 + 0*o**4 + 0*o**3 - 3/20*o**6 + 0. Let v(y) be the first derivative of t(y). Factor v(w).
-2*w**2*(9*w + 2)
Let y(g) be the first derivative of g**4 - 4*g**3/3 - 4*g**2 - 5. Find o such that y(o) = 0.
-1, 0, 2
Let k = 2 - 0. Suppose -x - 15 = -6*x, -15 = -r - 4*x. Factor -z + z**r + 0*z**4 - k*z**4 + z**4 + z**2.
-z*(z - 1)**2*(z + 1)
Let i be 2*(-3 - -1)*(-4)/80. Factor i*d**2 - 1/5 - 1/5*d**3 + 1/5*d.
-(d - 1)**2*(d + 1)/5
Suppose -k - 11 = -14. Let l(o) be the first derivative of 2*o**5 + 0*o - 2 - 9/2*o**4 + 14/3*o**k - 2*o**2 - 1/3*o**6. Factor l(y).
-2*y*(y - 2)*(y - 1)**3
Let u(j) be the third derivative of -1/15*j**3 - 1/30*j**4 + 0*j + 0 - 1/150*j**5 + 5*j**2. Solve u(t) = 0 for t.
-1
Suppose 42 = -4*f + 18*f. Factor -18*d**3 + f*d - 9/2*d**2 - 21/2*d**4 + 0.
-3*d*(d + 1)**2*(7*d - 2)/2
Let j = 17 + -13. Suppose -2*y**4 + 2*y**3 + 0*y**4 + 3*y**2 - 3*y + y**3 - y**j = 0. Calculate y.
-1, 0, 1
Let r = -45/7 - -149/21. Find k such that -1/3 + 0*k - 1/3*k**4 + 0*k**3 + r*k**2 = 0.
-1, 1
Suppose y + 2*j - 1 = 4, 0 = -4*y - 3*j + 20. Factor 6*r**3 - 11*r + 3 + 3*r**4 - 6*r**2 + 0*r**5 - 3*r**y + 8*r.
-3*(r - 1)**3*(r + 1)**2
Let j be (-9)/6 - (-75)/18. Factor -8/3*m**3 - j*m + 4*m**2 + 2/3 + 2/3*m**4.
2*(m - 1)**4/3
Let v(d) be the third derivative of d**6/18 - 7*d**5/30 + d**4/3 + 5*d**3/6 + d**2. Let w(m) be the first derivative of 