t z(v) = v**4 + v**3 - v**2 - v + 2. Let r(l) = b*t(l) - 3*z(l). Factor r(w).
-w*(w - 1)**2*(w + 1)
Let n be (-16)/12 - (-450)/336. Let k(s) be the third derivative of 0*s**3 + 0*s + 0 + 2/105*s**7 + 0*s**4 - 2*s**2 - 1/60*s**6 - n*s**8 + 0*s**5. Factor k(v).
-2*v**3*(v - 1)**2
Let c(q) be the first derivative of 2*q**5/5 + 4*q**4 + 12*q**3 - 54*q - 30. Factor c(s).
2*(s - 1)*(s + 3)**3
Suppose 5*h - 12 = 2*h. Let f = -2 + h. Find o, given that -4/3 + 4/3*o**f + 2/3*o**3 - 2/3*o = 0.
-2, -1, 1
Let h = 973/36 + -70/9. Suppose -49/4*y**3 - 1 - 8*y - h*y**2 = 0. What is y?
-1, -2/7
Let l(q) be the second derivative of -q**4/21 + 8*q**2/7 - 16*q. Determine t, given that l(t) = 0.
-2, 2
Factor -k**2 + 56*k + 39 - 139 - 96 - 3*k**2.
-4*(k - 7)**2
Let y(t) = t**5 + 2*t**4 - t**3 - 2*t**2 + 5. Let h(z) = -z**5 - 2*z**4 + z**3 + 2*z**2 - 4. Let f(i) = -5*h(i) - 4*y(i). Factor f(m).
m**2*(m - 1)*(m + 1)*(m + 2)
Find v, given that 2*v**3 + 97*v**2 - 2*v - 95*v**2 - 3*v**4 + v**4 = 0.
-1, 0, 1
Let a(c) be the second derivative of c**4/18 + 4*c**3/9 + 4*c**2/3 + c. Factor a(w).
2*(w + 2)**2/3
Suppose 4*z = -5*b + 15, -5*b + 3*z + 10 + 5 = 0. Suppose t + d - b + 1 = 0, -4*t + 2*d + 8 = 0. Find w such that 3*w**t - 4*w**2 + w + 2*w**2 = 0.
-1, 0
Let g(d) be the third derivative of 3*d**2 + 1/210*d**7 + 0*d**3 + 0 + 0*d**4 + 1/60*d**6 + 0*d**5 + 0*d. Find a, given that g(a) = 0.
-2, 0
Suppose 5*k**2 + 20*k + 10 + 35*k - 40*k = 0. Calculate k.
-2, -1
Factor 2/9*t**3 + 2/9*t + 4/9*t**2 + 0.
2*t*(t + 1)**2/9
Let r(g) be the second derivative of g**9/1008 - g**7/280 - 2*g**3/3 - 5*g. Let f(s) be the second derivative of r(s). Factor f(u).
3*u**3*(u - 1)*(u + 1)
Let 1/2*u**2 + 0 - 5*u = 0. Calculate u.
0, 10
Suppose 0 = -12*s + 7*s. Let r(f) be the first derivative of 1/10*f**2 - 1/15*f**3 + 2 + s*f. Suppose r(v) = 0. Calculate v.
0, 1
Let i(t) = 28*t. Let y be i(-5). Let r be 4/18 + y/(-18). Find b, given that -b**3 - 8*b + r*b = 0.
0
Let b(m) be the second derivative of 0*m**2 + 1/24*m**3 + 0 - 3*m - 1/48*m**4. Solve b(j) = 0 for j.
0, 1
Let n(k) be the third derivative of k**5/70 - 5*k**4/84 + 2*k**3/21 + 6*k**2. Factor n(i).
2*(i - 1)*(3*i - 2)/7
Let z(k) be the third derivative of k**5/480 - 5*k**4/96 + 25*k**3/48 - 12*k**2. Find o such that z(o) = 0.
5
Let b(p) = 2*p**2 - 42*p + 12. Let a be 2*1*-1*-8. Let i(c) = c**2 - 14*c + 4. Suppose -5*k + 20 = -4*v, -k = -2*k. Let g(z) = a*i(z) + v*b(z). Solve g(o) = 0.
1/3, 2
Let z be (1/2)/((-10)/(-60)). Suppose 3/7*c**2 + 6/7*c - 6/7*c**z + 0 - 3/7*c**4 = 0. Calculate c.
-2, -1, 0, 1
Let t be 1 - -3 - (8 + -11). Solve -x**2 + t*x**3 + 3*x**4 - 1 - 4*x**3 - 3*x - x**4 = 0 for x.
-1, -1/2, 1
Let r(w) be the second derivative of w**6/70 - 3*w**5/140 - w**4/28 + w**3/14 + w. Determine u so that r(u) = 0.
-1, 0, 1
Let y(n) = -3*n + 7*n**3 - 1 + 0 - 4 - 6*n**2 - 3*n**2. Let c(h) = 11*h**3 - 14*h**2 - 5*h - 8. Let i(q) = 5*c(q) - 8*y(q). What is x in i(x) = 0?
0, 1
Let x(o) be the third derivative of -5*o**8/1344 + o**7/280 + 17*o**6/480 - 19*o**5/240 + o**3/6 - 15*o**2. What is p in x(p) = 0?
-2, -2/5, 1
Let b = -24 - -24. Factor 2/9*i**2 + 4/9*i + b.
2*i*(i + 2)/9
Let j(f) be the third derivative of -2*f**7/105 - f**6/30 + f**5/5 + f**4/6 - 4*f**3/3 - 10*f**2. Let j(k) = 0. Calculate k.
-2, -1, 1
Let h be (3/(66/(-16)))/(-2). Factor 0 + 2/11*l**4 + 0*l + 0*l**2 - h*l**3.
2*l**3*(l - 2)/11
Let m(a) be the second derivative of 0 - 2*a + 3/20*a**5 + 0*a**3 - 1/12*a**4 - 1/10*a**6 + 1/42*a**7 + 0*a**2. Factor m(j).
j**2*(j - 1)**3
Suppose c + 4 = 4*n + 5*c, 1 = c. Let y(d) = d**2 - 2*d - 5. Let z be y(4). Factor -4/3*u**4 + 4/3*u**2 - 2/3*u + 2/3*u**5 + n*u**z + 0.
2*u*(u - 1)**3*(u + 1)/3
Let u(c) be the first derivative of -5*c**4 + 5*c**3/3 - 11. Factor u(j).
-5*j**2*(4*j - 1)
What is k in 1/6*k**2 + 25/6 - 5/3*k = 0?
5
Factor 3*c**2 + 4/3*c**4 - 2/3*c + 0 - 4*c**3.
c*(c - 2)*(2*c - 1)**2/3
Let d(y) = -2*y**2 - y - 7. Let q(x) = x + 1. Let h be 0 - -17 - (-3 + 3). Suppose 0 = 2*w + 7 - h. Let i(v) = w*q(v) + d(v). Determine a, given that i(a) = 0.
1
Let t(z) be the second derivative of -z**6/180 - z**5/60 + z**4/72 + z**3/18 + 4*z. Factor t(j).
-j*(j - 1)*(j + 1)*(j + 2)/6
Let y(w) be the first derivative of -w**4/48 - w**3/9 - 5*w**2/24 - w/6 - 36. Factor y(a).
-(a + 1)**2*(a + 2)/12
Let u(k) = -k**3 - 7*k**2 - 8*k - 9. Let o be u(-6). Factor 3/2*f**2 + 0*f + 0 + 3*f**o.
3*f**2*(2*f + 1)/2
Let s be 2*(-1)/(-4)*6. Factor -18*n**4 + 30*n**3 - 8*n**2 + n + n - 3*n**2 - s*n**2.
-2*n*(n - 1)*(3*n - 1)**2
Let a(v) = v**3 - 10*v**2 + 12*v - 3. Let w be a(9). Factor 0*b**3 - w*b**2 + 0*b**3 + 6*b + 6*b - 15*b**3.
-3*b*(b + 2)*(5*b - 2)
Let t(b) be the first derivative of -b**3/6 - 5*b**2/2 - 25*b/2 + 2. Factor t(l).
-(l + 5)**2/2
Let a(m) be the third derivative of 0*m + 0 - 1/30*m**5 - 1/24*m**4 + 1/120*m**6 - 2*m**2 + 1/3*m**3. What is u in a(u) = 0?
-1, 1, 2
Suppose 0 = -2*q + 2*x - 6, 4*q + 4*x - 3 = 9. Let -2/3*l**2 - 2/9*l - 2/9*l**4 - 2/3*l**3 + q = 0. What is l?
-1, 0
Let d be 0 + -2 - (3 - (-16)/(-3)). Let h(g) be the third derivative of 1/30*g**5 + 2*g**2 - d*g**3 + 0*g + 0 + 1/60*g**6 - 1/12*g**4. Factor h(p).
2*(p - 1)*(p + 1)**2
Let k(m) be the third derivative of m**6/540 + m**5/54 - 13*m**2. Factor k(j).
2*j**2*(j + 5)/9
Let k = -351 - -2461/7. Solve -2/7*s - 2/7*s**2 + k = 0.
-2, 1
Let f(u) = -4*u**3 - 4*u**2 + 8*u. Let b(x) = -12*x**3 - 12*x**2 + 24*x. Let h(j) = 5*b(j) - 14*f(j). Determine q, given that h(q) = 0.
-2, 0, 1
Let z(c) be the second derivative of 0*c**4 + 2/3*c**2 + 0 + 1/30*c**5 - 1/3*c**3 + 4*c. Factor z(m).
2*(m - 1)**2*(m + 2)/3
Let l(k) = k**3 - 2*k**2 + 2. Let p be l(2). Let m = -1256/3 - -419. Let 0 + 0*r - m*r**p = 0. Calculate r.
0
Let h(r) = -4*r + 0*r**2 + 0*r**3 - 1 - 5*r**2 - r**3 + r**2. Let o be h(-3). Solve 1/4*k**o + 1/4*k**3 - 1/4*k - 1/4 = 0 for k.
-1, 1
Let u(v) be the second derivative of -2*v**7/147 + 26*v**6/105 - 66*v**5/35 + 54*v**4/7 - 18*v**3 + 162*v**2/7 + 4*v. Factor u(l).
-4*(l - 3)**4*(l - 1)/7
Factor 3/4*b + b**2 + 1/4*b**3 + 0.
b*(b + 1)*(b + 3)/4
Suppose 2*p = -4*z - 6, -4*p - 16 = -2*z + 6*z. Let q be 1*1/z*0. Factor 1/2*m + 3/2*m**3 + q - 1/2*m**4 - 3/2*m**2.
-m*(m - 1)**3/2
Let -10/7*y**2 + 0*y + 2/7*y**3 + 0 = 0. Calculate y.
0, 5
Let y = 50 + -47. Let q(n) be the second derivative of 1/3*n**y - 1/15*n**5 - 1/9*n**4 + 0 - 1/63*n**7 - 1/3*n**2 - n + 1/15*n**6. Factor q(w).
-2*(w - 1)**4*(w + 1)/3
Let g(p) be the first derivative of -9*p**4 - 64*p**3/3 - 10*p**2 + 8*p + 25. Factor g(f).
-4*(f + 1)**2*(9*f - 2)
Factor 0*x - 1/3*x**2 + 0 + 0*x**3 + 1/3*x**4.
x**2*(x - 1)*(x + 1)/3
Suppose -51/4*r - 3/4*r**2 - 12 = 0. Calculate r.
-16, -1
Factor 5*q**2 + 40 + q - 6*q - 25*q.
5*(q - 4)*(q - 2)
Let h(r) be the first derivative of -3*r**4 + 3*r**3 + 9*r**2/4 - 3*r/2 - 1. Solve h(x) = 0 for x.
-1/2, 1/4, 1
Let m(s) be the first derivative of -8*s - 2/3*s**3 - 3 + 4*s**2. Suppose m(i) = 0. Calculate i.
2
Let k(v) be the second derivative of v**5/20 - v**4/6 + 5*v**3/6 - v**2/2 + 2*v. Let z(p) = -p**3 + p**2 - p. Let r(q) = k(q) + 3*z(q). Factor r(h).
-(h - 1)*(h + 1)*(2*h - 1)
Suppose -6 = -v - 0. Let b(n) be the second derivative of n - 1/25*n**5 + 0 + 1/10*n**4 - 2/15*n**3 + 1/10*n**2 + 1/150*n**v. Factor b(p).
(p - 1)**4/5
Let i(j) = j**2 - 11*j + 4. Let c be i(10). Let y(r) = 2*r + 12. Let n be y(c). Determine u, given that 1/3*u**2 - 1/3*u**3 + n*u + 0 = 0.
0, 1
Let v = 1/29 - -49/261. Solve 10/9*c**2 + v*c**4 + 0 + 8/9*c**3 + 4/9*c = 0.
-2, -1, 0
Let f be (-13)/(-42) + 40/48. Let b(h) be the first derivative of f*h + 12/7*h**2 + 4 + 10/21*h**3. Determine q, given that b(q) = 0.
-2, -2/5
Let k(h) be the second derivative of -1/105*h**7 + 0*h**3 - 1/15*h**4 + 3/50*h**5 + 0*h**6 + 0 - 7*h + 0*h**2. Factor k(l).
-2*l**2*(l - 1)**2*(l + 2)/5
Factor -6/7*y**3 + 8/7*y - 8/7*y**2 + 0 + 4/7*y**4 + 2/7*y**5.
2*y*(y - 1)**2*(y + 2)**2/7
Let v(m) = -m**3 + 5*m**2 + 2. Let w be v(5). Let z(x) = x + 3 - 1 - 6*x**2 - x**2 + 2*x**w. Let k(t) = 4*t**2 - t - 2. Let g(s) = 4*k(s) + 3*z(s). Factor g(u).
(u - 2)*(u + 1)
Let b(y) be the first derivative of -y**4/4 + y**3/3 + y**2/2 - y - 3. Determine t so that b(t) = 0.
-1, 1
Let g(m) = 3*m**5 + 9*m**4 + 3*m**3 - 4*m**2 - m. Let r(n