t p = 53 + -79. Let z(u) = p*q(u) + 6*y(u). Factor z(r).
-2*(r - 2)**2
Factor 3*m**3 + 3*m**4 - 4*m**4 - m**4 + 6*m**2 - m**4.
-3*m**2*(m - 2)*(m + 1)
Let y(b) be the third derivative of b**10/30240 + b**9/10080 - b**7/5040 - 5*b**4/24 + 2*b**2. Let w(d) be the second derivative of y(d). Factor w(o).
o**2*(o + 1)**2*(2*o - 1)/2
Let z(g) = -g**2 - g + 1. Let k(b) = -6*b**2 - 42*b + 74. Let t(n) = k(n) - 10*z(n). Suppose t(j) = 0. What is j?
4
Solve -2/3*u**4 + 2/3*u**3 + 0 + 0*u + 2/3*u**2 - 2/3*u**5 = 0.
-1, 0, 1
Let p(a) be the second derivative of -a**5/4 - 5*a**4/3 - 10*a**3/3 + 13*a. Determine t so that p(t) = 0.
-2, 0
Let o(k) be the first derivative of 3*k**5/5 - k**4/4 - k**3 + k**2/2 + 6. Find d such that o(d) = 0.
-1, 0, 1/3, 1
Suppose -168 = -37*f - 5*f. Find v such that -1/7*v**f + 0 + 0*v + 3/7*v**3 - 2/7*v**2 = 0.
0, 1, 2
Let q(t) be the first derivative of t**6/6 - 2*t**5/5 + 2*t**3/3 - t**2/2 - 11. Factor q(u).
u*(u - 1)**3*(u + 1)
Factor -8/3*c + 10/3*c**2 - 2/3.
2*(c - 1)*(5*c + 1)/3
Let c(f) be the first derivative of -2*f**3/3 - 4*f**2 - 8*f - 2. Factor c(l).
-2*(l + 2)**2
Let o(f) be the second derivative of f**4/24 - f**3/12 - 3*f**2/2 + 17*f. Determine n so that o(n) = 0.
-2, 3
Let z(l) be the first derivative of -2*l**5/65 + 2*l**3/13 + 2*l**2/13 - 14. Let z(d) = 0. What is d?
-1, 0, 2
Let 1/3*y**2 + 0 - 4/3*y = 0. Calculate y.
0, 4
Let q(s) = -6*s**4 + 7*s**3 - 8*s**2 + 7*s - 7. Let f(v) = -5*v**4 + 6*v**3 - 7*v**2 + 6*v - 6. Let t(z) = 7*f(z) - 6*q(z). Factor t(g).
g**2*(g - 1)*(g + 1)
Find x, given that x**4 - 2*x**3 - x**3 - x**4 + 3*x**5 = 0.
-1, 0, 1
Let z(p) be the first derivative of p**2/2 + 1. Let m be z(3). Solve 14*u**4 + 0*u**3 + 4*u**m + 6*u**5 - 2 - 7*u - 12*u**2 - 3*u = 0 for u.
-1, -1/3, 1
Factor -3/4*s**3 - 1/4*s + 3/4*s**2 + 0 + 1/4*s**4.
s*(s - 1)**3/4
Let z(b) = -5*b**5 - 3*b**4 - 3*b**3 + 3*b**2 + 4. Let l(t) = 4*t**5 + 2*t**4 + 2*t**3 - 2*t**2 - 3. Let a(k) = -4*l(k) - 3*z(k). Suppose a(s) = 0. Calculate s.
-1, 0, 1
Let l(n) be the first derivative of -8*n**2 + 2 + 0*n - 35*n**6 + 39*n**4 - 94/5*n**5 + 8*n**3. Find g, given that l(g) = 0.
-1, -2/5, 0, 2/7, 2/3
Let h(a) = a**3 + 5*a**2 + 2*a + 10. Let m be h(-5). Factor 0*y**3 + m - 1/6*y**4 + 1/3*y + 1/2*y**2.
-y*(y - 2)*(y + 1)**2/6
Let v be (-2)/((-28)/21*2). Determine c so that v*c**2 + 3/2*c + 0 - 3/4*c**3 = 0.
-1, 0, 2
Let x(k) be the first derivative of 0*k**2 + 1/30*k**6 - 5 + 1/15*k**3 - 1/25*k**5 - 1/20*k**4 + 0*k. Solve x(p) = 0.
-1, 0, 1
Let v = -2 + 4. Suppose -3*r - 14 = -17*r. Let 9*i**2 - 9*i**v + 4*i**3 - r - 3*i = 0. What is i?
-1/2, 1
Suppose -2*g - g = -9. Let z(v) = 2*v**3. Let t(f) = f**3. Suppose 0 = -s - 5*w + 19, -3*s - 4 = -3*w + 11. Let m(b) = g*t(b) + s*z(b). Factor m(p).
p**3
Let o(w) = 7*w**2 - 11*w + 9. Let r(d) = -11*d**2 + 17*d - 13. Let n(q) = 7*o(q) + 5*r(q). Solve n(a) = 0 for a.
1/3, 1
Let c(k) = k**2 - 2*k - 1. Let i be c(3). Suppose 0 = 4*l - 8, i*l - 5 = -3*f + 4*l. Determine o so that -1 - 60*o + 18*o**3 - 143*o**f - 7 - 150*o**2 = 0.
-2/5
Let s(p) be the first derivative of -p**4/12 + 2*p**3/9 - 3. Find b such that s(b) = 0.
0, 2
Let z(l) = 4*l**2 - 22*l + 36. Let q(d) = 8*d**2 - 43*d + 72. Let t(k) = -2*q(k) + 5*z(k). Find p, given that t(p) = 0.
3
Let r(o) be the second derivative of -5*o**4/36 - 5*o**3/18 - 27*o. Find d such that r(d) = 0.
-1, 0
Let g = -1 + 3. Suppose -4*d + 8 = -0*d - g*f, 4*d + 5*f = 8. Let 1/2*o**5 + 0*o**d + 0*o + 0 + 1/2*o**3 - o**4 = 0. Calculate o.
0, 1
Let j(z) = -3*z**3 + 14*z**2 - 5*z - 6. Let o(x) = x**2 - 1. Let i(h) = 5*j(h) - 35*o(h). Solve i(w) = 0 for w.
1/3, 1
Let g(r) = r**2 - 2*r - 3. Let b(d) = d + 1. Let u(j) = -6*b(j) - 3*g(j). Find a such that u(a) = 0.
-1, 1
Let o(v) = -7*v**3 + 7*v**2 + 2. Let q(i) = -15*i**3 + 15*i**2 + 5. Let g(x) = 5*o(x) - 2*q(x). Factor g(k).
-5*k**2*(k - 1)
Let r be (-4 - (0 + -3))*(-16)/8. Factor 2/11*f**r + 0 - 6/11*f.
2*f*(f - 3)/11
Let j(f) be the second derivative of 0 + f + 1/21*f**3 - 2/7*f**2 + 2/21*f**4 - 3/70*f**5. Solve j(h) = 0.
-2/3, 1
Let p(t) = t**3 - 4*t**2 - t + 4. Let b be p(4). Factor 1 - 3*s + 4*s**3 + 6*s**2 + 7*s + s**4 + b.
(s + 1)**4
Find q such that -2/13*q**4 + 320/13*q + 28/13*q**3 - 144/13*q**2 - 256/13 = 0.
2, 4
Let o be -1 - (27/9 + (-194)/48). Let v(q) be the second derivative of o*q**4 + 0*q**2 - 1/12*q**3 - 2*q + 0. What is d in v(d) = 0?
0, 1
Let n be 1 - 1*(-4 + 3). Let l(h) be the first derivative of -1/6*h**3 + 0*h + 3 - 1/4*h**n. Factor l(x).
-x*(x + 1)/2
Let 2/13*k**2 + 648/13 + 72/13*k = 0. What is k?
-18
Let d(f) be the second derivative of -f**9/189 + f**8/84 - f**7/210 - 5*f**3/3 + 9*f. Let u(o) be the second derivative of d(o). Let u(l) = 0. What is l?
0, 1/4, 1
Let n(x) be the third derivative of -x**7/42 + 5*x**6/24 - 3*x**5/4 + 35*x**4/24 - 5*x**3/3 - 7*x**2. Find i, given that n(i) = 0.
1, 2
Factor 32*z**3 + 27*z**4 - 4*z**2 + 0*z**5 - 7*z**4 + 4*z**5 + 20*z**2.
4*z**2*(z + 1)*(z + 2)**2
Let v be -1*(-4 - -1 - 1). Let q be ((-37)/(-4))/(4/16). Determine t, given that 4 + q*t**2 + 9*t**v + 13*t**3 + 20*t - 12*t**3 + 29*t**3 = 0.
-1, -2/3
Let q(a) be the third derivative of -a**9/15120 + a**8/6720 + 5*a**4/24 + 2*a**2. Let x(b) be the second derivative of q(b). Determine g, given that x(g) = 0.
0, 1
Let j(n) be the third derivative of -1/112*n**8 - 9/40*n**6 - 1/14*n**7 + 0*n**3 - 1/4*n**4 + 0 + 3*n**2 + 0*n - 7/20*n**5. Factor j(m).
-3*m*(m + 1)**3*(m + 2)
Let l(h) = h**2 + 9*h + 8. Let j be l(-8). Factor 14*b**2 + j*b - b - 15*b**2.
-b*(b + 1)
Find u such that -18/11 + 12/11*u + 6/11*u**2 = 0.
-3, 1
Let t(v) = v**3 + 7*v**2 - 9*v - 10. Let b be t(-8). Let q = 4 + b. Factor l**4 + l**5 + 0*l + 5*l - 2*l**2 + 1 - q*l**3 - 4*l.
(l - 1)**2*(l + 1)**3
Let t(c) = 4*c**2 + c. Let n be t(-1). Suppose -12 = -5*g + 13. Factor 3*b**g + 6*b**n - 2*b**5 + b**4 - 3*b**3 + 2*b**4 + b**2.
b**2*(b + 1)**3
Suppose 8/3 - 4/3*u - 4/3*u**2 = 0. What is u?
-2, 1
Let n(b) = -b**3 + 17*b**2 + 108*b - 8. Let l be n(-5). Factor -8/7*s - 2/7 - 4/7*s**3 - 10/7*s**l.
-2*(s + 1)**2*(2*s + 1)/7
Suppose 3 = -5*i + 2*i. Let s be i/((-2)/(-4) - 1). Suppose 1 + 5 + 0*b - 4 + 2*b**s + 4*b = 0. What is b?
-1
Let i be 2/1 - (-52)/28. Let b = -25/7 + i. Suppose -8/7*s**2 - b*s + 0 = 0. What is s?
-1/4, 0
Let c(t) = -t**3 - 5*t**2 + 13*t + 5. Let p(h) = -3*h**3 - 9*h**2 + 25*h + 9. Let a(k) = -11*c(k) + 6*p(k). Suppose a(g) = 0. Calculate g.
-1, 1/7, 1
Let v be 0/2*(-5)/10. Let h be v/(10/5 - 1). Factor 0 + 2/13*q**2 - 2/13*q**3 + h*q.
-2*q**2*(q - 1)/13
Suppose 5*w = 3*t + 29, 7*w - 4*w + 5*t - 31 = 0. Determine l, given that -4 + 370*l**2 + 9 - 127*l**2 + 108*l + w = 0.
-2/9
Let o be 24/15*10/4. Suppose 0 = -2*k + 2 + o. Solve -2/3 + 2/3*x**2 - 2/3*x**k + 2/3*x = 0 for x.
-1, 1
Suppose -12 = -4*m - 4*v, -v - 2*v = 5*m - 13. Let r(w) be the first derivative of 0*w**3 - 3*w**2 + 2*w**3 - 3*w + 1 + 5*w**3 - m - 3*w**4. Factor r(x).
-3*(x - 1)**2*(4*x + 1)
Let a(z) be the third derivative of z**7/1365 + z**6/390 - 2*z**5/65 - 10*z**4/39 - 32*z**3/39 + 26*z**2 + z. Determine g, given that a(g) = 0.
-2, 4
Let n(k) be the first derivative of -k**6/10 - 3*k**5/25 + 3*k**4/20 + k**3/5 - 7. Factor n(d).
-3*d**2*(d - 1)*(d + 1)**2/5
Determine i, given that -3/4*i - 3/4*i**2 + 9/2 = 0.
-3, 2
Let 3*l + 1 - 2 - 1 - 2*l + l**2 = 0. What is l?
-2, 1
Let d(z) be the first derivative of 0*z**2 - 2*z - 1/10*z**5 + 1/3*z**3 + 0*z**4 + 2. Let i(x) be the first derivative of d(x). Let i(f) = 0. What is f?
-1, 0, 1
Factor -54/7 - 6/7*v**2 + 36/7*v.
-6*(v - 3)**2/7
Suppose 12*p - 2*p = -220. Let h be p/121 - (-47)/77. Determine a so that 0*a**2 - 3/7*a**3 + 0 + h*a = 0.
-1, 0, 1
Let o(p) be the third derivative of p**7/1260 - p**5/60 + p**4/6 + 4*p**2. Let t(b) be the second derivative of o(b). Factor t(q).
2*(q - 1)*(q + 1)
Let l(g) = -10*g**2 + 20*g - 4. Let d(m) be the first derivative of 17*m**3 - 101*m**2/2 + 20*m + 1. Let o(k) = -2*d(k) - 11*l(k). Factor o(n).
2*(n - 2)*(4*n - 1)
Let v(z) be the first derivative of z**5/360 + z**4/72 + z**3/36 + z**2 - 5. Let c(g) be the second derivative of v(g). Factor c(x).
(x + 1)**2/6
Let h(r) = -r**3 - 4*r**2 + 4*r - 5. Let z be h(-5). Solve -5*g + 2*g**2 + 2 + z*g**2 + 3*g - 6 = 0.
-1, 2
Let m(h) be the