- p**2 + p + o. Factor k(u).
(u - 1)**2
Let p be 2/(-3)*1/(-7). Let a(m) be the third derivative of 0 + 0*m - 1/28*m**4 + p*m**3 + m**2 + 1/210*m**5. Factor a(i).
2*(i - 2)*(i - 1)/7
Let t(n) be the third derivative of 0*n**3 - 1/140*n**6 + 0*n - 1/735*n**7 - 1/84*n**4 + n**2 + 0 - 1/70*n**5. Factor t(r).
-2*r*(r + 1)**3/7
Suppose c - i = 3*i + 15, -9 = -5*c - 2*i. Determine q so that -q**2 + 4*q**c - 6*q**3 + 2*q + 2 - q**2 = 0.
-1, 1
Let t(u) = u**3 + u. Let l = -1 - 0. Let z(h) = 7*h**2 - 7*h**2 - h**2 - 10*h**3 + 1 - 2*h. Let j(m) = l*z(m) - 6*t(m). Factor j(g).
(g - 1)*(g + 1)*(4*g + 1)
Let n(q) be the first derivative of -1/6*q**3 + 1/2*q**2 + 5 - 1/16*q**4 + 2*q. Factor n(d).
-(d - 2)*(d + 2)**2/4
Let h(b) = -7*b**3 - 6*b**2 - 6*b - 6. Let r(l) = -6*l**3 - 5*l**2 - 5*l - 5. Let m(n) = -5*h(n) + 6*r(n). Let j be m(0). Factor j - 1/4*o**2 - 1/2*o.
-o*(o + 2)/4
Let i(u) = 2*u**2 - u - 1. Let o be i(-1). Factor -3*f**5 + 12*f**4 - 3*f - 18*f**3 + 9*f**2 + 9*f**2 - 4*f**2 - 2*f**o.
-3*f*(f - 1)**4
Let t(j) be the second derivative of 5*j**7/14 - j**6/6 - 11*j**5/4 - 5*j**4/4 + 20*j**3/3 + 10*j**2 + 10*j. Determine m, given that t(m) = 0.
-1, -2/3, 1, 2
Factor -4*a**3 + 4*a - 1 + a**2 + 5*a**3 - 6*a + a.
(a - 1)*(a + 1)**2
Let k(b) be the second derivative of -b**5/60 + b**4/12 + 5*b**2/2 + 4*b. Let p(q) be the first derivative of k(q). Factor p(l).
-l*(l - 2)
Suppose 4/3*w**3 - 4/3*w + 4/3*w**2 + 0 - 4/3*w**4 = 0. What is w?
-1, 0, 1
Solve -12/23*x**2 + 0*x**3 + 2/23*x**4 - 6/23 - 16/23*x = 0.
-1, 3
Let u(q) be the third derivative of -1/30*q**5 + 0*q**3 - 1/24*q**4 - 1/120*q**6 + 0 + 2*q**2 + 0*q. Factor u(c).
-c*(c + 1)**2
Factor -8/5*r**4 + 0*r + 0*r**2 + 0 + 2/5*r**5 + 8/5*r**3.
2*r**3*(r - 2)**2/5
Let g(d) = -d**3 + 3*d**2 + d - 3. Let p(i) = -i**3 + 7*i**2 + i - 7. Let q(t) = 7*g(t) - 3*p(t). Suppose q(x) = 0. What is x?
-1, 0, 1
Let w(k) be the second derivative of -k**4/24 - k**3/3 - k**2 - 14*k. Let w(h) = 0. Calculate h.
-2
Let r(k) be the second derivative of k + 2/3*k**3 + 1/30*k**6 - 3/20*k**5 + 0*k**2 + 0 + 0*k**4. Determine u so that r(u) = 0.
-1, 0, 2
Let b(o) = -o - 10. Let w be b(-13). Determine c, given that -8*c + 0 + 2*c**3 + 3*c**4 - 9*c**2 - 7*c + c**w - 6 = 0.
-1, 2
Suppose -v + 2 = m, -6 = 4*m - 4*v - 46. Let s = m + -3. Factor 2*c**2 - s*c - 3*c**4 - 2 + 3*c**5 - 2*c**5 + 3 + 2*c**3.
(c - 1)**4*(c + 1)
Let o(x) be the second derivative of -x**10/90720 + x**9/45360 + x**8/20160 - x**7/7560 - 2*x**4/3 - 4*x. Let r(z) be the third derivative of o(z). Factor r(v).
-v**2*(v - 1)**2*(v + 1)/3
Let 8 + 4/5*c**2 + 28/5*c = 0. Calculate c.
-5, -2
Solve 47*n**3 - 8*n**5 - 8*n**5 - 2 - 13*n - 4*n**4 + n**4 - 8*n**2 - 5*n**4 = 0 for n.
-2, -1/4, 1
Let u(p) be the second derivative of p**5/10 + p**4/6 - 2*p**3/3 + 2*p. Factor u(a).
2*a*(a - 1)*(a + 2)
Let g(a) = 4*a**2 - 3*a**2 + a**3 + 2 + a - 2*a**3. Let v be g(2). Let 0 + 0*r + 0*r**2 + 1/3*r**5 - 1/3*r**4 + v*r**3 = 0. What is r?
0, 1
Suppose -234*q**3 - 42*q**4 - 4*q**5 + q**5 - 648*q**2 - 486 - 52*q - 839*q = 0. What is q?
-3, -2
Factor 56*d**2 + 13 - 17*d**2 - 1 - 48*d - 9*d**3.
-3*(d - 2)**2*(3*d - 1)
Let a(m) be the third derivative of m**7/280 + 2*m**3/3 - 3*m**2. Let s(d) be the first derivative of a(d). Factor s(z).
3*z**3
Let j(v) = -5*v**4 - 5*v**3 + 5*v**2 - 6*v - 11. Let x(m) = m**4 + m**3 - m**2 + m + 2. Let y = -28 + 17. Let n(w) = y*x(w) - 2*j(w). Factor n(o).
-o*(o - 1)*(o + 1)**2
Let z be (-1)/((-3)/9 - 0). Let r = z - 3. Factor r*i + 1/3*i**2 - 1/3.
(i - 1)*(i + 1)/3
Let i(o) = 4*o**3 - o**2. Let u(r) = -r**3. Let l(v) = -i(v) - 3*u(v). Find b, given that l(b) = 0.
0, 1
Let b(i) = i**3 + 3*i**2 + 2*i + 3. Let q be b(-2). Let g(d) = 3*d**2 + 3*d - 1. Let l be g(-2). Factor y + 12*y**q + 6*y**5 + 2*y - l*y - 16*y**4.
2*y*(y - 1)**3*(3*y + 1)
Suppose -s + 4*s + 420 = 0. Let z be (-2)/(-5) + 16/s. What is o in 0 + 2/7*o**2 - z*o**4 - 2/7*o + 2/7*o**3 = 0?
-1, 0, 1
Let k(l) = 60*l**3 + 9*l**2 - 29*l. Let m(q) = 12*q**3 + 2*q**2 - 6*q. Let t(h) = -2*k(h) + 11*m(h). Find a such that t(a) = 0.
-1, 0, 2/3
Let g = -10 + 13. Suppose 5*l - 17 - 13 = -4*x, 0 = 2*x - 10. Factor 0*v**4 - 3*v - g + v**l + 1 + 3*v**3 + v**4.
(v - 1)*(v + 1)**2*(v + 2)
Let u = 7/2 + -47/14. Determine y so that -1/7*y**3 - u*y + 0 + 2/7*y**2 = 0.
0, 1
Let c(x) be the first derivative of -x**4/4 + x**3 - 3*x**2/2 + x + 21. Determine a, given that c(a) = 0.
1
Let i = -8 - -10. Let s(r) be the first derivative of -i - 2/3*r**3 + 2*r + 0*r**2. Suppose s(l) = 0. What is l?
-1, 1
Let j(v) be the first derivative of 0*v**2 + 5 + 0*v - 2/9*v**3 - 2/15*v**5 - 1/3*v**4. Let j(u) = 0. Calculate u.
-1, 0
Let r(w) be the second derivative of 2/3*w**3 + 2*w - 2/3*w**4 + 1/5*w**5 + 0*w**2 + 0. Solve r(q) = 0.
0, 1
Factor 10*n - 12 - 6*n + 4*n**3 + 24*n - 20*n**2.
4*(n - 3)*(n - 1)**2
Let m be (-625)/140 + 5 + 4/(-14). Determine u, given that -1/4*u**3 - 1/4 + m*u**2 + 1/4*u = 0.
-1, 1
Suppose -1/3*j**2 - 2/3*j + j**3 + 1/3*j**4 + 0 - 1/3*j**5 = 0. What is j?
-1, 0, 1, 2
Factor -12*j**2 - 37*j**3 + 4*j - 6 + 34*j**3 - 19*j.
-3*(j + 1)**2*(j + 2)
Let d(y) be the first derivative of -3*y**4/4 + 3*y**3 - 3*y**2 - 5. Factor d(h).
-3*h*(h - 2)*(h - 1)
Suppose -2*t = -1 + 9. Let j = t - -7. Suppose -2 - 2*s - 1 - 2*s**j + 3 - 4*s**2 = 0. Calculate s.
-1, 0
Let s(d) = -7*d. Suppose 3*a + 2 = -1. Let z be s(a). Suppose 0*j + 2*j**3 + 3*j - z*j + 1 + 6*j**2 - 6*j**3 + j**4 = 0. What is j?
1
Let i(f) = f**3 - 6*f**2 + 13*f - 9. Let o(p) = -p + 1. Let z(l) = -i(l) - o(l). Find g such that z(g) = 0.
2
Let p(m) = 3*m**2 + 5*m + 14. Let o(i) = 7*i**2 + 9*i + 29. Let b(c) = 4*o(c) - 9*p(c). Determine t so that b(t) = 0.
-1, 10
Let d(l) be the first derivative of -l**5/210 - l**4/28 - 2*l**3/21 - 3*l**2 - 4. Let q(n) be the second derivative of d(n). Suppose q(u) = 0. What is u?
-2, -1
Let w(b) be the first derivative of -b**6/720 + b**4/48 + 2*b**3/3 + 4. Let s(p) be the third derivative of w(p). Factor s(k).
-(k - 1)*(k + 1)/2
Let c(n) = n**2 - 11*n + 10. Let f(d) = -2*d**2 + 21*d - 19. Let t(i) = -5*c(i) - 3*f(i). Find o, given that t(o) = 0.
1, 7
Let y be 59/7 + (-11)/(539/(-28)). Suppose -3*d**4 + 2 - 23/4*d**3 + 27/2*d**2 - y*d + 9/4*d**5 = 0. Calculate d.
-2, 2/3, 1
Let h(j) be the third derivative of j**8/168 - j**7/35 + j**6/60 + j**5/10 - j**4/6 + 6*j**2. Factor h(w).
2*w*(w - 2)*(w - 1)**2*(w + 1)
Factor 9/2*m - 27/4 - 3/4*m**2.
-3*(m - 3)**2/4
Find u, given that 0 - 1/6*u - 1/6*u**2 = 0.
-1, 0
Let j be (-2 - -13)*(-1)/(-1). Let v(c) = -j*c**2 + 4*c + c - c. Let z(p) = p**2. Let x(u) = v(u) + z(u). Determine d so that x(d) = 0.
0, 2/5
Let u(h) be the second derivative of 0 + 4*h - 34/9*h**3 + 7/15*h**5 - 4*h**2 + 16/9*h**4. Factor u(c).
4*(c - 1)*(c + 3)*(7*c + 2)/3
Let x(f) be the second derivative of -1/10*f**5 + 0*f**4 + 1/3*f**3 + 0*f**2 - f + 0. Factor x(o).
-2*o*(o - 1)*(o + 1)
Let c(n) = -2*n**2 - 2*n + 2. Let d be c(-2). Let x be (-8)/d + (-2)/2. What is v in v + v**x - v**3 - v**3 = 0?
-1, 0, 1
Let i(b) be the second derivative of 0 + 3/10*b**5 - 4*b - b**2 + 5/6*b**4 + 1/3*b**3. Factor i(w).
2*(w + 1)**2*(3*w - 1)
Suppose 1/5*t + 4/5*t**2 - 1/10 = 0. Calculate t.
-1/2, 1/4
Let p(c) = c**3 + 4*c**2 + 2*c. Let n be p(-3). Solve -29*j**n + 14*j**3 + 4*j**2 + 4*j + 11*j**3 - 4*j**4 = 0 for j.
-1, 0, 1
Suppose 0 = -24*y + 25*y - 4. Let v(x) be the third derivative of -1/24*x**y + x**2 + 1/60*x**5 + 0*x - 1/3*x**3 + 0. Factor v(q).
(q - 2)*(q + 1)
Find n such that 0 - 3/7*n**4 + 3/7*n + 3/7*n**2 - 3/7*n**3 = 0.
-1, 0, 1
Suppose 0 = 4*j + 2*p - 8, -j - 4*p + 12 = -p. Factor -4/3 + 7/3*k**2 + j*k - k**3.
-(k - 2)*(k - 1)*(3*k + 2)/3
Suppose 5*f - 5*d + 905 = 0, 751 = -4*f - 0*d - 5*d. Let s = f + 2028/11. Factor 2/11*p + 0 - s*p**2.
-2*p*(2*p - 1)/11
Let j(s) be the third derivative of -s**6/420 + s**5/210 + s**4/21 - 4*s**3/21 - 8*s**2. Factor j(o).
-2*(o - 2)*(o - 1)*(o + 2)/7
Suppose -2/3*s**3 - 4*s**2 + 0 - 6*s = 0. What is s?
-3, 0
Solve -r**2 - 157*r + 5*r**2 - 20 + r**2 + 172*r = 0.
-4, 1
Let d(o) = -5*o**5 - 2*o**4 + o**3 - 2*o - 2. Let a(f) = -26*f**5 - 10*f**4 + 4*f**3 - f**2 - 11*f - 11. Let q(b) = -4*a(b) + 22*d(b). Solve q(c) = 0 for c.
-1, -2/3, 0, 1
Let y(h) = -4*h + 1. Let n be y(-1). Suppos