hat g(f) = 0.
-1, 1, 2
Let u(m) be the first derivative of -9/2*m**2 + 5*m**3 + 2 - 6*m. Factor u(r).
3*(r - 1)*(5*r + 2)
Let c(t) be the first derivative of 2/25*t**5 - 1/10*t**4 + 0*t**2 + 1/15*t**6 + 0*t - 2/15*t**3 + 4. Let c(a) = 0. Calculate a.
-1, 0, 1
Solve 0 + 1/2*h**4 - 1/2*h + 1/2*h**3 - 1/2*h**2 = 0.
-1, 0, 1
Determine x so that 0*x - 2/7*x**2 - 6/7*x**4 + 0 - 6/7*x**3 - 2/7*x**5 = 0.
-1, 0
Let z be (-4)/6 + 884/975. Let a(o) be the first derivative of 0*o**2 + z*o**5 + 2 + 0*o - 1/15*o**6 - 3/10*o**4 + 2/15*o**3. Factor a(f).
-2*f**2*(f - 1)**3/5
Let n(c) be the third derivative of -c**8/1440 + c**7/420 - c**6/540 + c**4/12 + c**2. Let l(m) be the second derivative of n(m). Factor l(x).
-2*x*(x - 1)*(7*x - 2)/3
Let f be 8 + -6 + (-2)/4. Determine o so that 0 + 3/2*o**2 + f*o = 0.
-1, 0
Suppose 3*x - 8 - 8 = -l, -4*x = 3*l - 28. Suppose l*h - 5*h = -4. Find t such that 5*t**2 - 3*t**2 - t**3 - h*t**2 = 0.
-2, 0
Let w = 7 - 3. Factor y**4 + 4*y**3 - w*y - y**5 + 9*y**2 + 5*y**4 + 3*y**2 - 17*y**3.
-y*(y - 2)**2*(y - 1)**2
Factor 6/5*f + 3/5*f**2 + 0.
3*f*(f + 2)/5
Let l(u) be the first derivative of u**5 + 5*u**4/4 - 20*u**3/3 - 10*u**2 + 31. Determine m so that l(m) = 0.
-2, -1, 0, 2
Let x be 2/7 + 2*1/(-56). Factor x*f - 1/4*f**3 + 1/4 - 1/4*f**2.
-(f - 1)*(f + 1)**2/4
Let p be (-1)/(-1 + (-1)/(-2)). Let j(v) = 2*v**2 - 2*v + 2. Let u be j(2). Suppose u*k + 0*k**2 + 0 + 2*k**3 - 1 + 6*k**p + 3 = 0. Calculate k.
-1
Let c(q) = -5*q**3 + 3*q**2 - 2*q. Let p(j) = 7*j + 15*j**3 - 16*j**3 + j**2 - 8*j. Let l(n) = -c(n) + 4*p(n). Let l(g) = 0. What is g?
-2, 0, 1
Let x(o) be the first derivative of -2*o**6 + 39*o**4/4 + 27*o**2/2 - 27*o - 4. Let b(q) = -q**5 + 3*q**3 + 2*q - 2. Let r(h) = -27*b(h) + 2*x(h). Factor r(t).
3*t**3*(t - 1)*(t + 1)
Let d be 7 - 1*(4 + -2). Let c(q) = 7*q - 29. Let b be c(6). Let 2*w**d - 30*w**3 - 16*w**2 + 4*w**2 + b*w**5 + 6*w**4 + 15*w + 6 = 0. What is w?
-1, -2/5, 1
Let w be 2 + 2*-2 - -2. Suppose w + 4 = s. Factor 4*i + 2*i**2 + 2*i**4 + 4*i**2 - 4*i**s.
-2*i*(i - 2)*(i + 1)**2
Let v(o) be the first derivative of -2*o**6/3 + o**4 + 6. Suppose v(q) = 0. Calculate q.
-1, 0, 1
Let b(u) = 6*u + 84. Let j be b(-14). Factor -2/11*f**4 + 0*f + 2/11*f**3 + 0 + j*f**2.
-2*f**3*(f - 1)/11
Let x(r) be the first derivative of -r**7/630 + r**6/360 + r**5/180 - r**4/72 - r**2/2 + 3. Let a(k) be the second derivative of x(k). Factor a(p).
-p*(p - 1)**2*(p + 1)/3
Suppose 2*x - 4*p + 19 = -3*p, 29 = -4*x - p. Let a = 8 + x. Factor 0*d**3 + 0*d**2 + 0*d + a - 1/2*d**4.
-d**4/2
Let x(n) be the second derivative of 1/18*n**3 - 1/60*n**5 - 4*n + 0 - 1/6*n**2 + 1/36*n**4. Factor x(y).
-(y - 1)**2*(y + 1)/3
Factor -6*s**5 + 13*s**5 + 3*s**5 + 9*s**3 - 4*s**3 - 15*s**4.
5*s**3*(s - 1)*(2*s - 1)
Let j(y) be the second derivative of -y**4/48 - y**3/24 + 5*y. Factor j(v).
-v*(v + 1)/4
Let p = -24 + 27. Factor 2*h**5 + 0*h**2 + 0 - 2/3*h**p + 0*h - 4/3*h**4.
2*h**3*(h - 1)*(3*h + 1)/3
Let n(m) be the third derivative of m**8/1848 - m**6/220 + m**5/165 + 3*m**2. Factor n(x).
2*x**2*(x - 1)**2*(x + 2)/11
Suppose 3*s + 5 + 1 = 4*l, 0 = 4*s + l - 11. Factor 2/3 - 4/3*c + 2/3*c**s.
2*(c - 1)**2/3
Let r(l) be the second derivative of 5*l**4/12 - 25*l**3/6 + 15*l**2 + 12*l + 3. Let r(s) = 0. Calculate s.
2, 3
Let i(o) = 6*o**4 - 13*o**3 - 6*o**2 + 13. Let v(h) = 3*h**4 - 6*h**3 - 3*h**2 + 6. Let u(c) = 6*i(c) - 13*v(c). Factor u(d).
-3*d**2*(d - 1)*(d + 1)
Let z(i) be the first derivative of -i**4/2 + 4*i**3/3 + 4*i**2 - 16*i + 5. Solve z(x) = 0 for x.
-2, 2
Determine r so that 3/4*r**5 + 1/4*r**4 + 0 - 3/4*r**3 + 0*r - 1/4*r**2 = 0.
-1, -1/3, 0, 1
Let b(y) be the second derivative of 1/27*y**7 + 2/9*y**2 + 0 + 20/27*y**4 + 5/9*y**3 + 2/9*y**6 + 5*y + 5/9*y**5. Factor b(q).
2*(q + 1)**4*(7*q + 2)/9
Let i be -1*1/2*6. Let p be 3 + -1*(-3)/i. Determine s so that 0 - 2/7*s - 2/7*s**p = 0.
-1, 0
Let p(m) = -6*m**2 - m. Let t be p(-1). Let s = 5 + t. Suppose -2/3*r**2 - 2/3*r**3 + s + 0*r = 0. Calculate r.
-1, 0
Let m(y) = y**4 + y**3 - y. Let r(k) = -34*k**4 - 70*k**3 - 16*k**2 + 6*k. Let c(g) = -6*m(g) - r(g). Factor c(o).
4*o**2*(o + 2)*(7*o + 2)
Let a(x) be the second derivative of -x**5/90 + x**4/18 - 2*x**3/27 + 5*x. Factor a(b).
-2*b*(b - 2)*(b - 1)/9
Suppose -4*y - 4*t + 24 = 0, 0*y = 5*y + 3*t - 26. Find b, given that 2/3*b - 1/3 + 1/3*b**y + 0*b**2 - 2/3*b**3 = 0.
-1, 1
Let l = -4 + 8. Let z(r) be the third derivative of 0*r**6 + 2*r**2 + 0*r**3 + 0*r - 1/420*r**7 + 1/120*r**5 - 1/1344*r**8 + 0 + 1/96*r**l. Factor z(v).
-v*(v - 1)*(v + 1)**3/4
Let a(s) be the second derivative of -3*s**5/40 + 5*s**4/12 + 3*s**3/4 - s**2 + 20*s. Factor a(p).
-(p - 4)*(p + 1)*(3*p - 1)/2
Let w(n) = n**3. Let q(g) = 4*g**5 + 12*g**4 + 4*g**3 + 4*g**2. Let m(l) = q(l) + 8*w(l). What is b in m(b) = 0?
-1, 0
Suppose -5*a - 305 = -0*a. Let q = -181/3 - a. Factor q + 0*w - 2/3*w**2.
-2*(w - 1)*(w + 1)/3
Solve 0*c**2 + 1/4*c**5 + 0 + 0*c + 0*c**4 - 1/4*c**3 = 0.
-1, 0, 1
Suppose -37*g + 49*g + 30 + 21*g**3 + 54*g**2 - 6 + 3*g**4 + 48*g = 0. What is g?
-2, -1
Let i(l) = 2*l**2 + l. Let v be i(-2). Factor -6*q**3 - 3 - 12*q - v*q**3 - 18*q**2 - 3*q**4 + 0*q.
-3*(q + 1)**4
Let h be 1 + -4 + 4 - 0. Let k be h/6*20/1. Factor k*v**3 + 6*v - 4/3 - 8*v**2.
2*(v - 1)**2*(5*v - 2)/3
Let k(x) be the second derivative of 3*x**6/20 + 33*x**5/40 + 15*x**4/8 + 9*x**3/4 + 3*x**2/2 - 9*x. Factor k(b).
3*(b + 1)**3*(3*b + 2)/2
Suppose 0 = f + 4*f + 30. Let v(k) = -k**3 - 7*k**2 - 7*k - 3. Let t be v(f). Find c, given that 4/3*c**2 + 0 - 2/3*c - 4/3*c**4 + 2/3*c**5 + 0*c**t = 0.
-1, 0, 1
Let u(a) be the third derivative of 1/280*a**7 - 1/24*a**4 + 5*a**2 + 0*a + 1/48*a**6 + 7/240*a**5 - 1/6*a**3 + 0. Factor u(z).
(z + 1)**2*(z + 2)*(3*z - 2)/4
Let h be (5 + 1)/(-2) + -2. Let p be 1/(h/(-2) - 2). Factor p*s**2 + 2 - 2.
2*s**2
Let b(u) = -u**3 - u**2 - u. Let p = -1 - 0. Let f(r) = 2*r**3 + 4*r**2 + 6*r. Let t(g) = p*f(g) - 4*b(g). Solve t(i) = 0 for i.
-1, 0, 1
Suppose x - 4*x + 8 = 5*s, -s - 3 = -4*x. Suppose 3 + s = b. What is n in 7*n**2 - 2*n**3 - 5*n**2 - 7*n**b - 3*n**3 = 0?
-1, 0, 2/7
Suppose 2*t + 0*t = 0. Find l such that t*l**3 + 0*l**3 - l**5 + l**3 = 0.
-1, 0, 1
Let u = 26/87 + 1/29. Let w(k) be the first derivative of 0*k + 1/2*k**2 - 1 - 1/4*k**4 + u*k**3 - 1/5*k**5. Let w(t) = 0. What is t?
-1, 0, 1
Let w(o) = 2*o**3 + 3*o**2 - 6*o + 4. Let d(q) = q**2. Let x(k) = 6*d(k) - 2*w(k). Find t such that x(t) = 0.
-2, 1
Let t = -15 - -17. Let -2*b**2 + 3*b**5 + 3*b**3 - 2*b - t*b**4 - b**2 + 9*b**4 = 0. What is b?
-1, 0, 2/3
Let u be 2*(-17)/12 + 3. Let t(n) be the second derivative of 0 + 0*n**3 + 1/15*n**6 + n + 0*n**2 + 1/5*n**5 + u*n**4. Factor t(r).
2*r**2*(r + 1)**2
Factor 4*a + 0*a + a**2 - 2*a.
a*(a + 2)
Suppose t + 3*v = -v - 12, t - 24 = 5*v. Factor 6/5*z**2 + 0 + 6/5*z**3 + 2/5*z**t + 2/5*z.
2*z*(z + 1)**3/5
Let u(p) = 2*p**3 - p**2 + 2*p - 1. Let z be u(1). Determine r so that -6*r**z + 5*r**2 - r**3 - r**4 + 3*r**3 = 0.
0, 1
Factor -8/7 + 2/7*k**2 + 0*k.
2*(k - 2)*(k + 2)/7
Let q = 15/113 + 1123/904. Let s = 1/8 + q. Suppose -1/2*y**4 + 3/2*y**3 - s*y**2 + 0 + 1/2*y = 0. Calculate y.
0, 1
Suppose 2*z - 3*w = w - 56, w + 1 = 0. Let t be (-4)/z - 4/(-195). Factor 0 - 2/13*f**3 - t*f**2 + 0*f.
-2*f**2*(f + 1)/13
Let m(o) be the first derivative of 2*o**5/75 + o**4/15 + 2*o**3/45 - 4. Determine b so that m(b) = 0.
-1, 0
Let u(g) be the second derivative of g**6/45 + g**5/20 - g**3/18 + 11*g. Let u(a) = 0. What is a?
-1, 0, 1/2
Let b(y) = 10*y**2 + y - 2. Let i be b(-2). Let t be (-42)/(-40) + i/(-45). Solve t*m**2 + 1/2*m + 1/4 = 0 for m.
-1
Let b(c) = 3*c**3 + 24*c**2 + 21*c + 9. Let h(q) = q**3 + 6*q**2 + 5*q + 2. Let f(g) = 2*b(g) - 9*h(g). Find i such that f(i) = 0.
-1, 0
Let g = 630 - 627. Find f, given that 0 - 6/5*f**2 - 4/5*f**g - 2/5*f = 0.
-1, -1/2, 0
Let x = 6 - 15. Let u = -23/3 - x. Factor 2/3*o**3 + 2/3*o + 0 - u*o**2.
2*o*(o - 1)**2/3
Let z(n) be the second derivative of 0 - 1/6*n**3 + 0*n**2 + 3*n - 1/20*n**5 - 1/6*n**4. Let z(v) = 0. What is v?
-1, 0
Let t be (-6)/10 - 514/(-840). Let p(u) be the third derivative of 0*u**3 - 1/420*u**6 + 0*u + 0*u**5 + 2*u**2 + t*u**4 + 0. Suppose p(a) = 0. What is a?
-1, 0, 1
Let i(x) be the third derivativ