r -2/3 - 1/3*d + 1/3*d**3 + 2/3*d**2.
(d - 1)*(d + 1)*(d + 2)/3
Suppose -44 = -r - 2*r + p, 59 = 4*r - p. Suppose d = -u + 3, 3*d = -2*d + r. Factor u + 0*v + 1/2*v**2.
v**2/2
Let g(x) be the first derivative of -2*x**6/9 + 4*x**5/45 + 8*x**4/9 + 16*x**3/27 + 22. Suppose g(r) = 0. Calculate r.
-1, -2/3, 0, 2
Find h, given that -9/5*h - 2/5 - 3/5*h**4 - 3*h**2 - 11/5*h**3 = 0.
-1, -2/3
Let s(x) = -x**2 + 5*x - 4. Let y be s(3). Let v = -263/30 - -55/6. Determine n, given that 2/5*n**y - v*n + 0 = 0.
0, 1
Suppose 3 + 12 = 5*a. Suppose 4*o + 5*q + 2 = 0, -a*o + 0*q + 8 = -q. Determine v so that 1 + 4*v**2 - 4 - v**o = 0.
-1, 1
Let v = -39 + 121/3. Factor -v*j**3 + 8/9 - 8/3*j + 2/9*j**4 + 26/9*j**2.
2*(j - 2)**2*(j - 1)**2/9
Determine c so that 0 + 4/3*c**3 - 1/3*c**2 - 4/3*c**4 + 0*c = 0.
0, 1/2
Solve v**3 + v**2 - 6*v + 4*v**3 - 2*v**3 - 4*v**2 = 0 for v.
-1, 0, 2
Let a = 484 - 484. Factor -8/9*k**4 - 10/9*k**3 - 2/9*k**2 + a + 0*k.
-2*k**2*(k + 1)*(4*k + 1)/9
Let c(m) = 3*m - 4. Let f(y) = -y + 1. Let i(j) = -c(j) - 4*f(j). Let q(v) = 7*v - 2*v - v**2 - 2*v. Let o(z) = 2*i(z) - q(z). Solve o(n) = 0.
0, 1
Let s(q) be the second derivative of -q**6/105 + 3*q**5/140 - q**4/84 + q. Solve s(p) = 0 for p.
0, 1/2, 1
Factor -12*x**3 + 24*x**2 + 16*x**3 + 14*x + 18*x.
4*x*(x + 2)*(x + 4)
Let u = -5233/2 - -117712/45. Let r = 9/10 + u. Factor -r*v**3 - 8/9*v - 8/9*v**2 + 0.
-2*v*(v + 2)**2/9
Let w(n) be the first derivative of n**6/18 - n**4/6 + n**2/6 + 10. Find i such that w(i) = 0.
-1, 0, 1
Let y(m) = -81*m**4 - 213*m**3 - 333*m**2 - 189*m - 24. Let z(b) = -23*b**4 - 61*b**3 - 95*b**2 - 54*b - 7. Let i(c) = 5*y(c) - 18*z(c). Factor i(s).
3*(s + 1)**3*(3*s + 2)
Let y(z) be the second derivative of -z**5/130 - z**4/39 + 4*z**3/39 + 8*z**2/13 - 3*z. Solve y(r) = 0.
-2, 2
Let r = 22 - 17. Let i(q) be the second derivative of -q - 1/2*q**3 + 0 + 0*q**4 + 3/20*q**r + 0*q**2. Factor i(j).
3*j*(j - 1)*(j + 1)
Let p(h) = h**5 + h**4 - h**2 + h + 1. Let b(f) = -f**5 - 3*f**4 - 2*f**3 + 4*f**2 - f - 3. Let y(s) = b(s) + 2*p(s). Factor y(c).
(c - 1)**3*(c + 1)**2
Let b(r) be the third derivative of 0 - 1/84*r**4 + 0*r - r**2 - 1/210*r**5 - 1/1260*r**6 + 1/3*r**3. Let m(w) be the first derivative of b(w). Factor m(t).
-2*(t + 1)**2/7
Suppose -12 = -19*k + 13*k. Factor 4/5 + k*g + 8/5*g**2 + 2/5*g**3.
2*(g + 1)**2*(g + 2)/5
Suppose 2/3 + 2*y**2 + 2/3*y**3 + 2*y = 0. What is y?
-1
Let m(q) be the second derivative of 0*q**2 + 3/70*q**5 - 2/21*q**4 + 1/21*q**3 - 6*q + 0 + 4/105*q**6 - 4/147*q**7. Let m(a) = 0. What is a?
-1, 0, 1/2, 1
Let c(u) be the second derivative of -1/18*u**3 + 4*u - 1/36*u**4 + 0*u**2 + 0. Find x such that c(x) = 0.
-1, 0
Let m(q) be the third derivative of q**7/2520 + q**6/360 + q**4/12 + 3*q**2. Let p(n) be the second derivative of m(n). Factor p(g).
g*(g + 2)
Suppose j - 3*j + 8 = 0. Let h(p) be the second derivative of -4/9*p**3 + 4/3*p**2 + 0 - p + 1/18*p**j. Let h(w) = 0. Calculate w.
2
Factor 32*u**5 + 7*u + 20*u**3 - 25*u**4 - 27*u**5 - 7*u.
5*u**3*(u - 4)*(u - 1)
Factor 7/4*g**4 + 0*g + 1/4*g**5 + 15/4*g**3 + 0 + 9/4*g**2.
g**2*(g + 1)*(g + 3)**2/4
Let l(c) be the second derivative of c**5/150 - c**4/15 + c**3/9 - 7*c. What is a in l(a) = 0?
0, 1, 5
Suppose 0 = 3*g + 4*r - 20, 2*r - 4 = 6. Solve -m**2 + g*m**2 + 2*m - m + 0*m = 0.
0, 1
Let d be (-22)/(-4) - ((-15)/(-6) + 0). Suppose 0*x - 10/3*x**4 + 14/3*x**d - 4/3*x**2 + 0 = 0. Calculate x.
0, 2/5, 1
Let j(d) = 3*d**4 - 12*d**3 + 2*d**2 - 2*d + 2. Let l(q) = -5*q**4 + 25*q**3 - 5*q**2 + 5*q - 5. Let n(o) = -5*j(o) - 2*l(o). Factor n(t).
-5*t**3*(t - 2)
Let j(f) be the first derivative of 4*f**5/15 - f**4/2 - 2*f**3/3 + 2*f**2/3 + 5. Solve j(n) = 0.
-1, 0, 1/2, 2
Let f = 2/83 + 71/498. Let z(k) be the second derivative of 0*k**2 - k + f*k**4 + 1/10*k**5 + 0*k**3 + 0. Factor z(p).
2*p**2*(p + 1)
What is n in 30*n**2 + 30*n - 1 - 37*n**2 - 68*n**2 - 2 = 0?
1/5
Let a(m) be the second derivative of 0*m**2 + 4*m + 0 + 1/56*m**7 + 1/2*m**3 + 3/20*m**6 + 39/80*m**5 + 3/4*m**4. Factor a(q).
3*q*(q + 1)**2*(q + 2)**2/4
Suppose -5*t + 32 - 7 = 0. What is m in -t - 2*m**3 + 5 - m**2 + 3*m**2 = 0?
0, 1
Let s(z) be the second derivative of z**7/11340 + z**6/3240 - z**4/3 - z. Let q(f) be the third derivative of s(f). Let q(u) = 0. What is u?
-1, 0
Let o(z) be the second derivative of -2/5*z**2 + 1/30*z**4 + 0 - 1/15*z**3 - 3*z. Determine s so that o(s) = 0.
-1, 2
Let q(b) be the second derivative of b**7/84 + b**6/20 + 3*b**5/40 + b**4/24 - 6*b. Determine u so that q(u) = 0.
-1, 0
Suppose -7*w**2 - 3*w**2 + 0*w**2 - 3*w**3 - 2*w**2 = 0. Calculate w.
-4, 0
Suppose 3*f = -2*f - 5*k + 15, 0 = 3*f - 2*k - 4. Let s = 15 + -13. Suppose 5*l**f - 40*l + 0*l**s - 8 - 50*l**2 - 5*l**2 = 0. What is l?
-2/5
Factor 11/3*n**2 + 0 - 3*n**3 - 2/3*n.
-n*(n - 1)*(9*n - 2)/3
Find j, given that 9/5*j + 3/5*j**5 + 6/5 + 0*j**4 - 12/5*j**3 - 6/5*j**2 = 0.
-1, 1, 2
Let t(r) be the second derivative of -r**4/4 - r**3/6 - 3*r. Let g(a) = a**2 + a + 1. Let l(f) = 2*g(f) + t(f). Factor l(s).
-(s - 2)*(s + 1)
Let g(u) = -39*u - 17 - 78*u**3 + 27*u**3 - 4*u + 6 - 107*u**2. Let z(f) = 13*f**3 + 27*f**2 + 11*f + 3. Let y(t) = -6*g(t) - 22*z(t). Factor y(o).
4*o*(o + 2)*(5*o + 2)
Let y be (-43782)/189 + (-2)/(-9). Let q = y + 232. Suppose -q - 2/7*l + 2/7*l**2 = 0. Calculate l.
-1, 2
Suppose -2*w + 16 = 4*b - 0*w, b + w - 2 = 0. Let m = 19/3 - b. Factor m*h**2 - h + 2/3.
(h - 2)*(h - 1)/3
Let k = 45 + -42. Let d(f) be the third derivative of 0*f + 0*f**5 + 0*f**k + 0 - 1/480*f**6 + 1/96*f**4 + 2*f**2. Factor d(q).
-q*(q - 1)*(q + 1)/4
Let u = 25 + -22. Let v(r) be the second derivative of 0 + 0*r**u - r - 1/30*r**5 + 0*r**2 + 0*r**4. Factor v(j).
-2*j**3/3
Let k(d) be the second derivative of 1/70*d**5 + 0 + 1/7*d**2 - 1/42*d**4 - 1/21*d**3 - 5*d. Suppose k(j) = 0. What is j?
-1, 1
Suppose -2*t = 3*m - 6 - 12, 5*t - 2*m = 7. Factor 4*x + x - 2*x - t*x**2.
-3*x*(x - 1)
Suppose 0 = 8*y - 54*y + 92. Solve 0*a + 2/3*a**3 + 2/3*a**y + 0 = 0 for a.
-1, 0
Let x be 9*-1 + 0/(-7). Let p(u) = -u - 7. Let z be p(x). Factor 0*q - 3*q**2 + 3 + 5 - z + 3*q.
-3*(q - 2)*(q + 1)
Let p be -1 - -3 - -1*1. Suppose w + 76 = 2*w. Solve 13*t**p + 16 - 72*t - w*t**3 + 9*t**3 - 5*t**2 + 113*t**2 = 0 for t.
2/3
Suppose 5*c - 55 = -3*s - 14, -8 = -2*c. Let g = -7 + s. Let 0*l**2 - 3*l**3 + 4*l**3 + g*l**2 = 0. What is l?
0
Let n(u) be the first derivative of -1/6*u**4 - 1/9*u**2 - 2/45*u**5 - 2/9*u**3 + 4 + 0*u. Factor n(j).
-2*j*(j + 1)**3/9
Let t(k) be the second derivative of 3*k**5/10 + 3*k**4/4 - 3*k**3/2 - 3*k**2 - 7*k. Let t(z) = 0. What is z?
-2, -1/2, 1
Let z be 0/(-1) - 4/(-2). Let f = 25 + -22. Let 3*x**3 + f + 9*x**z + 1 + 0*x**2 - 3*x**4 - 15*x + 2 = 0. What is x?
-2, 1
Let w(m) = 4*m**2 + 11*m + 7. Let g(d) = -12*d**2 - 34*d - 22. Let i(f) = -3*g(f) - 10*w(f). Factor i(r).
-4*(r + 1)**2
Let c be -2 + -21*(-2)/18. Solve 0*g + 0 + 1/3*g**3 + c*g**2 = 0.
-1, 0
Let f be 27/36*(-32)/(-108). Factor -f*n**2 + 0*n + 0 + 2/9*n**3.
2*n**2*(n - 1)/9
Let q = -351/2 - -189. Solve 3 + 21/2*x**2 + q*x = 0.
-1, -2/7
Let x(d) = 3*d**3 - 6*d**2 - 6*d. Let t(f) = 5*f - 2*f**3 + 0*f**2 - 2*f**2 + 6*f**2 + 2*f**2. Let z(l) = -6*t(l) - 5*x(l). What is j in z(j) = 0?
-2, 0
Let g be (2 - 56/10)/1. Let d = -49/15 - g. Determine j, given that 1/3*j**4 - d*j**5 - 2/3*j**2 + 2/3*j**3 - 1/3*j + 1/3 = 0.
-1, 1
Let c(u) be the second derivative of -2/21*u**7 + 0*u**2 + 0 - 2/15*u**6 + 4/3*u**3 + 5/3*u**4 + 3/5*u**5 - u. Factor c(t).
-4*t*(t - 2)*(t + 1)**3
Let j be (3 + 2)*16/(-5). Let d be (-2)/8 + (-84)/j. Let 8*v**4 - 2*v - 2*v**d + 4*v**2 + v**2 - 12*v**3 + 3*v**2 = 0. Calculate v.
0, 1
Let g(v) = -13*v**3 - 26*v**2 - 17*v - 4. Let h(c) = 0*c**2 + 0 + 2 + 13*c**2 + 9*c + 6*c**3. Let u(x) = -4*g(x) - 10*h(x). Factor u(i).
-2*(i + 1)*(i + 2)*(4*i + 1)
Let n(d) = -22*d**2 + 45*d - 10. Let w(s) = 111*s**2 - 225*s + 50. Let l(a) = 11*n(a) + 2*w(a). Solve l(i) = 0 for i.
1/4, 2
Let g(d) be the third derivative of 7*d**6/120 + 13*d**5/30 + 5*d**4/6 - 4*d**3/3 + 6*d**2. Factor g(x).
(x + 2)**2*(7*x - 2)
Let y(k) = -3*k**2 - 10*k + 7. Let a = -3 - -5. Let w(c) = 1 + 7*c - 6 - c**a + 3*c**2. Let i(p) = 7*w(p) + 5*y(p). Find j, given that i(j) = 0.
-1, 0
Let g(x) = 5*x**4