 2/3*g**2 - 4/3*g.
-2*g*(g - 2)*(g - 1)*(g + 1)/3
Let s(h) = -h**3 - 6*h**2 - 7*h - 4. Let a be s(-5). Let v be (-4)/4 + 10/a. What is b in -v*b**2 - 4/3*b - 2/3 = 0?
-1
Let b(u) be the first derivative of 25*u**6/39 + 68*u**5/13 + 349*u**4/26 + 136*u**3/13 + 36*u**2/13 + 3. Let b(p) = 0. What is p?
-3, -2/5, 0
Let k be (-141)/235 + (-196)/(-10). Solve -64/5*o - k*o**2 - 12/5 - 5*o**3 = 0.
-3, -2/5
Let o(r) = -r**3 + 7*r**2 - 6*r + 8. Let j be o(7). Let g be j/(-17) + (-2 - 0). Factor g*v + 1/4 - 1/4*v**2.
-(v - 1)*(v + 1)/4
Let g = -2 - -4. Let u be g - 2 - -5 - 1. Suppose 2 + 2*f + 0*f**2 + 0*f**4 + 2*f**5 - 2*f**2 - 4*f**3 - 2*f**2 + 2*f**u = 0. What is f?
-1, 1
Determine i so that -16*i**3 + 12*i**3 - 4*i**4 + 0*i**4 = 0.
-1, 0
Let j(r) be the first derivative of -1/120*r**5 + 1/480*r**6 + r**2 + 0*r + 0*r**3 + 1/96*r**4 + 2. Let x(g) be the second derivative of j(g). Factor x(k).
k*(k - 1)**2/4
Let w = 12 + -13. Let s be 4 + w - (-13 + 16). Solve 1/3*y**2 - 2/3*y + s + y**3 - 1/3*y**4 - 1/3*y**5 = 0.
-2, -1, 0, 1
Let t be (1064/16)/(-19)*12/(-35). Find b such that 4/5 + 2/5*b**2 + t*b = 0.
-2, -1
Let j(g) = 20*g**3 + 15*g**2 - 90*g - 55. Let i(q) = 3*q**3 + 2*q**2 - 13*q - 8. Let n(v) = 15*i(v) - 2*j(v). Factor n(f).
5*(f - 2)*(f + 1)**2
Suppose 6 + 2 = 4*p. Factor -3*u + p*u**2 + 2*u**3 + 5*u + 2*u**2.
2*u*(u + 1)**2
Factor m - 3/4*m**2 + 1/4*m**4 + 1 - 1/2*m**3.
(m - 2)**2*(m + 1)**2/4
Let i(g) be the first derivative of g**5/300 + g**4/30 + 2*g**3/15 + 3*g**2/2 - 4. Let q(a) be the second derivative of i(a). What is r in q(r) = 0?
-2
Let m(f) be the first derivative of 3 + 0*f + 2/3*f**3 + f**2. Find g such that m(g) = 0.
-1, 0
Let k(o) = -o**3 + 3*o + 2. Let p be k(-2). Let l(q) be the first derivative of 0*q + 0*q**3 - 1/12*q**p + 0*q**2 + 1. Let l(u) = 0. What is u?
0
Suppose 4/3*q - 10/3*q**2 + 0 - 8/3*q**4 - 22/3*q**3 = 0. What is q?
-2, -1, 0, 1/4
Let o(t) = -8*t**4 - 33*t**3 - 45*t**2 - 3*t + 3. Let y(u) = u**4 + u**3 + u - 1. Let g(s) = -o(s) - 3*y(s). Suppose g(b) = 0. What is b?
-3, 0
Let u(l) be the second derivative of l**6/165 - l**5/55 + 2*l**3/33 - l**2/11 - 3*l. What is b in u(b) = 0?
-1, 1
Let j(n) be the first derivative of -4*n**3/9 + 2*n**2/3 + 16*n - 20. Let j(w) = 0. What is w?
-3, 4
Factor 0 + 0*b**2 + 0*b + 4/7*b**3 - 2/7*b**4.
-2*b**3*(b - 2)/7
Let d = 673/456 + -7/38. Let t = -5/8 + d. Factor 0 + 4/3*z**2 - t*z - 2/3*z**3.
-2*z*(z - 1)**2/3
Let b(x) be the third derivative of x**7/1680 + x**6/80 + 9*x**5/80 - x**4/24 + 3*x**2. Let y(m) be the second derivative of b(m). Find p such that y(p) = 0.
-3
Suppose -33 = -22*l + 25*l. Let w(o) = 7*o**4 - o**2 + 6*o - 6. Let j(v) = 13*v**4 - 2*v**2 + 11*v - 11. Let f(t) = l*w(t) + 6*j(t). Factor f(p).
p**2*(p - 1)*(p + 1)
Let n(j) be the second derivative of -j**6/70 + 3*j**5/14 - 33*j**4/28 + 20*j**3/7 - 24*j**2/7 + 46*j. Find u such that n(u) = 0.
1, 4
Factor 0 + 2/5*d - 2/5*d**2.
-2*d*(d - 1)/5
Let g be (-6)/8 + 2*(-65)/(-120). Solve -2/3*j**3 - 2/3 + g*j + 4/3*j**2 + 1/3*j**5 - 2/3*j**4 = 0 for j.
-1, 1, 2
Let t be 7/(-18)*(-33)/770. Let i(r) be the third derivative of 0*r + t*r**5 + 2*r**2 + 1/240*r**6 + 0*r**4 + 0*r**3 + 0. Factor i(w).
w**2*(w + 2)/2
Let j(p) be the first derivative of 0*p + 1/3*p**3 - 1/2*p**2 - 1. Solve j(b) = 0.
0, 1
Let f = 14 - 11. Find x such that -8*x**5 + 4*x**5 - x**2 - 3*x**2 - 12*x**f - 12*x**4 = 0.
-1, 0
Let u(a) = 10*a**2 - 3*a. Let g(p) = p. Let x(k) = -3*k**2 - 3*k. Let w(o) = 4*g(o) + x(o). Let i(l) = -2*u(l) - 7*w(l). Suppose i(y) = 0. Calculate y.
0, 1
Let p(s) = -7*s + 20*s - 7*s + 1 + s**2. Let c(r) = -2*r**2 - 11*r - 1. Let j(d) = 4*c(d) + 7*p(d). Determine n, given that j(n) = 0.
-3, 1
Factor 0*c - 2/3*c**3 + 2/3*c**2 + 0.
-2*c**2*(c - 1)/3
Let t(i) be the second derivative of -i**4/60 + i**3/30 + i**2/5 + 9*i - 2. Find n such that t(n) = 0.
-1, 2
Let v(a) be the second derivative of -a**7/126 + 2*a**6/45 - a**5/12 + a**4/18 + 25*a. Find k, given that v(k) = 0.
0, 1, 2
Find i, given that 4/7*i + 4/7*i**2 + 0 = 0.
-1, 0
Suppose -9 = -5*v + 26. Factor -9*g - 4*g**2 - 4 + 6*g**2 + v*g.
2*(g - 2)*(g + 1)
Let h(d) = -7*d**4 + 3*d**3 - 9*d**2 - 7*d - 6. Let x(z) = z**4 - z**3 + z**2 + z + 1. Let g(j) = h(j) + 6*x(j). Factor g(o).
-o*(o + 1)**3
Let z(l) = -3*l**2 + l**4 + 2*l**2 + 2*l**2 - 1. Let x(s) = 4*s**4 + 8*s**2 - 6. Let m = 1 - 2. Let h(a) = m*x(a) + 6*z(a). Find v such that h(v) = 0.
-1, 0, 1
Let v(p) be the first derivative of -p**6/18 + p**4/4 - 2*p**3/9 - 49. Find f, given that v(f) = 0.
-2, 0, 1
Let i = 12 - 11. Let q = 6 - i. Solve -1/4*o + 1/4 + 1/4*o**4 - 1/2*o**2 + 1/2*o**3 - 1/4*o**q = 0.
-1, 1
Let y(n) be the second derivative of 6*n**7/35 - 2*n**6/25 - n**5/5 - n**4/15 + 8*n. Determine m, given that y(m) = 0.
-1/3, 0, 1
Let z(t) be the first derivative of -t**8/1680 - t**7/280 - t**6/120 - t**5/120 - t**3 + 2. Let h(k) be the third derivative of z(k). Factor h(i).
-i*(i + 1)**3
Let b = -1 + 4. Determine l, given that -l**4 + l**4 - 2*l**b + l + l**5 = 0.
-1, 0, 1
Let w(f) = 3*f**2 + 42*f. Let s be w(-14). Factor -g + s - 5/4*g**3 - 1/4*g**4 - 2*g**2.
-g*(g + 1)*(g + 2)**2/4
Let w(m) be the second derivative of -8*m**6/15 - 7*m**5/5 + 2*m**4/3 - 39*m. Let w(a) = 0. What is a?
-2, 0, 1/4
Suppose -4*q**2 + 1/3*q**5 + 0 + 4/3*q - 2*q**4 + 13/3*q**3 = 0. What is q?
0, 1, 2
Let a = 298 - 886/3. Find f, given that a + 2/3*f**2 - 8/3*f = 0.
2
Let c(s) = -s**4 + 2*s**2 - 8. Let m = -27 + 13. Let p(g) = -1. Let d be (-2)/(-4)*2*2. Let k(u) = d*c(u) + m*p(u). Let k(o) = 0. Calculate o.
-1, 1
Let g(o) be the second derivative of 0*o**2 + 4*o + 0 - 1/8*o**4 - 1/4*o**3. Solve g(r) = 0 for r.
-1, 0
Let i(x) = -x**3 - x**2 - x. Let p(v) = -8*v**3 - 10*v**2 - 5*v. Let g(y) = -6*i(y) + p(y). Let d(f) = 3*f**3 + 3*f**2. Let r(k) = 5*d(k) + 6*g(k). Factor r(c).
3*c*(c - 2)*(c - 1)
Let t(c) be the first derivative of -4*c - 1/2*c**3 - 1/4*c**4 - 1 + 0*c**2. Let j(p) be the first derivative of t(p). Factor j(h).
-3*h*(h + 1)
Let r(m) be the third derivative of -m**10/453600 + m**9/90720 + m**5/10 - m**2. Let z(o) be the third derivative of r(o). Factor z(a).
-a**3*(a - 2)/3
Let o be -4 + 18/4 + (-3 - -3). Factor o*r**4 + 1/2*r**5 - r**2 + 1/2 + 1/2*r - r**3.
(r - 1)**2*(r + 1)**3/2
Let x(a) be the second derivative of a**6/3 + 5*a**5/4 + 5*a**4/4 - 5*a**3/6 - 5*a**2/2 + 14*a. Factor x(o).
5*(o + 1)**3*(2*o - 1)
Let z(m) be the first derivative of 2/35*m**5 + 5 + 10/21*m**3 + 2/7*m**2 + 2/7*m**4 + 0*m. Factor z(j).
2*j*(j + 1)**2*(j + 2)/7
Let z(u) be the third derivative of -1/24*u**4 - 1/60*u**5 + 1/210*u**7 - 3*u**2 + 1/120*u**6 + 0 + 0*u**3 + 0*u. Factor z(o).
o*(o - 1)*(o + 1)**2
Suppose 11*w + 0*w - 3*w - 6 + 103*w**2 - 105*w**2 = 0. Calculate w.
1, 3
Let a be 17 + -18 - 1/(3/(-7)). Let h(y) be the first derivative of -y**2 + 2/9*y**3 - 2 + a*y. Factor h(l).
2*(l - 2)*(l - 1)/3
Let k(i) = -i**2 + i + 1. Let q(s) = 2*s**3 + 16*s**2 - 12*s - 12. Let z(o) = 12*k(o) + q(o). Find w such that z(w) = 0.
-2, 0
Let w(a) = a**5 - a**4 - a**3 - a**2 - a - 1. Let p(v) = v**5 - 16*v**4 - 6*v**3 + 4*v**2 - v - 6. Let x(t) = p(t) - 6*w(t). Determine c so that x(c) = 0.
-1, 0, 1
Factor 3*x**2 + 0*x + 0 - 23/3*x**4 - 10*x**3 - 4/3*x**5.
-x**2*(x + 3)**2*(4*x - 1)/3
Let m(w) be the third derivative of -1/24*w**3 - 2*w**2 + 0*w**6 + 0*w**4 + 0*w + 1/120*w**5 - 1/840*w**7 + 0. Let m(p) = 0. What is p?
-1, 1
Let w be -2 + 0 + 2 - (2 - 6). Factor 0 + 24/11*r**3 - 10/11*r**w - 8/11*r**2 + 0*r.
-2*r**2*(r - 2)*(5*r - 2)/11
Let d(n) be the third derivative of 1/4*n**3 + 0 + 0*n + 1/160*n**6 - 8*n**2 + 5/32*n**4 + 1/20*n**5. Solve d(r) = 0.
-2, -1
Suppose -7*h + 32 = h. Let 0 + 14*w**3 + 0*w - 49/2*w**h - 2*w**2 = 0. Calculate w.
0, 2/7
Factor -5/4*j - j**2 - 1/4.
-(j + 1)*(4*j + 1)/4
Let w(d) = -d**5 + 4*d**4 + 4*d**2 + 5*d - 6. Let y(k) = k**3 + k - 1. Let x(r) = w(r) - 6*y(r). Find g, given that x(g) = 0.
0, 1
Let d(i) = 2*i**2 - 8*i + 6. Let y be d(5). Suppose 0 = -3*x + c + 10, 0 = -5*x + 3*c - c + y. Factor -x*m**2 + 1 + 0*m**2 + 2*m**3 - 4*m**5 + 2*m**5 + 3*m**4.
-(m - 1)**3*(m + 1)*(2*m + 1)
Suppose 0 = 27*x - 90 + 9. Factor 69/2*s**4 - 21/2*s**5 + 39/2*s**2 - 81/2*s**3 + 0 - x*s.
-3*s*(s - 1)**3*(7*s - 2)/2
Let n(t) be the second derivative