 + 1/2*m**2 + 0*m + 0 + 7/2*m**p = 0. What is m?
-1, -1/3, 0
Suppose -5*j - 9 = -2*p, 5*j + 12 = 4*p - 3*p. Let s be (j + 1)*(-1 + 0). Determine f so that -3 + 8*f - 9*f**2 - 17*f - f**3 - s*f**3 = 0.
-1
Let y(m) = 2*m. Let w be y(3). Factor -2*k**3 - k**2 + 2*k**2 + 6*k**3 - w*k**2 + k.
k*(k - 1)*(4*k - 1)
Let s be 3 - 0 - (-5)/5. Factor o**2 - o**s - 1/2*o**5 + 0*o**3 + 1/2*o + 0.
-o*(o - 1)*(o + 1)**3/2
Suppose -3*m + 0*m - 3 = 0. Let v(h) = -h**5 + 0 + h**4 + 0*h**5 - 1. Let t(i) = -3*i**5 + 2*i**4 + i**3 - 2. Let y(l) = m*t(l) + 2*v(l). Factor y(n).
n**3*(n - 1)*(n + 1)
Factor -5*r**3 + 38*r**2 + 30*r**2 + 77*r**3 + 4*r**4.
4*r**2*(r + 1)*(r + 17)
Let j(g) be the third derivative of -g**7/525 - g**6/100 - g**5/50 - g**4/60 + g**2. Find i, given that j(i) = 0.
-1, 0
Solve 38*i - 53*i + 10 - 4*i**2 + 9*i**2 = 0 for i.
1, 2
Suppose -88*c + 30 = -73*c. Let -1/3 - 5/6*y + y**c + 3/2*y**3 = 0. Calculate y.
-1, -1/3, 2/3
Let a(d) be the second derivative of d**7/1260 - d**6/135 + d**5/45 + d**3/2 + 4*d. Let o(v) be the second derivative of a(v). Factor o(t).
2*t*(t - 2)**2/3
Let a(q) be the first derivative of -7*q**5/120 + 5*q**4/48 + q**3/6 - q**2 - 2. Let y(i) be the second derivative of a(i). Factor y(o).
-(o - 1)*(7*o + 2)/2
Let g(c) = -33*c**3 + 21*c**2 + 57*c - 3. Let y(i) = -8*i**3 + 5*i**2 + 14*i - 1. Let u(p) = 5*g(p) - 21*y(p). Determine h so that u(h) = 0.
-2, 1
Let u be (456/16)/((-2)/(-4)). Let l = u - 284/5. Solve l*j**3 - 1/5*j + 0 + 0*j**2 = 0 for j.
-1, 0, 1
Let j(a) be the second derivative of a**8/9240 - a**6/990 + a**4/132 + 2*a**3/3 - 2*a. Let b(c) be the second derivative of j(c). Factor b(d).
2*(d - 1)**2*(d + 1)**2/11
Suppose 3*u + 5*b = -75, 0*u + 2*b = 5*u + 156. Let l be (-13)/u + 3/18. Let 0*p + l*p**2 + 0 = 0. What is p?
0
Factor 2*c**4 - 2*c**2 - c**2 + c**2.
2*c**2*(c - 1)*(c + 1)
Let q(p) = p + 9. Let g = 9 - 14. Let m be q(g). Factor 12*y**2 - 8*y**3 - 2 - 2*y**m + 4 - 8*y + 4*y**4.
2*(y - 1)**4
Solve 7*k**3 - 33*k - 24*k - 2*k**3 + 52*k = 0.
-1, 0, 1
Let g(h) = 9*h**2 + 4*h - 5. Let y(t) = -4*t**2 - 2*t + 2. Suppose 0 = -4*k + 2 + 26. Let n(p) = k*y(p) + 3*g(p). Factor n(d).
-(d + 1)**2
Let j(x) = 15*x**2 + 166*x + 15. Let i be j(-11). Factor 1/3*z**2 + 0 + 0*z**3 - 1/3*z**i + 0*z.
-z**2*(z - 1)*(z + 1)/3
Let k = -39/8 - -21/4. Let o(r) be the first derivative of 1/12*r**3 + 2 + 1/2*r - k*r**2. Suppose o(w) = 0. What is w?
1, 2
Let j(w) be the first derivative of w**4/18 + 8*w**3/9 + 16*w**2/3 + 128*w/9 + 2. Determine u so that j(u) = 0.
-4
Let a(v) be the first derivative of -7*v**6/120 - v**5/30 + 7*v**4/24 + v**3/3 + 7*v**2/2 + 10. Let c(w) be the second derivative of a(w). Factor c(m).
-(m - 1)*(m + 1)*(7*m + 2)
Let h(p) be the third derivative of -p**5/100 + p**4/10 - 3*p**3/10 + 8*p**2. Factor h(k).
-3*(k - 3)*(k - 1)/5
Let f = 428 - 1711/4. Factor f + 1/4*g**4 + 3/2*g**2 + g**3 + g.
(g + 1)**4/4
Let n be ((-48)/216)/(2/(-8)). Factor -2/9 - n*j**3 + 8/9*j + 2/9*j**2.
-2*(j - 1)*(j + 1)*(4*j - 1)/9
Suppose p = 213 - 210. Solve -3/7*n**p + 0 + 0*n + 0*n**2 = 0.
0
Let v(x) = x + 9. Let r be v(-5). Let d(h) be the first derivative of 0*h + 1/5*h**5 + 0*h**r - 1/3*h**3 + 0*h**2 + 2. Solve d(l) = 0.
-1, 0, 1
Let n(a) = a**3 + 2*a**2 - a + 4. Let i be n(-3). Let g be 1/((-1 - i)/5). Solve -h**4 - 4*h**3 - g*h**2 + 0*h**2 + 4*h**2 + 2*h**3 = 0 for h.
-1, 0
Suppose -3 = -2*x + 15. Let n = x + -6. Factor -1/5*p**2 + 0*p + 0 + 1/5*p**n.
p**2*(p - 1)/5
Let p(y) be the first derivative of -y**5/10 - 11*y**4/24 - 13*y**3/18 - 5*y**2/12 + 46. Solve p(n) = 0.
-5/3, -1, 0
Let q = -3 + -1. Let x be (-3)/(-6)*q/(-7). Factor 2/7*j + 4/7*j**2 - 4/7*j**4 + 0 + 0*j**3 - x*j**5.
-2*j*(j - 1)*(j + 1)**3/7
Let k(b) be the first derivative of 2*b**6/3 - 16*b**5/5 + 4*b**4 + 8*b**3/3 - 10*b**2 + 8*b + 7. Factor k(d).
4*(d - 2)*(d - 1)**3*(d + 1)
Suppose -m = 3*r + m - 11, m = 1. Let o(d) be the first derivative of -1/15*d**r - 2/5*d - 3/10*d**2 + 1. What is w in o(w) = 0?
-2, -1
Let q(l) = -l - 3. Suppose 5 + 13 = -3*u. Let x be q(u). What is o in 1 - o + 0*o + o**x + o**2 - 2 = 0?
-1, 1
Let c(q) be the third derivative of -q**7/252 - q**6/180 + q**4/8 + q**2. Let t(z) be the second derivative of c(z). Find u, given that t(u) = 0.
-2/5, 0
Let p(v) be the first derivative of -3*v**4/32 + 3*v**3/8 + 23. Determine y, given that p(y) = 0.
0, 3
Let h(b) be the first derivative of 5 - 2/9*b**3 + 1/12*b**4 - 1/6*b**2 + 2/3*b. Factor h(o).
(o - 2)*(o - 1)*(o + 1)/3
Let u(i) be the second derivative of -1/4*i**4 + 0*i**2 + 0 + 0*i**3 + 4*i. Factor u(y).
-3*y**2
Let w(s) = -s - 2. Let c be w(-2). Suppose 5*v + r - 15 = c, -2*v + 2 = -3*r - 4. Factor 6*n**2 - n**v - 1 + 0*n**2 - 5*n**2 + n.
-(n - 1)**2*(n + 1)
Let k(m) = -m**2 - 5*m - 3. Let p be k(-2). Let b(u) be the first derivative of 3 - p*u**2 + 4*u + 2/3*u**3. Factor b(h).
2*(h - 2)*(h - 1)
Let w be 2/4*(2 - 4). Let y be 6*(w/3)/(-1). Find v such that -1 + y*v**2 + 0 + 3*v**2 - 4*v**2 = 0.
-1, 1
Let -2*w**2 + 3*w**2 + w + 4 - 3*w - 12 = 0. Calculate w.
-2, 4
Suppose -3*o - 4*k = 4, o = -3*o - 2*k - 2. Let o + 14/9*p**3 + 4/9*p**2 + 0*p = 0. Calculate p.
-2/7, 0
Suppose 0 = 4*q - o + 3*o - 24, 5*q - 30 = -4*o. Factor 5*l**3 - q*l**2 - 38*l - 3*l**3 + 38*l.
2*l**2*(l - 3)
Let r(w) be the third derivative of w**9/30240 - w**7/1680 + w**6/720 + w**4/8 + 4*w**2. Let h(n) be the second derivative of r(n). Factor h(t).
t*(t - 1)**2*(t + 2)/2
Let f = -6 - -8. Solve -16*t + 86*t**3 - 57*t**4 - 70*t**5 + 1 - 9 + 70*t**f - 5*t**4 = 0.
-1, -2/7, 2/5, 1
Find c such that -3*c**5 + 3*c**5 + 16*c + 2*c**5 - 14*c**4 - 40*c**2 + 0*c**5 + 36*c**3 = 0.
0, 1, 2
Let b(y) be the first derivative of y**5/120 + y**2 - 1. Let r(a) be the second derivative of b(a). Determine o, given that r(o) = 0.
0
Let n(t) = 7*t**4 - t**3 - 5*t**2 - 15*t - 2. Let d(r) = r**4 - r**3 + r**2 + 1. Let l(k) = -4*d(k) + n(k). Suppose l(a) = 0. What is a?
-1, 2
Let -a**2 - 2*a + 3*a - 7*a + 3*a**2 = 0. What is a?
0, 3
Let j be 12/(-30) + 1/(90/41). Let u(h) be the second derivative of -j*h**4 + 0 - 3*h - 1/3*h**2 - 2/9*h**3. Determine n, given that u(n) = 0.
-1
Let d = -1/150 + 38/75. Let y + 1/4 + 5/4*y**2 + d*y**3 = 0. Calculate y.
-1, -1/2
Suppose 3*n = 4*w + 13 + 12, -5*n + 30 = 5*w. Suppose 5*x = n*x - 6. Let 0 - 1/4*t**2 - 1/4*t**4 + 1/2*t**x + 0*t = 0. What is t?
0, 1
Let n = -7/2 - -4. Let i(f) be the first derivative of 2/15*f**5 + n*f**4 + 1/3*f**2 + 0*f + 2 + 2/3*f**3. Factor i(y).
2*y*(y + 1)**3/3
Let k(v) be the first derivative of 0*v - 2/5*v**5 + 0*v**4 + 1 - 1/2*v**2 + 2/3*v**3 + 1/6*v**6. Factor k(z).
z*(z - 1)**3*(z + 1)
Factor 4*g**2 - 7*g**2 - 2*g + 6*g**4 + 3*g**3 - 3*g**4 - g.
3*g*(g - 1)*(g + 1)**2
Factor -12*r + 2*r**3 + 28*r**5 - 10*r**4 - 23*r**5 + 32*r - 17*r**3 + 20*r**2.
5*r*(r - 2)**2*(r + 1)**2
Let u(w) be the first derivative of -3*w**5/5 + w**4/2 + 3*w**3 - 4*w - 6. Factor u(y).
-(y - 2)*(y + 1)**2*(3*y - 2)
Let n(c) = 30*c**3 + 42*c**2 + 12*c. Let w(y) = -45*y**3 - 63*y**2 - 18*y. Let u(f) = -f**2 - 10*f - 8. Let x be u(-8). Let a(g) = x*n(g) + 5*w(g). Factor a(h).
3*h*(h + 1)*(5*h + 2)
Let o(n) = n**2 + 7*n + 9. Let q be o(-6). Suppose 3*y - 5*c - 25 - 9 = 0, -3*y - c = -4. Factor -y*b**q - 3*b**3 + 3*b**3 + b**2 + 2*b**2.
-3*b**2*(b - 1)
Let w be -14*(-3)/(63/6). Let b be -1*0*(-1)/w. Factor 2/5*j**5 + 0*j + b + 24/5*j**3 + 12/5*j**4 + 16/5*j**2.
2*j**2*(j + 2)**3/5
Suppose 3*x + 6 = -4*w, -2*w + 6 = 2*w - 3*x. Factor 0 + 1/3*t**2 + w*t.
t**2/3
Let b(j) be the first derivative of -1/300*j**6 - 1/150*j**5 + 0*j**3 + 0*j**4 - 2 - 1/2*j**2 + 0*j. Let q(u) be the second derivative of b(u). Factor q(w).
-2*w**2*(w + 1)/5
Suppose -6/5*g**2 - 3/5*g**3 + 0 - 3/5*g = 0. What is g?
-1, 0
Suppose n - 6*n = 0. Suppose -m + 5*m - 8 = n. Factor 2 - 6*h - 8 + 3 - h**m - 6.
-(h + 3)**2
Let t = 965/363 - -1/121. Let f = 484/717 + -2/239. Determine i so that -4/3*i**2 + f*i - t*i**4 - 14/3*i**3 + 0 = 0.
-1, 0, 1/4
Let w(a) = -a**3 - 16*a**2 - a - 14. Let t be w(-16). Let d(n) be the first derivative of -1/3*n**3 + 0*n - 1 - n**t. Factor d(h).
-h*(h + 2)
Let p(t) = -6*t**4 - 10*t**3 + 10*t**2 + 42*t + 22. Let y(x) = -7*x**4 - 9*x**3 + 9*x**2 + 41*x + 21. Let n(q) = -3*p(q) + 2*y(q). Find k, given that n(k) = 0.
