h*(4*h + 1)*(7*h - 2)/9
Let f(a) be the first derivative of -26*a**3/21 - 11*a**2/7 + 4*a/7 + 29. Find s, given that f(s) = 0.
-1, 2/13
Factor -2*o**2 + 5*o**2 + 4*o**3 + o**2.
4*o**2*(o + 1)
Let p(k) be the second derivative of -k**5/150 + k**3/45 - 20*k. Find s, given that p(s) = 0.
-1, 0, 1
Let w(b) be the first derivative of -2*b - b**4 + 1/3*b**6 + b**2 - 2/5*b**5 + 4/3*b**3 + 5. Determine p so that w(p) = 0.
-1, 1
Let q(p) be the first derivative of 2/5*p**5 + 0*p + 0*p**2 + 0*p**4 + 5 + 0*p**3. Factor q(o).
2*o**4
Let z be -4 - -5 - (-249)/(-252). Let l(g) be the third derivative of 0*g - 2*g**2 + 0 - 2/21*g**3 + 1/84*g**4 + 4/105*g**5 + z*g**6. Factor l(d).
2*(d + 1)**2*(5*d - 2)/7
Factor 0*y**3 - 3/2*y**2 + 3/4*y**4 + 0*y + 3/4.
3*(y - 1)**2*(y + 1)**2/4
Let s(o) be the first derivative of 2*o**3/3 - o**2 - 4*o - 8. Factor s(x).
2*(x - 2)*(x + 1)
Let v(z) = 15*z**4 - 75*z**3 + 1439*z**2 - 10648*z + 29295. Let m(p) = 7*p**4 - 38*p**3 + 720*p**2 - 5324*p + 14647. Let q(h) = -13*m(h) + 6*v(h). Factor q(k).
-(k - 11)**4
Let y(u) = -u**3 - 4*u**2 + 6*u. Let m(p) = -p**3 - p**2 + p. Let v(f) = -6*m(f) + y(f). Solve v(i) = 0 for i.
-2/5, 0
Let a(g) be the second derivative of g**6/180 + 3*g. Factor a(o).
o**4/6
Find m, given that 3/2*m + 1/2*m**2 + 1 = 0.
-2, -1
Let h = -77 + 79. Suppose 3/5*s**5 + 12/5*s**h + 18/5*s**3 + 0 - 24/5*s - 3*s**4 = 0. Calculate s.
-1, 0, 2
Suppose 6*m = 2*m + 16. Factor -11*z + 15*z**m + 3*z**5 + 5*z**3 - 13*z + 13*z**3 - 12*z**2.
3*z*(z - 1)*(z + 2)**3
Let f(o) be the first derivative of -3*o**3 + 15*o**2/2 - 6*o + 15. Factor f(i).
-3*(i - 1)*(3*i - 2)
Let m(z) be the third derivative of z**7/10 - 13*z**6/120 - 13*z**5/40 - z**4/4 - 2*z**3/3 + z**2. Let j(l) be the first derivative of m(l). Factor j(k).
3*(k - 1)*(4*k + 1)*(7*k + 2)
Let d(w) be the third derivative of -w**7/6300 + w**6/900 - w**5/300 + w**4/12 - 3*w**2. Let q(v) be the second derivative of d(v). Factor q(j).
-2*(j - 1)**2/5
Let w be (-2)/5 - (-12)/5. Find x, given that -2*x**w + 6*x**2 - 3*x**2 + x**2 - 2*x = 0.
0, 1
Let u(c) be the third derivative of c**9/5040 - c**8/1680 + c**7/1680 - c**5/12 + c**2. Let t(i) be the third derivative of u(i). Find y, given that t(y) = 0.
0, 1/2
Let x(r) = -r - 1. Let p(g) = g**2 - 4*g - 4. Let v(k) = p(k) - 4*x(k). Let v(l) = 0. What is l?
0
Let s(o) be the second derivative of o**4/12 + o**3/2 + o**2 - 39*o. Factor s(d).
(d + 1)*(d + 2)
Let b(z) = z**3 + 6*z**2 - 8*z - 1. Let i be b(-7). Let o be 1/i - (-10)/84. Solve 0 - o*l**2 - 2/7*l = 0 for l.
-1, 0
Let n(p) be the third derivative of -3*p**8/112 - p**7/14 + 17*p**6/120 + 19*p**5/60 - p**4/3 - 2*p**3/3 + 34*p**2. Solve n(u) = 0.
-2, -1, -1/3, 2/3, 1
Let u be 524/(-196) + (0 - -3). Let f = -2/49 + u. Find h such that -2/7*h**5 + 2/7*h**4 - 2/7*h**2 + 0*h + f*h**3 + 0 = 0.
-1, 0, 1
Suppose -3*g + 68 = 4*r, -6*r + 3*r + g + 51 = 0. Suppose -5*t = -3*n + 31, n - 4*t = -t + r. Factor -2*j**n - 2*j**5 + 5*j**4 - 6*j**3 + 4*j**2 + j**4.
-2*j**2*(j - 1)**3
Suppose 97*k = 92*k - 5. Let q(a) = -3*a**3 - 8*a**2 + a - 6. Let o(t) = t + 3*t**2 - 4*t**2 + 1 + t**3 + 2*t**2. Let h(z) = k*q(z) - 4*o(z). Factor h(d).
-(d - 2)*(d - 1)**2
Let n be (-2 - (-9 - -4))*(-2)/(-12). Factor 0 - 1/4*h**2 + n*h.
-h*(h - 2)/4
What is t in -1/4*t**2 + 3/4*t - 1/2 = 0?
1, 2
Let w(m) be the second derivative of -m**4/48 - m**3/6 - m**2/2 - 2*m. Determine a so that w(a) = 0.
-2
Find d such that 20*d**2 + 4*d - 580*d**3 + 575*d**3 - 4*d = 0.
0, 4
Let p(l) be the first derivative of l**6/3 - 6*l**5/5 + 8*l**3/3 + 9. Factor p(w).
2*w**2*(w - 2)**2*(w + 1)
Let f(z) be the third derivative of -z**6/360 + z**5/20 - z**4/3 + 8*z**3/9 - 15*z**2. Determine t so that f(t) = 0.
1, 4
Let j(u) = -28*u**3 + 64*u**2 - 48*u + 12. Let m(y) = 28*y**3 - 64*y**2 + 47*y - 11. Let t(p) = -3*j(p) - 4*m(p). Suppose t(a) = 0. Calculate a.
2/7, 1
Let s(y) be the third derivative of 1/12*y**4 + 0*y + 4*y**2 + 0*y**3 - 1/30*y**5 + 0. What is t in s(t) = 0?
0, 1
Let n(u) be the third derivative of -u**6/30 - 11*u**5/60 + u**4/8 + 3*u**2. Factor n(q).
-q*(q + 3)*(4*q - 1)
Let l(v) = 3*v**2 - 18*v + 27. Let o = -12 - -8. Let h(b) = -15*b**2 + 90*b - 135. Let c(m) = o*h(m) - 21*l(m). Find t, given that c(t) = 0.
3
Suppose -3*r - 4*i = 2, 2*r + i - 12 = 5*i. Factor s**3 + 27*s**2 + 0 - s - s**4 + 0 - 26*s**r.
-s*(s - 1)**2*(s + 1)
Suppose 33 = -5*o + 2*o. Let n be (8 - 7)/(o/(-4)). Suppose -10/11*m**3 + 6/11*m**4 - 2/11*m**2 + 10/11*m - n = 0. Calculate m.
-1, 2/3, 1
Let l = 10/31 + -8/217. Let q(z) be the first derivative of 2/7*z**3 + 5/14*z**4 - 2 + 0*z - l*z**2. Factor q(u).
2*u*(u + 1)*(5*u - 2)/7
Suppose n - 1/4*n**4 + 5/4*n**2 + 1/4*n**5 - 5/4*n**3 - 1 = 0. Calculate n.
-2, -1, 1, 2
Let s(b) = 15*b**3 - 20*b**2. Let v(l) = -l**4 + 15*l**3 - 19*l**2 + l. Let p(y) = 4*s(y) - 5*v(y). Factor p(x).
5*x*(x - 1)**3
What is m in 4/5*m - 2/5*m**2 - 6/5*m**3 + 0 = 0?
-1, 0, 2/3
Let s(a) be the third derivative of -a**5/60 + a**4/6 - 2*a**3/3 + 2*a**2. Factor s(b).
-(b - 2)**2
Let h(u) = -u**2 + 1. Let i be h(1). Let r be 0*(i - 2/(-6)). Factor -3/2*p**3 + 0*p + r - 1/2*p**5 + 1/2*p**2 + 3/2*p**4.
-p**2*(p - 1)**3/2
Let c(r) be the first derivative of -r**5/120 - r**4/36 - r**3/36 - 2*r - 2. Let t(h) be the first derivative of c(h). Factor t(x).
-x*(x + 1)**2/6
Factor -86*z**2 - 74*z**2 + 864 - 2*z**4 + 16*z**2 - 32*z**3.
-2*(z - 2)*(z + 6)**3
Suppose -3*d + d = -0*d. Let g(c) be the second derivative of d*c**3 - 1/6*c**4 - 3/10*c**5 + 0 - 2/15*c**6 - 3*c + 0*c**2. Factor g(l).
-2*l**2*(l + 1)*(2*l + 1)
Suppose 0 = -25*x + 7*x + 54. Determine p, given that -1 + 3/4*p**2 - 1/4*p**x + 0*p = 0.
-1, 2
Let i = -2 + 6. Suppose 6*b**5 - 4*b**2 + 25*b**4 + 0*b**2 + 10*b**3 - i*b**3 - 9*b**4 = 0. Calculate b.
-2, -1, 0, 1/3
Suppose -3*o**3 + 30*o - 3*o**3 - 4*o**2 + o**3 - o**2 = 0. What is o?
-3, 0, 2
Let s = 3155/5558 - -3/794. Determine h so that -2/7 - 4/7*h**3 + 0*h**2 + 2/7*h**4 + s*h = 0.
-1, 1
Let v(x) = 8*x**2 + 6. Let i(p) = -p**2 - 1. Let j(r) = 6*i(r) + v(r). Solve j(t) = 0 for t.
0
Let o(p) be the second derivative of p**7/7 + p**6/20 - 3*p**5/5 - p**4/4 + p**3 + 3*p**2/4 - 5*p. Solve o(b) = 0.
-1, -1/4, 1
Let k(i) = -i**3 + 4*i**2 - 2*i + 3. Let d be k(4). Let p(g) = -g**2 - 5*g. Let f be p(d). Let f*v**2 - 2/7*v**3 + 0 + 0*v + 0*v**4 + 2/7*v**5 = 0. Calculate v.
-1, 0, 1
Let g(r) = -r**2. Let v(a) = a**2 + 6*a. Let k(d) = 4*g(d) + v(d). Factor k(l).
-3*l*(l - 2)
Suppose -46*i = -54*i + 56. Let p(o) be the first derivative of -12*o + 0*o**2 - 1 + 3/4*o**4 + i*o**3 - 9/5*o**5 - 1/2*o**6. Solve p(j) = 0.
-2, -1, 1
Factor 2/3*c**2 - 10/9*c + 4/9 + 2/9*c**3 - 2/9*c**4.
-2*(c - 1)**3*(c + 2)/9
Let d(t) be the third derivative of -7*t**2 + 0 + 3/2*t**3 + 3/20*t**6 + 0*t + 3/5*t**5 + 5/4*t**4 + 1/70*t**7. Find s such that d(s) = 0.
-3, -1
Determine z, given that 0 + 5/2*z - 1/4*z**3 - 9/4*z**2 = 0.
-10, 0, 1
Let z(n) be the second derivative of 0 - 3*n + 0*n**3 + 0*n**2 - 1/20*n**5 - 1/15*n**6 + 1/12*n**4. Factor z(y).
-y**2*(y + 1)*(2*y - 1)
Let y(b) = -28*b**2 - 24*b - 24. Let x(m) = -m**2 - m - 1. Let d(r) = 24*x(r) - y(r). Factor d(h).
4*h**2
Let o(x) = -3*x**2 - 10*x - 5. Let y(c) = -11*c**2 - 40*c - 20. Let t(m) = 9*o(m) - 2*y(m). Factor t(g).
-5*(g + 1)**2
Suppose x + 3*p = 15, -5 = 3*x + 2*p - 3*p. Factor x*k + 1/3 - k**2 + 2/3*k**3.
(k - 1)**2*(2*k + 1)/3
Let j = 0 + 2. Let -2 + 56*a**2 + a**3 - 11*a**3 - j - 52*a**2 + 10*a = 0. What is a?
-1, 2/5, 1
Let a be (-3 - (-282)/90)/8. Let o(t) be the third derivative of 0*t + 0*t**3 + 1/150*t**5 + 0 + a*t**4 - 2*t**2. Suppose o(y) = 0. What is y?
-1, 0
Suppose 20 - 2 = 6*v. Let f(o) be the first derivative of -3 + 0*o + 1/5*o**5 - 1/4*o**4 + 1/2*o**2 - 1/3*o**v. Find b such that f(b) = 0.
-1, 0, 1
Suppose 49 + 6*b - 2*b**2 - 49 = 0. Calculate b.
0, 3
Let j(c) be the first derivative of 3/16*c**4 + 1/4*c**5 - 1 + 0*c**2 + 0*c - 1/6*c**3. Suppose j(i) = 0. Calculate i.
-1, 0, 2/5
Determine b, given that -4*b - 20/7*b**2 - 4/7*b**3 - 12/7 = 0.
-3, -1
Suppose 1 = -s + 3. Let j be s/(-4) - 1347/(-6). Factor -162*f**5 - 60*f**3 - j*f - 594*f**4 - 804*f**3 - 32 - 269*f**2 - 355*f**2.
-2*(f + 1)*(3*f + 2)**4
Suppose 0 = 7*c - 129 + 31. Let m = -11 + c. Factor 4/5*l**4 + 0*l + 