
Let g be 14/4 + (-4)/8. Suppose z + g = 4*n + 4, -1 = n - z. Factor 8*r - 1 - 4*r + n*r**2 + 2*r**3 - 5*r**2.
(r - 1)**2*(2*r - 1)
Let y(h) = -h**3 - h**2 + h. Let r(j) = j**3 + 5*j**2 - j - 2. Let s = 13 + -11. Let d be (-7 + 4 + s)/(-1). Let x(a) = d*r(a) + 3*y(a). Factor x(w).
-2*(w - 1)**2*(w + 1)
Factor -2/3*v - 2/21*v**2 + 12/7.
-2*(v - 2)*(v + 9)/21
Factor 3*f**4 + 32 + 28*f + f**4 + 36*f**3 - 64*f**3 - 36*f**2.
4*(f - 8)*(f - 1)*(f + 1)**2
Let v(k) be the third derivative of k**5/30 + 5*k**4/4 - 16*k**3/3 - 128*k**2. Suppose v(n) = 0. Calculate n.
-16, 1
Let x be ((-34)/45 + 15/75)/((-65)/78). Factor 0*j + 0 - x*j**2.
-2*j**2/3
Let h(x) be the second derivative of -x**7/21 - 8*x**6/5 - 108*x**5/5 - 448*x**4/3 - 560*x**3 - 1152*x**2 + x - 508. Let h(k) = 0. What is k?
-8, -6, -2
Let u(r) be the third derivative of -r**8/6720 - r**7/630 + r**6/240 + 3*r**5/20 - r**4/12 - 2*r**2. Let l(v) be the second derivative of u(v). Factor l(j).
-(j - 2)*(j + 3)**2
Let k(d) be the second derivative of -d**10/151200 + d**8/33600 + 7*d**4/12 - 17*d. Let m(s) be the third derivative of k(s). Let m(t) = 0. What is t?
-1, 0, 1
Let c(v) = 11*v**4 + 36*v**3 + 73*v**2 - 583*v. Let l(j) = -2*j**4 - 6*j**3 - 12*j**2 + 97*j. Let q(p) = -6*c(p) - 34*l(p). Factor q(k).
2*k*(k - 5)**2*(k + 4)
Suppose -5*v = -y - 8, 5*v - 2*y = -0 + 6. Let u(g) be the first derivative of 1/8*g**v - 1/6*g**3 + 1/2*g - 1/16*g**4 + 7. What is m in u(m) = 0?
-2, -1, 1
Let u = -15560 + 15563. Suppose 2/3*s**5 - 8/3*s + 20/3*s**2 - 8/3*s**4 - 16/3 + 2/3*s**u = 0. What is s?
-1, 2
Let -13*a**4 + 4*a**5 - 46*a**3 + 10*a**3 + 108*a**2 + a**4 = 0. What is a?
-3, 0, 3
Let h(x) be the second derivative of 0 + 2/21*x**4 - 1/35*x**5 - 6*x + 0*x**2 - 2/35*x**6 + 0*x**3. Factor h(y).
-4*y**2*(y + 1)*(3*y - 2)/7
Suppose 5*z = -10, -158*z = -x - 160*z + 4. Factor -x*o - 26/3*o**2 - 8/3 - 4*o**3 - 2/3*o**4.
-2*(o + 1)**2*(o + 2)**2/3
Let 35*d**3 + 36*d - 14*d**3 - 4*d**2 - 44*d**2 + 0*d - 3*d**4 = 0. What is d?
0, 2, 3
Let y(g) = 11*g**2 - 22*g + 2. Let a be y(2). Factor -3/2*b**a - 3*b**3 + 3/2 + 3/4*b**5 + 0*b**4 + 9/4*b.
3*(b - 2)*(b - 1)*(b + 1)**3/4
Suppose 0 = 189*z - 186*z + 3. Let r be (-4 - -2)*z/5. Determine v, given that 2/5*v**2 + 0 + r*v = 0.
-1, 0
Let x(s) be the second derivative of 3*s**5/20 + 37*s**4/12 + 15*s**3/2 + 11*s**2/2 - 103*s. Factor x(i).
(i + 1)*(i + 11)*(3*i + 1)
Let a be (-4)/16 - (-98)/8. Factor 16*i**2 + a*i + 2*i**2 - 24 - 21*i**3 + 3*i**4 + 6*i**3.
3*(i - 2)**3*(i + 1)
Let q(f) = 25*f - 77. Let i be q(6). Let a be (i + -1)*(-12)/(-168). Suppose -170/7*u**4 + 0 + 72/7*u**2 - 150/7*u**5 + a*u**3 + 16/7*u = 0. Calculate u.
-1, -2/5, 0, 2/3
Suppose 46*c**2 - 1/4*c**4 + 100*c + 0 + 17/4*c**3 = 0. What is c?
-4, 0, 25
Factor -1080*n**3 + 6*n + 541*n**3 + 7*n**4 - 25*n**2 + 551*n**3.
n*(n - 1)*(n + 3)*(7*n - 2)
Let t = -1916 + 1918. Suppose -2/9*b - 2/9*b**t + 0 + 2/9*b**4 + 2/9*b**3 = 0. Calculate b.
-1, 0, 1
Factor -1/9*m**3 + 0 - 4/9*m + 4/9*m**2.
-m*(m - 2)**2/9
Let d = -2003/3 - -2005/3. Suppose d*o**3 + 0 + 8/3*o - 8/3*o**2 = 0. What is o?
0, 2
Let -155*k**2 - 361*k - 674*k + 360 + 374*k**2 + 446*k**2 - 415*k = 0. What is k?
2/7, 36/19
Let 0*i + 0 + 39/5*i**3 + 9/5*i**5 + 39/5*i**4 + 9/5*i**2 = 0. What is i?
-3, -1, -1/3, 0
Let n = 286 + -284. Let x(w) be the first derivative of 0*w - 2 + 0*w**3 + 1/12*w**4 - 1/6*w**n. Suppose x(a) = 0. Calculate a.
-1, 0, 1
Let d(i) be the third derivative of i**6/660 + 7*i**5/330 - i**4/132 - 7*i**3/33 - i**2 - 27. Solve d(a) = 0.
-7, -1, 1
What is m in 64 + m**4 - 39*m**2 + 4*m + 13*m**3 - 27*m**2 + 18*m**2 = 0?
-16, -1, 2
Let c = 184 + -181. Let z(s) be the first derivative of 0*s + 1/3*s**5 - 1/3*s**2 + 2/3*s**4 - 1 + 1/9*s**c. Find y, given that z(y) = 0.
-1, 0, 2/5
Factor -28*c**3 + 3*c**4 - 7*c**4 + 71*c**2 - 33*c - 3*c**2 + 10*c - 13*c.
-4*c*(c - 1)**2*(c + 9)
Let k(j) be the third derivative of j**8/420 + j**7/210 - j**6/45 + 7*j**3/6 + 14*j**2. Let m(d) be the first derivative of k(d). Factor m(p).
4*p**2*(p - 1)*(p + 2)
Suppose 0 = 2*b - 62 + 2. Let v be ((-64)/(-24))/(b/27). Determine n so that 46/5*n - 42/5*n**2 - v = 0.
3/7, 2/3
Let g(u) be the second derivative of 4*u**4/21 + 19*u**3/21 - 15*u**2/7 + 245*u. Let g(h) = 0. Calculate h.
-3, 5/8
Let x(j) be the first derivative of 9/28*j**4 + 9/7*j**3 + 0*j - 3/35*j**5 - 23 + 15/14*j**2. Suppose x(c) = 0. Calculate c.
-1, 0, 5
Suppose 134 = 13*u + 17. Let m(j) = 2*j**3 - 17*j**2 - 9*j + 2. Let h be m(u). Solve -9/4 - 3/4*k**h - 3*k = 0.
-3, -1
Let n be (-46)/14 - (-8)/28. Let m be 14/n*(-2 + -1). Factor 0*u**3 - m*u**5 + 17*u**5 + u**3 - 4*u**3.
3*u**3*(u - 1)*(u + 1)
Let n = 5023/2785 + -2/557. Factor n*c + 0 - 3/5*c**2.
-3*c*(c - 3)/5
Factor 0 + 0*w**2 + 0*w + 4/3*w**5 + 4/3*w**4 - 8*w**3.
4*w**3*(w - 2)*(w + 3)/3
Suppose -3*d - 32*d**2 + 9*d**2 - 61*d + 19*d**2 = 0. Calculate d.
-16, 0
Find g such that 22/3*g**2 - 24 + 1/3*g**4 + 11/3*g**3 - 20*g = 0.
-6, -1, 2
Let o(w) = -3*w**2 + 5*w + 2. Let d be o(2). Let t(l) be the third derivative of d*l**5 + 0*l + 0*l**3 - 10*l**2 + 1/540*l**6 - 1/108*l**4 + 0. Factor t(f).
2*f*(f - 1)*(f + 1)/9
Let x = 30306 + -636338/21. Factor x*s**3 + 10648/21*s + 29282/21 + 2/21*s**4 + 484/7*s**2.
2*(s + 11)**4/21
Let g be 11/(-4)*(-80)/(-60) + 5. Factor 0 - 6*s**3 - 14/3*s**2 - 2/3*s**5 - g*s - 10/3*s**4.
-2*s*(s + 1)**3*(s + 2)/3
Let u(d) be the second derivative of -d**5/15 + 4*d**4/9 + 2*d**3/9 - 8*d**2/3 + 154*d - 2. What is l in u(l) = 0?
-1, 1, 4
Let j(g) be the second derivative of -g**4/96 - 7*g**3/48 + 9*g**2/8 - 195*g. Factor j(v).
-(v - 2)*(v + 9)/8
Let h(p) be the first derivative of -2/15*p**2 - 2/45*p**3 - 10 + 0*p. Factor h(c).
-2*c*(c + 2)/15
Let c(u) be the first derivative of -1/21*u**6 + 4/21*u**3 + 0*u - 4/35*u**5 + 1/7*u**2 + 0*u**4 + 11. Factor c(s).
-2*s*(s - 1)*(s + 1)**3/7
Let f(y) be the first derivative of -5/3*y**3 + 0*y + 57 - 5*y**2. Find h, given that f(h) = 0.
-2, 0
Let o(w) be the third derivative of w**8/336 - w**6/40 - w**5/30 - 10*w**2 + 1. Factor o(z).
z**2*(z - 2)*(z + 1)**2
Let q(z) = -5*z**2 + 9*z - 7. Let c(x) be the first derivative of -4*x**3/3 + 4*x**2 - 6*x + 10. Let h(u) = 7*c(u) - 6*q(u). Let h(t) = 0. What is t?
-1, 0
Let f(w) be the second derivative of -25*w**4/3 + 115*w**3/3 - 155*w**2 - 17*w - 2. Let z(y) = -9*y**2 + 21*y - 28. Let l(i) = -4*f(i) + 45*z(i). Factor l(o).
-5*(o - 4)*(o - 1)
Let -938*x**4 + 5*x + 100*x - 490 + 305*x**2 + 75*x**3 + 943*x**4 = 0. What is x?
-7, -2, 1
Let x(y) be the second derivative of 5*y**7/21 + y**6/6 - 4*y**5 - 10*y**4/3 + 80*y**3/3 + 40*y**2 + 76*y. Let x(u) = 0. What is u?
-2, -1/2, 2
Let v = 34018 - 34015. Suppose -12/7 + 6/7*w**2 - 22/7*w + 4/7*w**v = 0. Calculate w.
-3, -1/2, 2
Let r(n) be the second derivative of n**7/840 - n**6/360 - n**3/2 - 5*n. Let k(u) be the second derivative of r(u). Determine s so that k(s) = 0.
0, 1
Let g be 826/63 + -11 - 2. Factor -2/9*l + 4/9*l**3 + 1/3*l**4 + 0 - g*l**2.
l*(l + 1)**2*(3*l - 2)/9
Let y(u) = 4*u**3 + 33*u**2 + 76*u + 20. Let h(s) = -108*s**2 - 151*s + 42*s**2 - 28*s**3 - 39 + 20*s**3. Let m(o) = 4*h(o) + 7*y(o). Let m(f) = 0. What is f?
-4, -1/4
Let g(u) be the first derivative of u**4/2 - 208*u**3 + 32448*u**2 - 2249728*u - 238. Solve g(i) = 0.
104
Suppose -5*k = -4*v + 17, -2 - 1 = 3*k. Let 2/3*t**2 - 1/3*t**v + 1/3*t - 2/3 = 0. Calculate t.
-1, 1, 2
Factor -14/3*v**2 - 8/3*v**3 - 2/9*v**4 + 196/9*v + 0.
-2*v*(v - 2)*(v + 7)**2/9
Let t(x) = 4*x**5 + 96*x**4 + 832*x**3 + 2800*x**2 + 1768*x - 5488. Let g(i) = -2*i**3 - i. Let j(n) = -4*g(n) - t(n). Solve j(c) = 0 for c.
-7, -4, 1
Let o(c) = -5*c**2 - 16*c - 32. Let x(i) = i**2. Let a be 2 - 0 - (-7 + 8). Let b(r) = a*o(r) + 3*x(r). Determine h so that b(h) = 0.
-4
Let z = 28/67 + -1613/4020. Let k(j) be the third derivative of -7*j**2 + 0*j**6 + 4/525*j**7 + 0*j - 1/50*j**5 + 0*j**3 + z*j**4 + 0. Let k(c) = 0. What is c?
-1, 0, 1/2
Let c be (-24)/(-16) + (-18)/(-4). Factor 10*f**3 - 2*f**4 + 6*f**4 - c*f**3.
4*f**3*(f + 1)
Suppose -31 = -5*o + 5*c + 4, -5*o - 2*c = -7. Find q, given that -12*q**4 - 2*q**3 + 15*q**2 + 4*q**o + 4*q**3 + 3*q**3 - 3 - 9*q = 0.
-1, -1/4, 1
Factor 8/17 + 0*m - 6/17*m**2 + 2/17*m**3.
2*(m - 2)**2*(m + 1)/17
Suppose 83*z +