 -1, 1
Let h be 6/(-9) - 38/(-48). Let p = h - -11/40. Factor 0*a - p*a**2 + 2/5.
-2*(a - 1)*(a + 1)/5
Let i(h) be the third derivative of 0*h - 3*h**3 + 0 - 10*h**2 + 1/112*h**8 + 8/105*h**7 - 25/8*h**4 + 1/15*h**6 - 31/30*h**5. Suppose i(p) = 0. Calculate p.
-3, -1, -1/3, 2
Solve c**4 - 3*c**4 + 2*c**3 - 161*c**2 + 6*c + 0*c**4 + 171*c**2 = 0.
-1, 0, 3
Let m(i) be the first derivative of i - 1/16*i**4 - 10 - i**2 + 5/12*i**3. What is c in m(c) = 0?
1, 2
Let u be (7 - 6) + 2 + (-2 - -2). Let h(t) be the second derivative of 1/6*t**4 + 0*t**u + 0*t**2 + 5*t + 0 + 1/10*t**5. Factor h(c).
2*c**2*(c + 1)
Let d be (424/13)/(16/(-96)). Let w = 196 + d. Suppose -2/13*p - 4/13 + 2/13*p**3 + w*p**2 = 0. What is p?
-2, -1, 1
Let p(j) be the first derivative of -7*j**6/15 + 494*j**5/25 + 364*j**4/5 - 80*j**3/3 - 1072*j**2/5 + 608*j/5 + 412. Find d such that p(d) = 0.
-2, 2/7, 1, 38
Suppose -w - 2 + 4 = 0. Let i be (-4 - w - -5)*0. Let i*h + 0 - 4/5*h**2 = 0. Calculate h.
0
Let j(z) = -6*z - 4*z**2 + 5 + 8*z**2 - z**2. Let g be j(1). Factor 0*i - 1/4*i**4 - 1/4*i**5 + 1/4*i**3 + 1/4*i**g + 0.
-i**2*(i - 1)*(i + 1)**2/4
Let b be 15/(-9)*(-11)/((-55)/(-15)). Suppose i + b*w - 23 = 0, -2*i - 2*w - 3*w + 26 = 0. Factor 12/5*u**i - 24/5*u**2 + 3*u - 3/5.
3*(u - 1)*(2*u - 1)**2/5
Let v(p) be the third derivative of 1/140*p**6 - 1/28*p**4 + 0*p + 0 - 5/42*p**3 + 1/1470*p**7 + 1/105*p**5 + 39*p**2. Find n, given that v(n) = 0.
-5, -1, 1
Let t(d) be the first derivative of d**6/3 - 8*d**5/5 - 11*d**4/2 - 4*d**3 + 68. What is w in t(w) = 0?
-1, 0, 6
Let t be (3 - (-4)/(-4))/((-6)/(-138)). Suppose -t = -22*g - 2. Factor 4/3 - 4/3*a + 1/3*a**3 - 1/3*a**g.
(a - 2)*(a - 1)*(a + 2)/3
Let m = -1488 + 1493. Let a(d) be the second derivative of 1/34*d**4 + 0 + 0*d**2 + m*d + 2/51*d**3 + 1/170*d**5. Factor a(o).
2*o*(o + 1)*(o + 2)/17
Let y(s) be the first derivative of -s**4/12 - 64*s**3/9 - 190*s**2 - 1200*s - 329. Find o, given that y(o) = 0.
-30, -4
Let v(n) be the first derivative of n**4/16 + 25*n**3/12 + 47*n**2/8 + 23*n/4 + 23. Factor v(o).
(o + 1)**2*(o + 23)/4
Let v(d) be the third derivative of -d**7/245 + d**6/420 + 6*d**5/35 + 3*d**4/7 - 16*d**3/21 + 32*d**2. Find o, given that v(o) = 0.
-2, 1/3, 4
Let j = 120417/10625 + -1/31875. What is k in -k**2 - 11/3 - j*k = 0?
-11, -1/3
Suppose -3*f = 3*f - 18. Let p(v) be the first derivative of -2/3*v**f - 3 - 3/2*v**2 + 2*v. Factor p(s).
-(s + 2)*(2*s - 1)
Let k(n) be the second derivative of n**5/300 + n**4/60 - n**3/10 + 19*n**2/2 + 8*n. Let a(v) be the first derivative of k(v). Factor a(u).
(u - 1)*(u + 3)/5
Let 8*n**4 - 32*n**3 - 675*n**5 + 679*n**5 - 36*n - 47*n**2 - 25*n**2 = 0. What is n?
-3, -1, 0, 3
Let s be 2 + -5 - (-26 + 20). Let z(v) be the third derivative of 0 + 0*v**s + 0*v + v**2 + 1/20*v**5 + 1/4*v**4. Factor z(y).
3*y*(y + 2)
Let a = -113 + 116. Let r(t) = 95*t**3 - 85*t**2 - 95*t + 155. Let u(l) = -8*l**3 + 7*l**2 + 8*l - 13. Let j(o) = a*r(o) + 35*u(o). Factor j(g).
5*(g - 2)*(g - 1)*(g + 1)
Let c(x) = -x**3 - 1. Let k(z) = 2*z**3 - 16*z**2 - 24*z + 4. Let a(q) = -4*c(q) - k(q). Factor a(r).
2*r*(r + 2)*(r + 6)
Let f = -151 + 457/3. Let m = 677 - 2027/3. Suppose m*w - f*w**3 - 2/9 + 16/9*w**4 - 14/9*w**2 = 0. What is w?
-1, 1/4, 1/2, 1
Let d = -2 + 3. Let w(p) be the third derivative of p**5/6 - p**4/4 + 32*p**2. Let z(u) = -u**2 + u. Let q(t) = d*w(t) + 8*z(t). Suppose q(m) = 0. Calculate m.
-1, 0
Let u be (190/(-30) - -9)*78/(-4). Let c be (-111)/(-108) + 13/u. Factor c*i**2 + 4/3*i - 4/9.
(i + 2)*(7*i - 2)/9
Let g(m) be the second derivative of 15*m - 1/80*m**5 - 1/12*m**4 - 1/4*m**2 + 0 - 5/24*m**3. Factor g(r).
-(r + 1)**2*(r + 2)/4
Let o be 793/427 - (-1)/7. Factor 25/4*i**3 - o*i**4 - 2 + 1/4*i**5 + 7*i - 19/2*i**2.
(i - 2)**3*(i - 1)**2/4
Let a = -466 + 466. Let z(i) be the second derivative of 0*i**2 + 0 - 1/165*i**6 - i + 0*i**4 + 0*i**3 + a*i**5. Factor z(w).
-2*w**4/11
Let m be 0 - -2 - (2 - 2)/1. Find o, given that 3*o**3 + 48*o + 3*o**m + o**2 + 20*o**2 = 0.
-4, 0
Factor -8/7 - 10/7*f + 3/7*f**2.
(f - 4)*(3*f + 2)/7
Let a(l) = 6*l + 17. Let j be a(-2). Let c(g) be the second derivative of g - 1/18*g**4 + 0*g**2 + 0*g**3 + 0 + 1/30*g**j. Factor c(h).
2*h**2*(h - 1)/3
Let m(l) be the third derivative of l**7/630 + 7*l**6/180 - 67*l**5/180 + 11*l**4/9 - 2*l**3 - 510*l**2. Factor m(u).
(u - 2)*(u - 1)**2*(u + 18)/3
Let p(f) be the second derivative of f**4/6 + 7*f**3/3 - 8*f**2 + 64*f. Suppose p(q) = 0. What is q?
-8, 1
Let n(p) be the first derivative of -p**4/2 - 16*p**3/3 - 21*p**2 - 36*p + 61. Solve n(z) = 0.
-3, -2
Let a(p) be the third derivative of 3*p**6/200 - 19*p**5/100 - 39*p**4/20 - 28*p**3/5 - 6*p**2 - 12. Suppose a(l) = 0. Calculate l.
-2, -1, 28/3
What is k in 1/2*k**2 + 5929/2 - 77*k = 0?
77
Let i = 105 - 101. Factor 30*o**2 - 33*o**2 + 7*o**4 - i*o**4.
3*o**2*(o - 1)*(o + 1)
Let h(y) = -4*y**4 - 3*y**3 + 5*y**2 + 3*y - 6. Let l(s) = s**4 + s**3 - s**2 - s + 1. Let w(v) = -2*h(v) - 10*l(v). Factor w(b).
-2*(b - 1)*(b + 1)**3
Let t(v) be the third derivative of 2*v - 7/108*v**4 - 1/9*v**3 - 1/135*v**5 - 18*v**2 + 0. Factor t(c).
-2*(c + 3)*(2*c + 1)/9
Let c(d) be the third derivative of d**5/30 - d**4 + 11*d**3/3 + 27*d**2 + d. Suppose c(t) = 0. What is t?
1, 11
Factor -366*c**2 + 1966*c**2 + 4*c**5 - 28*c**3 - 156*c**4 + 1468*c**3 + 0*c**5 + 0*c**5.
4*c**2*(c - 20)**2*(c + 1)
Let u(z) be the third derivative of -z**9/9072 + z**8/2520 - z**6/540 + z**5/360 - 3*z**3 + 17*z**2. Let x(q) be the first derivative of u(q). Factor x(m).
-m*(m - 1)**3*(m + 1)/3
Let y(s) be the second derivative of s**4/4 + 122*s - 2. Find v such that y(v) = 0.
0
Let j = -1096 - -4387/4. Solve -3*n + 15/4*n**2 - j*n**3 + 0 = 0 for n.
0, 1, 4
Let f(k) be the first derivative of 3*k**4/4 + 16*k**3 + 153*k**2/2 + 108*k - 613. Determine h, given that f(h) = 0.
-12, -3, -1
Let j(g) be the second derivative of -g**6/30 + 2*g**5/15 - g**4/6 - 3*g**2 + 14*g. Let r(p) be the first derivative of j(p). Suppose r(z) = 0. What is z?
0, 1
Let o(z) be the third derivative of z**6/1260 - z**5/630 - z**4/252 + 5*z**3/2 + 24*z**2. Let b(a) be the first derivative of o(a). Factor b(m).
2*(m - 1)*(3*m + 1)/21
Let x be ((-15)/(-20))/(996/16). Let i = x + 247/166. Suppose -i*l + 0 - 3/4*l**3 - 9/4*l**2 = 0. What is l?
-2, -1, 0
Let g(u) = 6*u - 25. Let v be g(5). Let k be 2/8 - (v - 5). Factor -1/4*z**3 + 5/4*z + k*z**2 + 3/4.
-(z - 3)*(z + 1)**2/4
Factor -45 - 4*k**2 + 11 - 145 - 114 - 11 + 92*k.
-4*(k - 19)*(k - 4)
Let q(g) = -3*g**2 - 3*g + 6. Let f(z) = -z**3 - 3*z**2 - 3*z + 7. Let n(a) = 3*f(a) - 4*q(a). Factor n(w).
-3*(w - 1)**2*(w + 1)
Let h(d) = 3*d**2 - 5*d + 1. Let i be h(2). Let m(t) be the third derivative of 1/120*t**5 + 1/12*t**i + t**2 + 0*t + 0 + 1/24*t**4. Factor m(l).
(l + 1)**2/2
Let n(g) = g**3 + g**2 + g + 1. Let w(k) = -4*k**3 - 6*k - 2. Let l(t) = -6*n(t) - 2*w(t). Factor l(m).
2*(m - 1)**3
Factor 51/4*u**2 + 0 - 3/4*u**3 - 12*u.
-3*u*(u - 16)*(u - 1)/4
Let s(k) = -14*k**3 + 88*k**2 - 262*k + 308. Let m(d) = 5*d**3 - 30*d**2 + 87*d - 103. Let b(c) = -8*m(c) - 3*s(c). Determine t, given that b(t) = 0.
2, 5
Suppose 91*j = -95*j + 195*j - 18. Factor 0 + 6/5*a + 9/5*a**j + 3/5*a**3.
3*a*(a + 1)*(a + 2)/5
Let z(l) be the third derivative of l**6/1800 + l**5/600 - 5*l**3/3 - 3*l**2. Let g(x) be the first derivative of z(x). What is n in g(n) = 0?
-1, 0
Let k(i) = -3*i - 4 - 12 + i. Let f be k(-9). Find u, given that -4 + 0*u**2 + 7*u**2 - u**2 - 4*u**2 + f*u = 0.
-2, 1
Let a(t) = 9*t**3 - 50*t**2 + 91*t - 15. Let m(d) = 17*d**3 - 100*d**2 + 181*d - 33. Let k(v) = 5*a(v) - 3*m(v). Find p, given that k(p) = 0.
1/3, 2, 6
Let r(i) be the second derivative of -5*i**7/6 - 22*i**6/3 - 24*i**5 - 100*i**4/3 - 40*i**3/3 - 25*i + 4. What is m in r(m) = 0?
-2, -2/7, 0
Let z(t) be the first derivative of 2*t**3/21 - 2*t**2 - 30*t/7 - 132. Factor z(x).
2*(x - 15)*(x + 1)/7
Let c(z) be the second derivative of -z**5/15 + 25*z**4/9 - 94*z**3/9 + 46*z**2/3 + 153*z. Suppose c(m) = 0. What is m?
1, 23
Let s(m) = 48*m - 42. Let k(f) = f**3 + f**2 - f + 1. Let t(l) = 3*k(l) - s(l). Find x such that t(x) = 0.
-5, 1, 3
Solve 39*w + 36*w - 20 - w - 16*w + 6*w**2 = 0.
-10, 1/3
Let l be 18/(-117) + (-67)/(-13). Suppose -