
Let a(l) = -19*l + 7. Let k be a(-6). Let b = k + -57. Factor b*h + h**3 - 56*h + 5*h**4 - 4*h**2 - 4*h**5 + 3*h**5 - 7*h**3.
-h*(h - 2)**3*(h + 1)
Suppose 31 = -6*d + 49. Find p such that -140*p**4 + 124*p**4 - 228*p**2 - 122*p**3 - 110*p - 46*p**d - 18 = 0.
-9, -1/2
Let h(l) be the first derivative of 217 - 3/5*l**2 - 2/25*l**5 + 2/3*l**3 + 0*l - 1/10*l**4. Let h(u) = 0. What is u?
-3, 0, 1
Let a(y) be the first derivative of y**6/1080 - y**5/72 + y**4/18 + 9*y**3 - 91. Let f(x) be the third derivative of a(x). Determine n so that f(n) = 0.
1, 4
Let i be ((-38)/10)/19 + 238/(-10). Let b be (i/32)/((-6)/16). Let -2*n**2 + 0 - 2/3*n**4 + 2/3*n + b*n**3 = 0. Calculate n.
0, 1
Let d(x) be the third derivative of -15 + 1/68*x**4 + 4*x**2 + 4/255*x**5 - 1/255*x**6 - 3/17*x**3 + 0*x. What is b in d(b) = 0?
-1, 3/2
Let d(u) be the second derivative of u**6/280 - 2*u**5/35 - 11*u**4/56 + 9*u**3/7 + 37*u**2/2 + 49*u. Let m(g) be the first derivative of d(g). Factor m(c).
3*(c - 9)*(c - 1)*(c + 2)/7
Suppose -9*m = -198 - 288. Let j = -52 + m. Determine p, given that 0*p**3 - 2/3*p**4 + 2*p**j + 0 - 4/3*p = 0.
-2, 0, 1
Factor s + 4/5 + 1/5*s**2.
(s + 1)*(s + 4)/5
Let b(n) = n**3 - 7*n**2 + 5*n + 12. Suppose 0 = -2*d - 3*w, 0*w = 3*d - 4*w - 34. Let c be b(d). Factor 41*q**2 + 44*q**2 + c - 88*q**2 + 3*q.
-3*(q - 2)*(q + 1)
Let h(j) be the second derivative of j**6/20 - 9*j**5/40 + j**3 + 912*j - 1. Factor h(f).
3*f*(f - 2)**2*(f + 1)/2
Let t(d) = 13*d - 178. Let f be t(13). Let p be f/24 + -2*(-186)/480. Let 2/5 - p*b**2 - 3/5*b = 0. Calculate b.
-2, 1/2
Let f(x) be the first derivative of x**6/18 - 22*x**5/15 + 5*x**4/4 + 130*x**3/9 - 38*x**2/3 - 56*x - 374. Suppose f(o) = 0. Calculate o.
-2, -1, 2, 21
Let n(x) be the second derivative of -x**4/14 - 41*x**3/7 - 120*x**2/7 - 2221*x. Factor n(j).
-6*(j + 1)*(j + 40)/7
Let c(i) be the first derivative of 20*i**2 - 10/3*i**3 + 0*i + 5 - 5/4*i**4. Factor c(o).
-5*o*(o - 2)*(o + 4)
Let z(a) = 23*a**2 - 163*a + 1367. Let o(v) = 4*v**2 - 27*v + 228. Let b = 0 + 34. Let m(k) = b*o(k) - 6*z(k). Factor m(t).
-2*(t - 15)**2
Let y(x) = -60*x**4 + 622*x**3 + 2272*x**2 - 21*x + 21. Let g(i) = 14*i**4 - 156*i**3 - 568*i**2 + 5*i - 5. Let s(p) = -21*g(p) - 5*y(p). Factor s(n).
2*n**2*(n + 4)*(3*n + 71)
Let u(z) be the first derivative of z**7/350 + 11*z**6/600 + z**5/25 + z**4/30 + 79*z**2/2 + 17. Let p(q) be the second derivative of u(q). Factor p(m).
m*(m + 1)*(m + 2)*(3*m + 2)/5
Let i(z) = 20*z + 2. Let m be i(-4). Let s = -70 - m. Find l such that 44 - l**2 + 2*l**2 + 0*l**2 - s - 12*l = 0.
6
Let n(u) be the first derivative of 4*u**5/5 - 44*u**4 - 184*u**3/3 + 88*u**2 + 180*u - 461. Determine g, given that n(g) = 0.
-1, 1, 45
Let p(k) be the second derivative of k**7/840 + k**6/40 + k**5/5 + 5*k**4/6 - k**3/6 - 41*k**2/2 + 29*k. Let s(t) be the second derivative of p(t). Factor s(d).
(d + 2)**2*(d + 5)
Let s(l) be the second derivative of -4*l**5/45 + l**4/18 + 5*l**3/27 - 33*l. Let s(z) = 0. What is z?
-5/8, 0, 1
Let y(d) be the second derivative of 23/2*d**5 - 1536*d**2 + 1/63*d**7 - 2/3*d**6 - 2 - 940/9*d**4 + 13*d + 1600/3*d**3. Suppose y(n) = 0. Calculate n.
3, 8
Let q(g) be the third derivative of g**5/40 - 3*g**4/2 + 119*g**3/4 + 188*g**2. Factor q(n).
3*(n - 17)*(n - 7)/2
Let a(k) be the second derivative of -12/11*k**2 + 23/66*k**4 - 1/22*k**5 - 4 + 2*k - 20/33*k**3. Suppose a(f) = 0. Calculate f.
-2/5, 2, 3
Let h(q) be the first derivative of -q**4/16 - 7*q**3/12 - 15*q**2/8 - 9*q/4 - 2317. Determine r, given that h(r) = 0.
-3, -1
Let q = 51334 - 51331. Factor 0 - 2/3*c + 1/3*c**4 + 2/3*c**q - 1/3*c**2.
c*(c - 1)*(c + 1)*(c + 2)/3
Let m be (4/14)/((-3)/(-21)). Factor -10*t**2 + m*t - 8*t + 2*t**2 + 5*t**2.
-3*t*(t + 2)
Let k(v) = v**2 + 32*v - 171. Let n be k(-51). Let s be (1/(-4)*1)/(n/(-1064)). Factor 1/3*m**3 - 1/2 - 1/6*m**4 + 2/3*m**2 - s*m.
-(m - 3)*(m - 1)*(m + 1)**2/6
Suppose 96 = m + 2*p + 63, -3*m = 4*p - 69. Factor 4/7*i**2 + 0*i + 0 + 4/7*i**4 - 8/7*i**m.
4*i**2*(i - 1)**2/7
Suppose 6*m - 34 = -d, 90 = m + 1261*d - 1257*d. Factor -18 + 37/2*t - 1/2*t**m.
-(t - 36)*(t - 1)/2
Let n = -1309864/3 - -436637. Factor 19/12*y**3 + 25/6 - n*y**2 + 455/12*y.
(y - 5)**2*(19*y + 2)/12
Suppose -j - 2*y + 10 = 0, 7 = j + y + 2. Let d(t) be the second derivative of 6*t - 3*t**2 + 4/3*t**3 - 1/6*t**4 + j. Determine f, given that d(f) = 0.
1, 3
Let o(g) be the first derivative of -42*g - 85 + 122/3*g**3 - 3/2*g**4 + 43*g**2. Let o(m) = 0. Calculate m.
-1, 1/3, 21
Factor -15/2*d**2 + 0 - 9/2*d - 7/2*d**3 - 1/2*d**4.
-d*(d + 1)*(d + 3)**2/2
Let n(p) = p**4 + 9*p**3 + p**2 + 41*p - 2. Let m(t) = t**3 + t**2 + 24*t - 1. Let a(o) = -10*m(o) + 5*n(o). Factor a(z).
5*z*(z - 1)*(z + 1)*(z + 7)
Let p(h) = -5174*h + 31046. Let d be p(6). Find l such that 46/3*l**d + 0 + 637/6*l**4 - 4/3*l - 63*l**3 - 343/6*l**5 = 0.
0, 2/7, 1
Let m(o) be the first derivative of o**6/360 - o**4/6 + 8*o**3/9 - 66*o**2 - 25. Let r(l) be the second derivative of m(l). Factor r(p).
(p - 2)**2*(p + 4)/3
Let k(u) be the first derivative of -u**6/120 - u**5/40 + 3*u**4/4 + u**3/3 - 75*u + 84. Let h(s) be the third derivative of k(s). Factor h(o).
-3*(o - 2)*(o + 3)
Let c(v) be the second derivative of -v**7/42 - 71*v**6/30 - 1147*v**5/20 + 4103*v**4/12 - 148*v**3/3 - 2738*v**2 - 4283*v. Solve c(u) = 0.
-37, -1, 2
Suppose -8922 + 4542 - 4*r**2 + 4596 - 60*r = 0. Calculate r.
-18, 3
Let c(p) = -150*p**2 - 16295*p + 3125. Let o(f) = -226*f**2 - 24442*f + 4681. Let u(w) = -7*c(w) + 5*o(w). Factor u(j).
-5*(j + 102)*(16*j - 3)
Let y(n) be the second derivative of -6*n**2 + 7/3*n**3 + 2*n**4 + 3 + 2/15*n**6 + 1/7*n**7 - 10*n - 9/5*n**5. Let y(q) = 0. Calculate q.
-3, -2/3, 1
Let i(t) be the third derivative of -t**7/42 + 5*t**6/12 - 2*t**5 - 25*t**4/12 + 125*t**3/6 - 2685*t**2. Solve i(r) = 0.
-1, 1, 5
Suppose 10*m - 28 = 3*m. Suppose -m*a + 4 = -4. Factor 5 - 15*n + 0*n**a - 3*n**3 + 12*n**2 + 1.
-3*(n - 2)*(n - 1)**2
Let j(u) be the third derivative of 0 + 37*u**2 + 0*u + 1/6*u**3 - 1/8*u**4 - 1/15*u**5. Factor j(t).
-(t + 1)*(4*t - 1)
Suppose 4 = 2*u, 5*s + 8*u - 12*u = 7. Suppose -1643 - 192*i**s - 4*i**4 - 473 - 2734*i - 1823*i**2 - 665*i**2 - 484*i - 1198*i = 0. What is i?
-23, -1
Let a(i) = -3*i**2 - 1464*i + 1502. Let f(s) = -2*s**2 - 730*s + 752. Let d(q) = 4*a(q) - 7*f(q). Factor d(k).
2*(k - 372)*(k - 1)
Suppose 29744/3 + 416/3*f - 164/3*f**2 + 4/3*f**3 = 0. What is f?
-11, 26
Let x(r) be the second derivative of r**6/6 + 53*r**5/4 - 580*r. Suppose x(c) = 0. Calculate c.
-53, 0
Let m(r) be the first derivative of 3*r**5 - 137 + 75/2*r**2 - 162*r + 217*r**3 + 429/4*r**4. Find x, given that m(x) = 0.
-27, -1, 2/5
Suppose 4 = 2*c - 2*g, -5*c + 4 + 2 = -3*g. Suppose c = 7*w - w - 714. Let -w + 111 - 2*v**2 + 4*v**2 = 0. Calculate v.
-2, 2
Factor -93 + 650 + 1171*o + 1993*o + 4728*o**2 - 36*o**3 - 29.
-4*(o - 132)*(3*o + 1)**2
Let p(q) = -4*q**2 + 3598*q + 3. Let o be p(0). Factor -30 - 5/2*t**o + 15/2*t**2 + 10*t.
-5*(t - 3)*(t - 2)*(t + 2)/2
Let f(r) be the third derivative of r**8/560 - r**6/24 + r**4/2 + 28*r**3/3 - 11*r**2 - r. Let y(x) be the first derivative of f(x). Let y(i) = 0. Calculate i.
-2, -1, 1, 2
Let z(w) be the second derivative of 1/273*w**7 + 0*w**4 + 0*w**2 + 0 + 2/65*w**6 - 26*w + 0*w**3 + 9/130*w**5. Find i such that z(i) = 0.
-3, 0
Let -2/3 - 14/9*y**2 + 44/9*y = 0. Calculate y.
1/7, 3
Let s(r) be the second derivative of -r**7/231 + 4*r**6/11 - 90*r**5/11 - 6*r + 596. Let s(c) = 0. Calculate c.
0, 30
Let z be 8/(-36)*23/(-23). Let v be (-18)/(-135) + 8/90 + 0. Factor 2/9*p**4 + 0 - v*p**3 - z*p**2 + 2/9*p.
2*p*(p - 1)**2*(p + 1)/9
Let o(x) = -9*x + 60. Let t be o(-11). Solve 162*w**2 + 9 - 15 - 3*w - t*w**2 = 0.
-1, 2
Let l be 2/27 + (-8641770)/(-3078) - 5/(10/(-18)). What is h in 2/3*h**2 + l - 260/3*h = 0?
65
Let y(h) be the third derivative of h**7/735 + 37*h**6/140 - 227*h**5/210 - 37*h**4/28 + 226*h**3/21 - 2178*h**2. Suppose y(l) = 0. Calculate l.
-113, -1, 1, 2
Suppose 2*f - 142*f = -594*f. Factor 2/3*r**2 + f + 0*r - 2/3*r**3.
-2*r**2*(r - 1)/3
Suppose 106*h = 61*h. Suppose 8*p + 16 = 12*p + g, h = -g + 4. Solve -4/5*s**2 + 2/5*s**5 - 6/5*s**p + 0 + 0*s + 0*s**4 = 0.
-1, 0, 2
Let h(b) be the third deriva