 2
Suppose 96*k - 91*k = 5*h + 15, 9 = 3*k. Let d(c) be the second derivative of h*c**2 - 10/3*c**3 - 5/12*c**4 + 9*c + 0. Factor d(q).
-5*q*(q + 4)
Let a(d) be the second derivative of -d**6/40 - 9*d**5/40 - 3*d**4/4 - 5*d**3/4 - 9*d**2/8 - 13*d + 2. Suppose a(o) = 0. Calculate o.
-3, -1
Let n(b) be the first derivative of 4*b**6/21 - 198*b**5/35 + 272*b**4/7 + 596*b**3/7 - 260*b**2/7 - 1014*b/7 - 34. Solve n(f) = 0.
-1, 3/4, 13
Let g = 42238 - 211174/5. Factor -2/5*d**3 + 24/5 + g*d - 2*d**2.
-2*(d - 2)*(d + 1)*(d + 6)/5
Let r(l) be the second derivative of l**9/3024 + l**8/336 + 5*l**7/504 + l**6/72 + 47*l**4/6 - 31*l - 2. Let t(p) be the third derivative of r(p). Factor t(n).
5*n*(n + 1)**2*(n + 2)
Let z(g) = 68*g**2 + 14964*g - 14912. Let x(q) = 10*q**2 + 2138*q - 2130. Let p(b) = -20*x(b) + 3*z(b). Factor p(v).
4*(v - 1)*(v + 534)
Suppose -30*g + 309 - 249 = 0. Let a(x) be the second derivative of -1/3*x**4 + 0 + 3*x - g*x**2 - 4/3*x**3. Determine z so that a(z) = 0.
-1
Let c(o) = 4*o**3 + 22*o**2 - 118*o - 90. Let n(y) = y**3 - 55*y - 1. Let m(d) = 2*c(d) - 4*n(d). Factor m(r).
4*(r - 2)*(r + 2)*(r + 11)
Let x(s) be the third derivative of -s**8/504 + s**6/10 - 2*s**5/45 - 19*s**4/12 - 4*s**3 + 167*s**2 + 10*s. Determine k so that x(k) = 0.
-4, -1, 3
Let q(z) be the first derivative of 2*z**3/45 + 48*z**2/5 - 58*z/3 - 2260. Find n, given that q(n) = 0.
-145, 1
Let g = -602216 - -602218. Find i, given that 6/7*i + 2/7*i**g + 0 = 0.
-3, 0
Let 414*k + 271*k - 425*k - 4*k**2 + 900 - 4*k**3 = 0. Calculate k.
-5, 9
Let g(r) be the third derivative of 19*r**5/15 - 31*r**4/3 + 32*r**3 - 124*r**2 + 7*r. Factor g(m).
4*(m - 2)*(19*m - 24)
Factor 4*l**5 + 1906*l**2 - 1962*l**2 - 13*l**3 + l + 16*l**4 - 6*l**3 + 7*l**3 - 33*l.
4*l*(l - 2)*(l + 1)**2*(l + 4)
Let x(g) be the second derivative of 9/10*g**3 + 0 + 5/12*g**4 + 1/5*g**2 + 232*g. Find w such that x(w) = 0.
-1, -2/25
Let v(o) = 15*o - 221. Let r be v(15). Suppose r = -6*t + 5*t, 5*t = -s - 18. Factor 9 - 1/2*c**3 + 1/4*c**4 - 11/4*c**s + 3*c.
(c - 3)**2*(c + 2)**2/4
Let b(z) be the first derivative of 5*z**6/6 + 21*z**5 - 125*z**4/4 - 305*z**3/3 + 270*z**2 - 220*z - 16. Factor b(c).
5*(c - 1)**3*(c + 2)*(c + 22)
Factor -1/6*r**3 + 13/6*r**2 - 32 - 8/3*r.
-(r - 8)**2*(r + 3)/6
Let z(i) be the third derivative of i**8/6720 - i**7/840 + i**6/240 - i**5/120 + 13*i**4/6 - 39*i**2. Let l(r) be the second derivative of z(r). Factor l(s).
(s - 1)**3
Let p be 26/12 - (-36)/(-216). Let g = 4 + 0. Factor -3*v - 32*v**p + 0*v**3 - g*v**4 + 5*v**3 + 19*v + 15*v**3.
-4*v*(v - 2)**2*(v - 1)
Solve -32*q**3 - 2*q**2 - 150*q**4 + 3*q**5 - 196*q**4 + 58*q**2 + 320*q**4 - q**5 = 0 for q.
-2, 0, 1, 14
Let b(w) be the third derivative of -100/3*w**3 + 55/12*w**4 + 0 - 75*w**2 - 1/12*w**5 + 0*w. Find s, given that b(s) = 0.
2, 20
Suppose 22*c - 57*c - 12285 = 0. Let u = 353 + c. Factor 0*g**3 - 1/4 + 0*g - 1/4*g**4 + 1/2*g**u.
-(g - 1)**2*(g + 1)**2/4
Suppose -156 + 51 = -7*g. Suppose -3*q = -g*q + 2*q. Find l, given that q*l**5 + 183*l**3 - 177*l**3 - 21*l**4 + 11*l**5 + 4*l**5 = 0.
0, 2/5, 1
Find j such that 9*j**2 + 5*j + 28*j + 75*j + 9*j**2 - 20*j**2 = 0.
0, 54
Let o(t) be the third derivative of -7*t**6/360 + 5*t**5/9 + 119*t**4/18 - 8*t**3 - 1227*t**2. Suppose o(q) = 0. Calculate q.
-4, 2/7, 18
Let x(l) be the first derivative of 0*l**5 + 1/3*l - 1/9*l**3 - 1/4*l**2 - 1/36*l**6 + 1/6*l**4 - 72. Solve x(j) = 0 for j.
-2, -1, 1
Suppose -24*a + 7*a = 34. Let c(v) = v**2 - 1. Let y(l) = 6*l**2 - 32*l + 46. Let s(i) = a*c(i) + y(i). Factor s(k).
4*(k - 6)*(k - 2)
Let j = -6519 + 13541/2. Let r = j + -250. Solve -3*k + 0 + 9/2*k**2 + 0*k**3 - r*k**4 = 0 for k.
-2, 0, 1
Let t(y) = 8*y**3 - 16348*y**2 + 8421385*y - 8405000. Let s(n) = -4*n**3 + 8168*n**2 - 4210691*n + 4202500. Let r(w) = 5*s(w) + 3*t(w). Let r(j) = 0. What is j?
1, 1025
Let f = -6998 + 28131/4. Let n = 981/28 - f. Determine w, given that 0 - 4/7*w + n*w**2 = 0.
0, 2
Let k(n) be the second derivative of -n**4/3 + 2640*n**3 - 7840800*n**2 - 1514*n. Find b such that k(b) = 0.
1980
Let a(k) = 15*k**3 + 24*k**2 + 109*k + 88. Let j(d) = 37*d**3 + 47*d**2 + 218*d + 178. Let r(i) = 5*a(i) - 2*j(i). Find b, given that r(b) = 0.
-21, -4, -1
Let j(v) be the second derivative of -v**7/2 - v**6/5 + 21*v**5/20 + v**4/2 - 762*v. Let j(i) = 0. What is i?
-1, -2/7, 0, 1
Suppose -4*m + 9*m + z - 379 = 0, 0 = z - 4. Let l be ((-27)/(-42))/(-9 + m/7). Factor -3/8*q**2 + 0 + l*q.
-3*q*(q - 1)/8
Let o(j) = -38*j + 231. Let q be o(6). Solve -26*s + 7*s**2 - 4*s + 18*s**2 + 9*s**2 - s**2 - 3*s**q = 0.
0, 1, 10
Suppose -32*b - 3*b = -70. Suppose 2*s - 3*s + 1790*s**b + 3*s - s**3 - 1789*s**2 = 0. Calculate s.
-1, 0, 2
Suppose 148 = m + 1. Suppose -6*h = 21 - m. Solve -43 - 55 - 3*z**2 + h*z + 80 = 0 for z.
1, 6
Let c = 40/811 + 3935/2433. Suppose c*y + 1/3*y**2 - 2 = 0. What is y?
-6, 1
Let f(n) = -22*n**2 - 30 + 219*n**2 + 206*n + 39*n**2. Let r(k) = 47*k**2 + 41*k - 6. Let b(v) = 2*f(v) - 11*r(v). Determine y so that b(y) = 0.
-1, 2/15
Let v(y) be the second derivative of -y**6/135 + 14*y**5/45 + 245*y**4/54 + 225*y - 6. What is g in v(g) = 0?
-7, 0, 35
Let p be (207/(-18) - -11) + (-1761)/(-2). Suppose 0 = -902*r + p*r. Factor -2/3*z**2 + 4/9*z + r + 2/9*z**3.
2*z*(z - 2)*(z - 1)/9
Let n(b) be the first derivative of -b**4/6 - 1642*b**3/9 + 274*b**2 - 12405. Factor n(l).
-2*l*(l - 1)*(l + 822)/3
Let h be 8 + 2 - (2 + 8). Let l(b) be the second derivative of 0*b**2 + 4*b - 1/24*b**4 + 1/4*b**3 + h. Solve l(z) = 0 for z.
0, 3
Let k(c) be the second derivative of -c**5/60 + 13*c**4/24 - 46*c**2 + 2*c - 8. Let t(u) be the first derivative of k(u). What is j in t(j) = 0?
0, 13
Find q, given that 4*q - 15*q**2 + 10*q**2 + 3*q - 9*q + 10 + 7*q = 0.
-1, 2
Let d be (76/(-7))/(8/7*(-17)/68). Let w(b) be the third derivative of 0 + 1/60*b**5 + 2/3*b**3 + 0*b + 1/6*b**4 + d*b**2. Factor w(q).
(q + 2)**2
Let p(w) be the first derivative of w**4/2 + 178*w**3/3 + 174*w**2 + 1769. Factor p(c).
2*c*(c + 2)*(c + 87)
Suppose -60*d + 168 = -18*d. Suppose -2*c + 2*q = 173 - 183, -d*q = c + 10. Suppose -2187/4 - 81/4*m**c - 3/4*m**3 - 729/4*m = 0. What is m?
-9
Factor 64/5*h**2 + 2/5*h**3 - 136/5*h + 0.
2*h*(h - 2)*(h + 34)/5
Suppose -42/5*y**2 + 246/5 + 7*y + 1/5*y**3 = 0. What is y?
-2, 3, 41
Let u(i) be the third derivative of 2/21*i**4 - 3/70*i**5 + 0*i**3 + 0 + 74*i**2 + 1/420*i**6 + 0*i. Let u(f) = 0. What is f?
0, 1, 8
Solve 2/9*r**4 + 66992/3*r**2 + 1268/9*r**3 - 1268/9*r - 200978/9 = 0 for r.
-317, -1, 1
Factor 39*b**4 - 3*b**5 - 632*b**2 - 512 - 29*b**4 + 2*b**5 + 781*b + 47*b**3 + 307*b.
-(b - 8)**2*(b - 1)**2*(b + 8)
Let q be (-84)/(-330)*80 + -16. Solve 1/11*c**2 + 26/11*c + q = 0.
-24, -2
Suppose 32*i - 13181*i**3 + 2*i**5 + 13269*i**3 + 64*i - 152*i**2 - 22*i**4 = 0. What is i?
0, 2, 3, 4
Let v(m) = -20*m**3 + 604*m**2 - 1180*m - 1808. Let f(y) = 36*y**3 - 1209*y**2 + 2362*y + 3614. Let w(j) = 4*f(j) + 7*v(j). Factor w(r).
4*(r - 150)*(r - 3)*(r + 1)
Let c = 887303 - 7985726/9. Factor 0 - 1/3*f**2 - 10/9*f + c*f**3.
f*(f - 5)*(f + 2)/9
Let r = 1991 + -1977. Let j(d) be the third derivative of 0*d + 0 + 5/8*d**3 + r*d**2 - 1/80*d**5 - 1/8*d**4. Suppose j(a) = 0. Calculate a.
-5, 1
Let q = -11564 + 1618969/140. Let z(c) be the second derivative of 1/70*c**6 + 12*c + 0*c**3 + 1/14*c**4 + 0 + 0*c**2 + q*c**5. Solve z(r) = 0 for r.
-2, -1, 0
Let h = 975529 - 4876997/5. Factor 256/5 - h*v + 28/5*v**3 - 876/5*v**2.
4*(v - 32)*(v + 1)*(7*v - 2)/5
Factor 205924*d - 1542564 - 4*d**2 + 3*d**2 - 3*d**2 - 210892*d.
-4*(d + 621)**2
Let t be 8 + (-3 - (2 - 3) - 1). Suppose 2*v + 1 = t. Factor -14*l**v + 19*l**2 - 7*l**2 + 2.
-2*(l - 1)*(l + 1)
Let h be 108*(-1 + 7/3). Suppose 0 = 29*n - 65*n + h. Factor -1/5*d**n - 4/5*d + 2*d**2 + 1/5*d**3 - 24/5.
-(d - 3)*(d - 2)*(d + 2)**2/5
Let k(p) be the first derivative of 2523/5*p + 522*p**2 + 9*p**4 + 958/5*p**3 - 79 + 3/25*p**5. Let k(y) = 0. Calculate y.
-29, -1
Factor 11*k**2 + 1/2*k**3 + 30*k - 108.
(k - 2)*(k + 6)*(k + 18)/2
Let g(c) be the third derivative of -c**5/210 - 1969*c**4/84 - 562*c**3/3 - 8051*c**2 + 1. Factor g(d).
-2*(d + 2)*(d + 1967)/7
Suppose -21 = 11*v + 408. Let z = v + 42. Factor 17*p + 4*p**4 - 14*p**4 + 25*p**2 + 5*p*