6*v**2 + 7 + 0*v + 0*v**3 - 9/8*v**4. Find m, given that q(m) = 0.
-9, 0
Factor 288 + 1/2*h**2 - 24*h.
(h - 24)**2/2
Let h(f) be the first derivative of 2*f**6/3 + 252*f**5/5 + 675*f**4 - 12996*f**3 + 66096*f**2 - 139968*f + 102. Find r, given that h(r) = 0.
-36, 3
Suppose 0 = -918*q + 917*q. Suppose q = 25*s - 54 + 4. Determine i so that 4/9*i - 2/9*i**s - 2/9 = 0.
1
Let j(a) be the first derivative of 0*a - 735/4*a**4 + 280/3*a**3 - 10*a**2 - 61. Factor j(r).
-5*r*(7*r - 2)*(21*r - 2)
Let i(q) be the first derivative of -1/300*q**6 + 0*q**2 + 1/100*q**5 - 10 - q + 0*q**3 + 0*q**4. Let y(c) be the first derivative of i(c). Factor y(w).
-w**3*(w - 2)/10
Let r(m) = 7*m**2 - 49*m + 44. Let a be r(6). Let v(k) be the first derivative of -a*k - 34 + 3/2*k**2 - 1/4*k**4 + 0*k**3. Solve v(u) = 0 for u.
-2, 1
Let t(f) be the third derivative of -7/120*f**5 + 0 - 1/672*f**8 + 4*f**2 - 1/24*f**4 + 0*f**3 - 1/84*f**7 - 3/80*f**6 + 19*f. Factor t(h).
-h*(h + 1)**3*(h + 2)/2
Suppose -2*q = -o - q + 4, -q - 10 = -4*o. Factor 6*n - 6*n + n**o + 3*n.
n*(n + 3)
Let g be (6/(-18))/(4/(-3))*10/175. Let v(t) be the third derivative of 0*t**3 + 0*t + 0 + 5*t**2 - g*t**7 + 0*t**6 + 0*t**5 + 0*t**4 + 1/112*t**8. Factor v(j).
3*j**4*(j - 1)
Let m(y) be the second derivative of -y**7/42 + y**6/10 + y**5/2 + 7132*y. Factor m(u).
-u**3*(u - 5)*(u + 2)
Let z = -497565 - -497569. Factor -35/3*y**3 + 5/3*y**z + 35/3*y + 40/3 - 15*y**2.
5*(y - 8)*(y - 1)*(y + 1)**2/3
Let c(x) be the third derivative of 0*x**3 + 0*x - 1/15*x**5 + 0 + 1/210*x**7 - 1/120*x**6 + 1/6*x**4 - 23*x**2. Factor c(y).
y*(y - 2)*(y - 1)*(y + 2)
Let p(t) = -t**2 - 2*t + 135. Let k be p(9). Let y(d) = d**2 - 35*d - 34. Let u be y(k). Factor 1/11 + 2/11*j + 1/11*j**u.
(j + 1)**2/11
Suppose 106/5*k**2 + 103/5*k - 42 + 1/5*k**3 = 0. What is k?
-105, -2, 1
Suppose -393*k = -298*k - 380. Let s(o) be the first derivative of 0*o + 3/5*o**5 + 35 + 6*o**2 + 9*o**3 + 9/2*o**k. Suppose s(f) = 0. What is f?
-4, -1, 0
Let y(s) be the third derivative of -s**7/70 - 3*s**6/4 + 8*s**5/5 + 15*s**4/4 - 31*s**3/2 + 4109*s**2. Determine k so that y(k) = 0.
-31, -1, 1
Let w(q) be the third derivative of -q**6/60 + q**5/3 + 2*q**4 - 713*q**2. Suppose w(x) = 0. Calculate x.
-2, 0, 12
Let n(u) = 8*u + 267. Let s be n(-33). Let f(y) be the first derivative of 1/8*y**4 + 0*y + 5/6*y**s + 22 + 3/4*y**2 - 1/10*y**5. Determine w so that f(w) = 0.
-1, 0, 3
Let n(t) be the third derivative of -1 + 1/12*t**5 + 0*t - 4*t**2 + 0*t**3 + 20/3*t**4. Factor n(a).
5*a*(a + 32)
Let g = -7213 + 7217. Suppose 4/13*y**3 + 8/13*y**2 - 6/13*y - 8/13*y**g + 2/13*y**5 + 0 = 0. Calculate y.
-1, 0, 1, 3
Solve -132*a - 343*a + 91*a + 15*a**4 - 2*a**5 + 9*a**4 - 6*a**3 - 416*a**2 = 0.
-3, -1, 0, 8
Let t be 13/(1092/8)*(6 - 44/8). Let k(i) be the second derivative of 1/147*i**7 + 0*i**5 + 28*i + 0*i**2 - t*i**3 - 1/21*i**4 + 0 + 2/105*i**6. Factor k(c).
2*c*(c - 1)*(c + 1)**3/7
Let g(q) be the second derivative of q**7/189 - q**6/45 - 31*q**5/90 + 11*q**4/54 + 26*q**3/9 - 56*q**2/9 - 4584*q. Suppose g(b) = 0. Calculate b.
-4, -2, 1, 7
Suppose 0 = 15*q - 2567 + 392. Factor -49*z**3 + 26*z**2 - 176*z - 42*z**2 - q*z**2 - 64.
-(z + 1)*(7*z + 8)**2
Let q be 79/27 + (-20)/(-270). Let o(h) be the first derivative of 0*h - 5*h**q + 11 - 5/2*h**2. Factor o(x).
-5*x*(3*x + 1)
Let i(l) = l**3 + 7*l**2 + 5*l - 16. Let d be i(-5). Let g be (-1 + 3)*d/27. Let 2/3*w**2 - g + 0*w = 0. Calculate w.
-1, 1
Let i be ((6/(-33))/(-1))/(840/770). Let a(c) be the third derivative of 5/8*c**4 - i*c**5 + 0 - 5/6*c**3 + 0*c + 13*c**2. Solve a(g) = 0 for g.
1/2, 1
Find v, given that 152/3*v + 0*v**2 - 6*v**3 - 2/3*v**4 + 64 = 0.
-8, -2, 3
Suppose -7*h + 27 - 90 = 0. Let r be (-6 - 52/h)*-3. Let r*v**5 + 0 + 0*v + 2/3*v**4 - 2/3*v**3 - 2/3*v**2 = 0. Calculate v.
-1, 0, 1
Let i(u) = -2*u**2 - 65*u + 64. Let k(d) = 112*d + 5*d**2 + 112*d - 28*d + d**2 - 192. Let c(n) = 20*i(n) + 6*k(n). Factor c(a).
-4*(a - 1)*(a + 32)
Let r(q) be the third derivative of 0*q - 4/7*q**3 - 1/56*q**6 + 1/14*q**4 + 1/490*q**7 + 44 + 3/70*q**5 + 2*q**2. Determine y so that r(y) = 0.
-1, 2
Let q(m) be the third derivative of m**2 + 1/36*m**5 - 1/630*m**7 + 0*m**3 + 1/180*m**6 + 0*m - 1/12*m**4 + 5. Suppose q(w) = 0. Calculate w.
-2, 0, 1, 3
Let v = 280 + -360. Let x be (v/120)/(2/(-10)). Factor 2/9*t - 2*t**4 + 0 - 14/9*t**2 + x*t**3.
-2*t*(t - 1)*(3*t - 1)**2/9
Let j be (-42 + 84)*((-5)/2)/5. Let h be 108/j - (-1 + 6 - 11). Solve -3/7*b**2 + h - 3/7*b = 0 for b.
-2, 1
Suppose -3520 - 39840*l**2 - 12153*l**4 + 57423*l**3 - 7107*l**4 + 93*l**5 - 28080*l + 6857*l**3 + 312*l**5 = 0. What is l?
-2/9, 2, 44
Let a(u) be the second derivative of 625/8*u**3 - 15625/8*u**2 - 25/16*u**4 - 14*u + 1/80*u**5 - 1. Suppose a(f) = 0. What is f?
25
Let c(x) be the third derivative of 0*x + 0*x**5 + 5/8*x**4 + 0 + 73*x**2 - 5/3*x**3 - 1/24*x**6. Factor c(s).
-5*(s - 1)**2*(s + 2)
Factor -394/11*f**3 + 2/11*f**4 + 0 + 210*f**2 - 3438/11*f.
2*f*(f - 191)*(f - 3)**2/11
Let g(h) be the second derivative of -h**7/147 + 202*h**6/105 - 10201*h**5/70 + 1915*h. Solve g(d) = 0.
0, 101
Find q, given that -135/2 + 81/4*q + 3/4*q**2 = 0.
-30, 3
Let c(i) = -7*i**4 - 49*i**3 + 53*i**2 - 11*i - 11. Let l(b) = -10*b**4 - 50*b**3 + 54*b**2 - 14*b - 10. Let g(u) = 6*c(u) - 5*l(u). Factor g(s).
4*(s - 4)*(s - 1)**2*(2*s + 1)
Let u = -75 + 77. Let j be -2 + u + 1 - -1. Factor 2*k + 24*k**2 - 12*k**j - 13*k**2.
-k*(k - 2)
Suppose -468*r + 179 = -4766 - 3947. Let g(x) be the first derivative of 2/9*x**3 - 4/3*x**2 - r + 0*x. Find y such that g(y) = 0.
0, 4
Let -167/2*u**2 + 0 - 1/2*u**3 + 84*u = 0. Calculate u.
-168, 0, 1
Let y(f) be the third derivative of -f**8/2240 + 13*f**7/840 - f**6/20 + 5*f**4/6 - 56*f**2. Let s(v) be the second derivative of y(v). Factor s(m).
-3*m*(m - 12)*(m - 1)
Let p(v) be the second derivative of -v**7/24 + 29*v**6/120 - 3*v**5/80 - 73*v**4/48 + 7*v**3/12 + 6*v**2 - 11*v - 86. Find x such that p(x) = 0.
-1, 8/7, 2, 3
Let s(t) be the first derivative of 140 + 4418*t + 2/3*t**3 + 94*t**2. Factor s(q).
2*(q + 47)**2
Let l = 12 - 2. Let t(c) = 2*c + 16. Let f be t(l). What is d in 27*d - 1 + 5*d - 3 + f*d**2 = 0?
-1, 1/9
Let n be (-392)/40 + 21 - (-30)/75. Factor -n*g - 4 + 6/5*g**2.
2*(g - 10)*(3*g + 1)/5
Let f(q) = -76*q**3 + 76*q - 336. Let k(r) = 3*r**3 + r**2. Let x(v) = -f(v) - 24*k(v). Find b, given that x(b) = 0.
-4, 3, 7
Let g(r) be the first derivative of 1/25*r**5 - 2/5*r**2 + 61 + 3/20*r**4 + 0*r + 0*r**3. What is t in g(t) = 0?
-2, 0, 1
Let s(q) be the second derivative of -2*q**6/15 - 3*q**5 - 46*q**4/3 + 64*q**3 + 256*q**2 - 289*q. Factor s(x).
-4*(x - 2)*(x + 1)*(x + 8)**2
Let z(v) be the first derivative of v**4/2 + 242*v**3/21 + 524*v**2/7 + 40*v - 1730. Factor z(n).
2*(n + 7)*(n + 10)*(7*n + 2)/7
Factor -1/2*n**4 + 0 + 0*n + 33/2*n**2 - 4*n**3.
-n**2*(n - 3)*(n + 11)/2
Let z(n) be the second derivative of -2*n**5/135 + 5*n**4/36 - n**3/3 + 16*n**2 - 7*n + 1. Let j(o) be the first derivative of z(o). Factor j(g).
-2*(g - 3)*(4*g - 3)/9
Let s(x) = -3*x + 10. Let f be s(2). Factor 14 - 296*q**2 - 208 - 528*q - 94 - 60*q**3 - 4*q**f.
-4*(q + 1)*(q + 2)*(q + 6)**2
Let c(p) be the third derivative of p**8/141120 - p**7/17640 + p**6/5040 - 19*p**5/15 + 8*p**2 + 2. Let o(f) be the third derivative of c(f). Factor o(i).
(i - 1)**2/7
Let y(h) be the first derivative of -1/3*h**3 + 94*h**2 + 305 - 8836*h. Let y(k) = 0. What is k?
94
Suppose -5*g + o + 36 = 0, -2*g = 13*o - 14*o - 15. Factor -g*r**2 + 6 + 12*r + 6 + 4*r**2 + 4*r**2 + 2*r**2.
3*(r + 2)**2
Let c be (-20)/4 + (19/(399/196) - 1). Let g(v) be the second derivative of 0*v**2 + 18*v + 0 - 1/6*v**4 - c*v**3. Determine n so that g(n) = 0.
-10, 0
Let r be 1/(-4) - 22/8. Let j = -16206 - -16204. Let b(l) = -2*l**2 - 22*l + 24. Let s(k) = 2*k**2 + 22*k - 24. Let q(x) = j*s(x) + r*b(x). Factor q(f).
2*(f - 1)*(f + 12)
Let v be 3*1/18 - 34/(-12). Let g(n) be the first derivative of -5*n - 3/2*n**2 - 21 - 1/20*n**4 + 3/5*n**v. What is u in g(u) = 0?
-1, 5
Find v, given that 8/7 + 92/7*v**3 - 22/7*v**2 + 20/7*v**5 - 40/7*v + 86/7*v**4 = 0.
-2, -1, 1/5, 1/2
Let v(o) be the first derivative of -o**3/15 - 9*o**2/10 - 8*o/5 - 439. Solve v(m) = 0 for m.
-8, -1
Le