
4*l**2*(l - 2)*(l + 1)
Let b(n) = 3*n**2 + 83*n + 70. Let s(q) = -5*q**2 - 125*q - 106. Let h(v) = 7*b(v) + 5*s(v). Determine c, given that h(c) = 0.
-10, -1
Suppose -5*p + 103 = -4*r, 8*p = 3*p + 5*r + 105. Suppose 3*q = -3*s + 2*q + p, 4*s + q - 24 = 0. Find i, given that -14*i**2 - i**s + 14*i**2 = 0.
0
Let v be ((-6)/5)/(9325/(-250) + 37). Solve 6/7 - v*f**2 + 22/7*f**4 - 4/7*f**3 - 6/7*f**5 + 10/7*f = 0.
-1, -1/3, 1, 3
Solve 6*p**2 - 53 + 38*p - 16 + 97*p = 0 for p.
-23, 1/2
Suppose 0 = t + 3*t + 220. Let z = t - -221/4. Suppose 3/4*p + z*p**2 + 1/2 = 0. What is p?
-2, -1
Let g(m) be the first derivative of -4*m**5/5 + 21*m**4 - 352*m**3/3 + 264*m**2 - 256*m - 196. Factor g(y).
-4*(y - 16)*(y - 2)**2*(y - 1)
Let y(r) = r**3 + 20*r**2 - 21*r + 2. Let n be y(-21). Let w(s) be the second derivative of -s - 2/15*s**3 + 0 + 1/30*s**4 + 0*s**n. Factor w(d).
2*d*(d - 2)/5
Let w be (-6 - (-455)/75)*1. Let o(c) be the first derivative of 1/5*c + 4 + 0*c**2 - w*c**3. Solve o(z) = 0 for z.
-1, 1
Let j(m) = -8*m**4 + 70*m**3 - 448*m**2 + 386*m + 6. Let y(s) = 7*s**4 - 68*s**3 + 448*s**2 - 387*s - 5. Let t(n) = -5*j(n) - 6*y(n). Let t(q) = 0. What is q?
0, 1, 14
Let m(o) be the third derivative of 0 + 1/1260*o**6 - o**3 - 4*o**2 + 1/105*o**5 + 1/21*o**4 + 0*o. Let k(a) be the first derivative of m(a). Factor k(c).
2*(c + 2)**2/7
Let c be -3*(8/14)/(-4). Factor -6/7 - 9/7*h**3 + 9/7*h + 3/7*h**4 + c*h**2.
3*(h - 2)*(h - 1)**2*(h + 1)/7
Let p(f) be the second derivative of -3*f**2 - 31*f - 1/10*f**5 + 5/3*f**3 - 1/6*f**4 + 0. Solve p(v) = 0.
-3, 1
Let y = 38 - 36. Suppose -10*s**3 + 7*s - 2*s**3 - 6*s - 4*s**y + 11*s + 4*s**4 = 0. What is s?
-1, 0, 1, 3
Let -87/5*m + 1/5*m**2 + 86/5 = 0. Calculate m.
1, 86
Let s be ((-175)/15 + 11)*(13 + -1). Let w be s/(-10) - (-128)/40. Find x such that 0*x**w + 0*x**2 + 0 + 0*x + 0*x**3 - 2/9*x**5 = 0.
0
Let p(n) be the second derivative of n**6/450 - n**5/50 - 2*n**4/15 + n**3 + 4*n. Let t(x) be the second derivative of p(x). Let t(b) = 0. What is b?
-1, 4
Let m(t) be the first derivative of 3*t**4/16 + t**3/4 - 255*t**2/8 + 825*t/4 + 433. Determine u so that m(u) = 0.
-11, 5
Let p be 4 - (-24)/60*(5 + 0). Let j = -38/7 + p. Factor 8/7*r + j*r**2 + 0.
4*r*(r + 2)/7
Factor -4/11 - 8/11*j - 5/11*j**2 - 1/11*j**3.
-(j + 1)*(j + 2)**2/11
Let g(y) be the first derivative of 15*y**4/4 + 18*y**3 + 18*y**2 - 24*y - 122. Factor g(q).
3*(q + 2)**2*(5*q - 2)
Let x(c) = -c**5 - c**4 + c**3 - c**2 + c - 1. Let j(s) = -12*s**5 - 24*s**4 - 6*s**3 + 6*s**2 + 9*s - 3. Let g(y) = -j(y) + 3*x(y). Let g(m) = 0. Calculate m.
-1, 0, 2/3
Let f be (-20)/60 - 58/6. Let b be 4 - (-15)/f*-2. Find m such that -m**3 + 6 - 6 - b*m**2 + 8*m**2 = 0.
0, 1
Let z(q) be the second derivative of -q**5/60 + q**3/18 - 2*q - 24. Factor z(x).
-x*(x - 1)*(x + 1)/3
Let w = -302 - -304. Let p(u) be the second derivative of -1/2*u**3 - 9/10*u**5 + u - 2/5*u**6 + 0 + 0*u**w - u**4 - 1/14*u**7. Factor p(o).
-3*o*(o + 1)**4
Let t(h) be the first derivative of -h**6/280 - h**5/140 + h**4/56 + h**3/14 - 11*h**2 + 14. Let o(r) be the second derivative of t(r). Factor o(m).
-3*(m - 1)*(m + 1)**2/7
Determine g, given that 353*g**3 + 0*g**5 - 2016*g + 83*g**3 - 68*g**4 + 2*g**5 + 60*g**3 - 5184 + 1568*g**2 = 0.
-2, 2, 18
Let u be 14/(-2)*-7*(-5)/(-280). Factor -1/8*k**5 - k - 5/2*k**2 - u*k**4 - 9/4*k**3 + 0.
-k*(k + 1)*(k + 2)**3/8
Let h(i) be the second derivative of i**7/84 + 3*i**6/10 + 11*i**5/4 + 25*i**4/3 - 125*i**3/4 - 625*i**2/2 - 41*i. Factor h(d).
(d - 2)*(d + 5)**4/2
Let a(r) be the first derivative of -4*r**3/3 + 64*r**2 + 122. Let a(u) = 0. Calculate u.
0, 32
Factor 0 - 100/3*k**3 - 16*k + 7/3*k**4 + 196/3*k**2.
k*(k - 12)*(k - 2)*(7*k - 2)/3
Let f(s) = s**2 + 7*s + 6. Let g be f(-3). Let x(q) = 2*q**2 - 4*q - 6. Let z(w) = -2*w**2 + 3*w + 5. Let h(y) = g*z(y) - 5*x(y). Solve h(m) = 0 for m.
-1, 0
Find h, given that -139*h**2 + 12*h + 95*h**2 + 3*h**4 + 0*h**4 + 68*h**2 + 15*h**3 = 0.
-2, -1, 0
Suppose -4*b**3 + 2*b**2 - 16*b**2 + 3*b**2 + 15*b**2 + 24*b = 0. What is b?
-2, 0, 3
Let v = -5 + 7. Suppose -w = -0*w - 4*w. Factor 1/2*l - 3/2*l**v + w - 2*l**3.
-l*(l + 1)*(4*l - 1)/2
Suppose -7*u = 7 - 21. Suppose 3/8*r - 1/8*r**3 + 0*r**u + 1/4 = 0. What is r?
-1, 2
Let x(o) be the third derivative of -o**9/362880 - o**8/60480 - o**5/6 + 2*o**2. Let a(m) be the third derivative of x(m). Suppose a(u) = 0. Calculate u.
-2, 0
Let f(r) be the third derivative of 0*r**4 + 0*r**5 - 13*r**2 + 0 + 0*r**3 - 1/1785*r**7 - 1/1020*r**6 + 0*r. Factor f(i).
-2*i**3*(i + 1)/17
Let d(x) be the third derivative of x**5/15 + 52*x**4/3 + 5408*x**3/3 - 183*x**2 + 2. Factor d(h).
4*(h + 52)**2
Let d = -9/502 + 11107/3514. Find j such that 18/7*j**3 + 8/7 - d*j**2 - 32/7*j = 0.
-1, 2/9, 2
Solve -4/7*u**4 + 562/7*u + 337/7*u**2 + 120/7 + 5*u**3 = 0 for u.
-4, -2, -1/4, 15
Let o be 2 + (1 - -3)/4. Factor 0*g**5 - 3*g**5 + 48*g**3 - 3*g - 42*g**o.
-3*g*(g - 1)**2*(g + 1)**2
Let t = 1600 - 1031. Let r = t - 2831/5. Find p such that 4/5 - r*p - 4/5*p**2 + 14/5*p**3 = 0.
-1, 2/7, 1
Suppose 4*y - 178 + 3*y**4 + 169 - 26*y**2 - 33*y - y**3 + y**5 + 2*y - 5*y**3 = 0. Calculate y.
-3, -1, 3
Let s = -525 + 529. Let b(q) be the third derivative of 1/240*q**5 + 0 + 1/480*q**6 - 7*q**2 + 0*q**3 + 0*q**s + 0*q. Solve b(k) = 0.
-1, 0
Let v = 10963 + -10961. Solve 4/3 + 2/3*u**2 + v*u = 0.
-2, -1
Let o(t) be the third derivative of -t**8/8064 - t**7/2016 + 3*t**5/4 - 2*t**2. Let f(q) be the third derivative of o(q). Let f(c) = 0. Calculate c.
-1, 0
Let m(d) be the first derivative of -d**6/360 + d**5/30 - d**4/8 - 3*d**3 + 20. Let y(o) be the third derivative of m(o). Solve y(p) = 0 for p.
1, 3
Suppose 4*y**2 + 16*y**2 - y**4 + 26*y - 2*y**2 - 4*y + 2*y**3 + 8 - y**4 = 0. What is y?
-1, 4
Let z(n) be the second derivative of -n**7/7980 - n**6/570 - 3*n**5/380 - n**4/57 - 9*n**3/2 + 36*n. Let p(r) be the second derivative of z(r). Factor p(m).
-2*(m + 1)**2*(m + 4)/19
Let m(j) be the first derivative of -3*j**2 + 7*j - j**3 - 1/8*j**4 - 5. Let l(k) be the first derivative of m(k). Factor l(a).
-3*(a + 2)**2/2
Let r = -1572/7 + 225. Suppose -3*k = -z - 6, 12*z + k = 14*z + 2. Suppose z - 3/7*v - r*v**2 = 0. Calculate v.
-1, 0
Factor -20*i + 1/2*i**4 + 0 - 9*i**2 + 3/2*i**3.
i*(i - 4)*(i + 2)*(i + 5)/2
Suppose 3*n - 2 = -8. Let l = -2 - n. Factor 1/3*x**2 + 0 + l*x.
x**2/3
Suppose 2*m - 19 = 3*p + m, 5*p - 2*m + 33 = 0. Let s = p + 8. Solve 0*w**2 - 2*w**2 - 59*w**s + 4*w + 57*w**3 = 0.
-2, 0, 1
Let r(h) = -10*h**3 + 485*h**2 - 5760*h + 5. Let n(s) = 15*s**3 - 728*s**2 + 8640*s - 8. Let b(k) = 5*n(k) + 8*r(k). Factor b(x).
-5*x*(x - 24)**2
Let -1666*d**2 - 553*d + 218*d + 1401*d**2 - 3456*d**2 - 153*d - 16 = 0. What is d?
-4/61
Let u(g) = 2*g - 12. Let x be u(2). Let r be (18/(-28))/(6/x). Solve -r*l + 6/7*l**2 + 2/7 - 2/7*l**3 = 0 for l.
1
Let o(v) be the third derivative of -v**8/30240 + v**7/5670 + 7*v**6/3240 + v**5/135 - v**4/24 + v**2. Let l(d) be the second derivative of o(d). Factor l(r).
-2*(r - 4)*(r + 1)**2/9
Let q(g) be the second derivative of g**5/120 - g**4/16 - g**3/3 + 7*g**2 - 15*g. Let m(c) be the first derivative of q(c). Determine t so that m(t) = 0.
-1, 4
Suppose 3*i - 3 - 12 = 0. Suppose 3*v - 4*r = 5, 5*v = 2*r + 8 + 5. Factor -i + 3*k**4 - v*k**2 + 5.
3*k**2*(k - 1)*(k + 1)
Solve 25/2*a + 375/2 - 25/6*a**2 + 1/6*a**3 = 0 for a.
-5, 15
Let c = 22 - 6. Let i = c - 14. Determine h, given that -h**2 + 3*h - 2*h**i + 6 - 6*h**2 = 0.
-2/3, 1
Let y(z) be the third derivative of -7/2*z**3 + 13/8*z**4 - 1/4*z**5 + 48*z**2 + 0*z + 0 - 1/40*z**6. Factor y(i).
-3*(i - 1)**2*(i + 7)
Suppose -3*n**2 + 2484 + 36*n - 2412 + 7*n**2 = 0. Calculate n.
-6, -3
Let s(u) = 9*u**3 - 540*u**2 + 10807*u - 72014. Let m(o) = -3*o**3 + 180*o**2 - 3602*o + 24004. Let a(p) = 7*m(p) + 2*s(p). Factor a(c).
-3*(c - 20)**3
Factor -10/3*d**2 + 28/3*d + 0 - 2/3*d**3.
-2*d*(d - 2)*(d + 7)/3
Suppose -190*o + 83*o + 35*o - 37*o**2 - 36 + 4*o**4 + 5*o**2 + 8*o**3 = 0. What is o?
-3, -1, 3
Let c(h) be the first derivative of -h**5/25 - h**4/20 + 2*h**3/15 + 31. Factor c(t).
-t**2*(t - 1)*(t + 2)/5
Suppose -2*z + 4*m + 10 = 3*z, -4*z = 4*m - 44. Let o be (z/4)/(1/6). Let -o*y**2 + 3*y**5 + 9*y**2 + 3*y - 6*y**3 