.
-2*(q - 2)*(q - 1)**3
Let p = -1336 + 1338. Factor 5/2*v + 3/2 + v**p.
(v + 1)*(2*v + 3)/2
Let d(p) be the second derivative of -p**6/15 - p**5/40 + 23*p**4/24 - 9*p**3/4 + 9*p**2/4 + p - 11. Determine s, given that d(s) = 0.
-3, 3/4, 1
Let c = 1345 + -1345. Let y(t) be the second derivative of 0 - 4/3*t**3 + c*t**2 - 8*t + 2/5*t**5 + t**4. Factor y(u).
4*u*(u + 2)*(2*u - 1)
Let l be (-2)/6 + 116/(-12). Let g be (-116)/l + 16/40. Find x, given that 3*x**5 - 26 + 6*x**2 - g*x**4 - 9*x + 6*x**3 + 29 + 3*x**4 = 0.
-1, 1
Let u(p) be the first derivative of -p**6/36 + 13*p**5/30 + 7*p**4/12 - 970. Factor u(k).
-k**3*(k - 14)*(k + 1)/6
Let k = -5997/104 - -465/8. Factor 0*p**2 + 8/13*p - k*p**3 + 0 + 2/13*p**4.
2*p*(p - 2)**2*(p + 1)/13
Let x = 76 + -33. Determine a, given that a - x*a**4 - 2*a**3 + a**5 + 43*a**4 = 0.
-1, 0, 1
Suppose 40 = -9*q + 14*q - 5*n, 21 = 3*q - 2*n. Let d(s) be the second derivative of 0 - 2/45*s**3 + 0*s**2 - 13/90*s**4 - 11*s - 11/150*s**q. Factor d(x).
-2*x*(x + 1)*(11*x + 2)/15
Let r(w) be the first derivative of 3*w**5/5 + 5*w**4/2 + w**2 + 2*w + 16. Let s(f) = -f**4 + f + 1. Let p(x) = -r(x) + 2*s(x). Determine c so that p(c) = 0.
-2, 0
Let r(c) be the first derivative of -c**3/3 + 2*c**2 + 3*c - 7. Let g be r(4). Let -g*o + o - o - 3*o**2 = 0. Calculate o.
-1, 0
Let j(s) = 20453*s**3 - 41472*s**2 + 1148*s - 10. Let x(n) = 2*n**3 - n**2 - 1. Let r(m) = -j(m) + 2*x(m). Solve r(p) = 0.
2/143, 2
Factor 14 + 40*f**2 + 5 - 19 - 16*f**3 - 2*f**4.
-2*f**2*(f - 2)*(f + 10)
Let i(p) = -23*p - 69. Let h be i(-3). Let q(z) be the third derivative of h*z - 1/140*z**7 + 8*z**2 + 0*z**5 + 0*z**4 + 3/80*z**6 + 0 + 0*z**3. Factor q(c).
-3*c**3*(c - 3)/2
Let s(l) = -11*l**4 + 44*l**3 - 54*l**2 + 24*l - 5. Let o(t) = 45*t**4 - 177*t**3 + 217*t**2 - 97*t + 21. Let p(j) = 2*o(j) + 9*s(j). Factor p(g).
-(g - 3)*(g - 1)*(3*g - 1)**2
Let v(b) be the third derivative of -b**6/240 + b**5/15 - 7*b**4/48 - 107*b**2. Determine g so that v(g) = 0.
0, 1, 7
Let t be 41/20 - (-48)/(-24). Let n(r) be the first derivative of 1/6*r**3 + 3 - t*r**5 + 0*r**4 - 1/4*r + 0*r**2. Find v such that n(v) = 0.
-1, 1
Factor -39*n**3 + n**4 - 210 + 7*n**3 - 465 + 1260*n - 498*n**2 - 52*n**3 - 4*n**4.
-3*(n - 1)**2*(n + 15)**2
Let w(o) = -3*o**2 + 48*o + 2. Let p = -161 + 177. Let v be w(p). Find t, given that 0 - 1/3*t**5 + 1/3*t**3 - 1/3*t**v + 0*t + 1/3*t**4 = 0.
-1, 0, 1
Factor -1/7*a - 6/7 + 1/7*a**2.
(a - 3)*(a + 2)/7
Let l(u) be the first derivative of -u**5/15 + u**4/4 + 5*u**3/9 - u**2/2 - 4*u/3 + 222. Factor l(b).
-(b - 4)*(b - 1)*(b + 1)**2/3
Factor 0*v + 0 + 1/8*v**3 - 1/4*v**2.
v**2*(v - 2)/8
Let l be 21/36 - (-1 - 9/(-6)). Let p(t) be the second derivative of -4*t - 1/24*t**4 + 0*t**2 - l*t**3 + 0. Factor p(h).
-h*(h + 1)/2
What is g in -31 + 1265*g**2 - 1264*g**2 + 1 + 7*g = 0?
-10, 3
Suppose 845*m**4 - 138*m - 40 + 14*m - 116*m + 530*m**2 - 260*m + 1105*m**3 - 1940*m**2 = 0. What is m?
-2, -2/13, 1
Let d(v) be the third derivative of -242*v**7/945 + 77*v**6/270 + 8*v**5/27 + 2*v**4/27 + 16*v**2 + 4*v. Suppose d(s) = 0. What is s?
-2/11, 0, 1
Let g = 873/7 + -865/7. Find w such that -60/7*w**3 + 44/7*w - g + 36/7*w**4 - 44/7*w**2 = 0.
-1, 1/3, 2
Let t(d) be the first derivative of -d**6/48 - d**5/8 - 3*d**4/32 + 5*d**3/24 + d**2/4 - 7. Determine q so that t(q) = 0.
-4, -1, 0, 1
Let n(p) be the second derivative of -p**5/12 - 43*p**4/9 - 1513*p**3/18 - 289*p**2/3 - 2*p - 34. Factor n(t).
-(t + 17)**2*(5*t + 2)/3
Factor -13/11*t**2 - 15/11*t**4 + 0*t + 1/11*t**5 + 0 + 27/11*t**3.
t**2*(t - 13)*(t - 1)**2/11
Let h be (-124)/651*(-2)/4*6. Suppose -h*l**3 + 0*l**2 + 0 + 4/7*l = 0. What is l?
-1, 0, 1
Let z be (15/275)/((-47)/(-1410)). Let c(j) = -j**3 + j**2 - j - 1. Let y be c(-1). Suppose -24/11*o + 8/11 + 4/11*o**3 - 6/11*o**4 + z*o**y = 0. Calculate o.
-2, 2/3, 1
Let x(d) be the first derivative of 34 - 1/3*d**6 - 9/2*d**4 - 2*d**2 + 2*d**5 + 0*d + 14/3*d**3. Factor x(w).
-2*w*(w - 2)*(w - 1)**3
Let y(j) = 14*j**2 + 153*j - 7. Let n be y(-11). Let d(f) be the second derivative of -6*f**2 - 4*f**3 + 7*f - 5/4*f**n + 0 - 3/20*f**5. Solve d(l) = 0 for l.
-2, -1
Let b = 27 - 25. Let d = 1 + b. Suppose d - 2*g**3 - 3 - 13*g**3 + 6*g**2 = 0. What is g?
0, 2/5
Let g = 119 + -50. Let o + g*o**3 - 3*o**2 - 68*o**3 + o = 0. What is o?
0, 1, 2
Factor 2/9*l**3 + 16/9*l - 20/9*l**2 + 2/9*l**4 + 0.
2*l*(l - 2)*(l - 1)*(l + 4)/9
Let c(o) be the first derivative of o**6/51 + 14*o**5/85 + 11*o**4/34 - 38*o**3/51 - 60*o**2/17 - 72*o/17 + 58. Find d such that c(d) = 0.
-3, -2, -1, 2
Let u(o) be the second derivative of -o**2/2 - 4*o - 7. Let d(b) = 2*b**3 - 2*b**2 - 5. Let i(t) = d(t) - 5*u(t). Determine s so that i(s) = 0.
0, 1
Let p = 699 - 689. Let y(n) be the third derivative of p*n**2 - 1/6*n**4 + 2/3*n**3 + 0 + 0*n + 1/60*n**5. Factor y(g).
(g - 2)**2
Suppose 2*m - 111 = 143. Let o = m - 507/4. Find w such that 0*w**2 - 1/4*w + 0 + o*w**3 = 0.
-1, 0, 1
Factor 12 - 8*a - 280*a**2 + 23*a - 2 + 285*a**2.
5*(a + 1)*(a + 2)
Let f(v) be the first derivative of 40/3*v**3 - 4*v**2 - 31/2*v**4 - 27 + 6*v**5 + 0*v. Suppose f(a) = 0. What is a?
0, 2/5, 2/3, 1
Let u = -35 - -38. Factor -4*v**5 + 5*v**4 - 4*v**u - 9*v**4 - 12*v**4 - 8*v**3.
-4*v**3*(v + 1)*(v + 3)
Suppose b = -b - 156. Let f be -3 + (0 - 2 - b/14). Suppose -2/7*c**2 - f + 6/7*c = 0. Calculate c.
1, 2
Suppose -3*v + 4*v + 3 = 0. Let z(g) = -2*g. Let h be z(v). Find u such that -2*u + 4*u**2 - h*u**2 + 0*u + 0*u = 0.
-1, 0
Let y = 265 - 265. Let w(k) be the first derivative of -5 - 1/6*k + y*k**2 + 1/18*k**3. Find r such that w(r) = 0.
-1, 1
Let l = -14272 - -14274. Determine y, given that 0*y + 1/2*y**l + 0 = 0.
0
Let j(d) be the first derivative of -d**6/3 - 16*d**5/5 - 19*d**4/2 - 8*d**3 + 491. Suppose j(b) = 0. What is b?
-4, -3, -1, 0
Suppose -3*h - 2 = -5*k - 20, 4*k - 24 = -4*h. Factor 3 + c**2 - c + 2*c - h*c + 1.
(c - 4)*(c - 1)
Let h(x) be the first derivative of -x**8/1848 + x**7/1155 - 18*x**2 + 25. Let v(g) be the second derivative of h(g). Factor v(q).
-2*q**4*(q - 1)/11
Let w(k) be the third derivative of 0*k + 0 - 1/260*k**6 - 1/1365*k**7 + 0*k**3 - 1/130*k**5 - 16*k**2 - 1/156*k**4. Find l such that w(l) = 0.
-1, 0
Determine t so that -3*t**2 - 10 + 2*t**3 + 15*t**2 - 18 + 6*t + 8 = 0.
-5, -2, 1
Suppose -2*u + 5*u + 3*b - 9 = 0, 2*u = b - 6. Let r be -6*2/(-4) + u. Factor -2*k**4 + 2*k**r + 16 + 4*k**3 - 16 + 3*k - 7*k.
-2*k*(k - 2)*(k - 1)*(k + 1)
Let f(o) = -3*o**2 - 5*o - 3. Suppose 3*s + 446 = 443. Suppose -3*k = -0*k - 3. Let j(v) = -v**2 + v + 1. Let x(u) = k*j(u) + s*f(u). Factor x(a).
2*(a + 1)*(a + 2)
Suppose -5*r - 3*n - 15 = 0, 25 = -0*r - 3*r - 5*n. Suppose r = h - 0*h - 2. What is a in -4 - 5*a**h + 22*a**3 - 45*a**3 + 24*a**3 + 8*a = 0?
1, 2
Solve -6/17*h + 2/17 + 6/17*h**2 - 2/17*h**3 = 0 for h.
1
Let s be (16/28)/(-1)*35/(-30). Solve -s - 50*o**2 + 250/3*o**3 + 10*o = 0.
1/5
Let v = -13004/45 - -289. Let t(p) be the second derivative of 2*p + v*p**5 - 1/9*p**2 - 5/54*p**4 + 0 + 4/27*p**3. Suppose t(l) = 0. What is l?
1/2, 1
Let c be (80/3)/(-5)*-3. Let s = c - 11. Factor 13*g**3 + 0*g**4 - 4*g**s - 5*g**3 + 4*g**4.
-4*g**3*(g - 2)*(g + 1)
Let m be (-70)/28 - 38/(-8). Factor 0 - m*z - 3/4*z**2.
-3*z*(z + 3)/4
Let k be -2 + 1 + -2 - (-14)/(-112)*-24. Factor k + 0*a + 1/6*a**4 - 1/2*a**2 - 1/3*a**3.
a**2*(a - 3)*(a + 1)/6
Factor 13*u**3 - 1231*u - 68*u**2 + 7*u**3 + 1295*u + 2*u**4 - 3*u**4.
-u*(u - 16)*(u - 2)**2
Determine m so that -8*m + 96 + 1/6*m**2 = 0.
24
Suppose 2*y**2 + 31*y - 64*y + 29*y + 2*y**3 = 0. What is y?
-2, 0, 1
Let b = -30 - -1621/54. Let x(c) be the second derivative of 0*c**2 + c + 0 - 1/27*c**3 + b*c**4. Let x(a) = 0. Calculate a.
0, 1
Let b = 11/780 + 1/52. Let q(u) be the second derivative of -1/2*u**4 - 1/5*u**5 - 2*u - 2/3*u**3 - 1/2*u**2 - b*u**6 + 0. Let q(z) = 0. Calculate z.
-1
Let c(g) be the third derivative of 23*g**6/1140 - g**5/285 - 23*g**4/57 + 8*g**3/57 - 2*g**2 + 48. Suppose c(m) = 0. Calculate m.
-2, 2/23, 2
Let i = -1101/5 + 221. Factor -i - 2/5*u + 2/5*u**2.
2*(u - 2)*(u + 1)/5
Let k = -42281/9 + 4703. Solve 8/9 + 28/9*d**3 + 2/3*d**4 + k*d**2 + 32/9*d = 0 for d.
-2, -1, -2/3
Let z = -31 - -34. What is t in 1990*t**2 + 50*t**z - 28*t