. Let c(b) = 0. Calculate b.
1, 3/2
Let t = -819/5 + 164. Find s such that -t + 0*s + 1/5*s**2 = 0.
-1, 1
Let k = 2 + 2. Suppose k*g - 3 = 9. Let 3/2*y**2 + 1/4*y**4 + y + y**g + 1/4 = 0. What is y?
-1
Let -3/4*q - 1/2*q**2 + 1/2 = 0. What is q?
-2, 1/2
Let p = 1 - -11. Suppose -4*q**2 - 18*q + 0 + q**2 - 3 + p*q = 0. What is q?
-1
Let u = -4 - -6. Suppose 4*v**2 - 2*v**3 - 2*v**3 + u*v**3 - 2*v = 0. What is v?
0, 1
Let y(x) be the first derivative of 464*x**3/3 - 42*x**2 - 8*x + 40. Determine g so that y(g) = 0.
-2/29, 1/4
Let g(j) = -3*j + 11. Let b(a) = -a. Let r(y) = -2*b(y) + g(y). Let h be r(9). Suppose d**3 - h*d**4 + 0*d**4 - d**5 - 2*d**3 = 0. What is d?
-1, 0
Let r(l) be the second derivative of 2/15*l**6 - 1/3*l**4 + 0*l**2 + 0*l**5 + 0 - 1/3*l**3 + 1/21*l**7 + l. Factor r(s).
2*s*(s - 1)*(s + 1)**3
Let h(x) be the first derivative of 100*x**3/3 + 20*x**2 + 4*x + 3. Suppose h(a) = 0. What is a?
-1/5
Let o(k) be the first derivative of -k**5/50 + k**4/20 - k**2/10 + k/10 + 41. Find y, given that o(y) = 0.
-1, 1
Factor 29*w**5 + 6*w - 75*w**2 + 4*w + 165*w**3 - 145*w**4 + 16*w**5.
5*w*(w - 1)**3*(9*w - 2)
Let o(m) = -2*m - 4. Let i be o(-2). Let v(q) be the first derivative of 1 + 0*q**2 + 0*q**4 + i*q - 1/15*q**3 + 1/25*q**5. Factor v(g).
g**2*(g - 1)*(g + 1)/5
Let h(b) be the second derivative of 1/42*b**4 + 0 + 2/35*b**5 + b + 0*b**2 - 1/35*b**6 - 2/21*b**3. Determine k, given that h(k) = 0.
-2/3, 0, 1
Let f(n) be the third derivative of -3*n**2 + 0*n**3 + 0*n**4 + 0 + 1/150*n**5 + 0*n. Let f(q) = 0. Calculate q.
0
Let r(m) = -m**2 - 14*m + 8. Let t be r(-14). Suppose -13*i**5 + t*i**5 + 9*i**4 + 3*i**3 + 2*i - 2*i**4 - 7*i**2 = 0. What is i?
-1, 0, 2/5, 1
Let o(p) be the first derivative of -2/3*p**3 + 0*p**4 - 1/2*p**2 + 2/5*p**5 + 0*p + 1/6*p**6 - 2. Solve o(k) = 0 for k.
-1, 0, 1
Let o(a) be the third derivative of -a**6/90 - a**5/30 + a**4/3 - a**3/6 + a**2. Let f(k) be the first derivative of o(k). Factor f(s).
-4*(s - 1)*(s + 2)
Let w(a) be the third derivative of -a**7/35 - a**6/8 - a**5/20 + a**4/4 + 3*a**2. Factor w(b).
-3*b*(b + 1)*(b + 2)*(2*b - 1)
Suppose 5*y - 19 + 4 = 0. Let l be (4 + 0 + -4)/y. Factor 1/4*w**4 - 3/4*w**2 + l*w**3 - 1/2*w + 0.
w*(w - 2)*(w + 1)**2/4
Let j(q) = q**2 - 4*q + 1. Let z be j(5). Let b(d) = -2*d**2 + 2. Let t(p) = -6*p**2 + 6. Let c(a) = z*t(a) - 17*b(a). Find g such that c(g) = 0.
-1, 1
Let k = -109 + 1636/15. Let p(r) be the second derivative of 0*r**3 + 0 + 2*r + 0*r**2 + k*r**6 - 1/6*r**4 - 7/20*r**5 + 1/6*r**7. Factor p(n).
n**2*(n - 1)*(n + 1)*(7*n + 2)
Let c(w) be the third derivative of w**10/7560 + w**9/1260 + w**8/560 + w**7/630 - 7*w**5/60 - 5*w**2. Let x(d) be the third derivative of c(d). Factor x(q).
4*q*(q + 1)**2*(5*q + 2)
Suppose 4*a = 8*a - 12. Factor -2*y**5 + 30*y**2 + 9*y**a + 3 + 15*y**4 - y**5 - 39*y**3 - 15*y.
-3*(y - 1)**5
Let j(s) be the second derivative of s**5/130 - s**4/39 - 4*s. Determine l, given that j(l) = 0.
0, 2
Let k = 13/8 - 41/40. Let s(p) be the first derivative of k*p**5 - 4 + 6*p**2 + 0*p + 0*p**3 - 9/4*p**4. Factor s(u).
3*u*(u - 2)**2*(u + 1)
Factor -3/5*v - 4/5 + 3/10*v**2 + 1/10*v**3.
(v - 2)*(v + 1)*(v + 4)/10
Let g(a) be the second derivative of 2*a + 0 - 1/2*a**2 + 1/2*a**3 - 1/4*a**4 + 1/20*a**5. Let g(k) = 0. What is k?
1
Let x be (-2 - 15/(-10))*-12. Let l(j) be the second derivative of 0 - j + 5/84*j**7 - 1/2*j**2 - 1/12*j**3 - 2/15*j**x + 5/12*j**4 - 1/10*j**5. Factor l(a).
(a - 1)**3*(a + 1)*(5*a + 2)/2
Factor -12/13 + 2/13*t**3 - 10/13*t + 4/13*t**2.
2*(t - 2)*(t + 1)*(t + 3)/13
Solve -4/19 + 2/19*u**3 - 2/19*u + 4/19*u**2 = 0 for u.
-2, -1, 1
Factor 0*r**2 + 0 - 3/7*r**3 + 0*r**4 + 0*r + 3/7*r**5.
3*r**3*(r - 1)*(r + 1)/7
Factor 5*o**5 + o**3 + 10*o**2 + o**3 - 26*o**3 + 9*o**3.
5*o**2*(o - 1)**2*(o + 2)
Let m = -5 + 11. Let h be m/15*15/3. Let 0 + 0*w**3 + 0*w**h + 1/3*w**4 + 0*w + 1/3*w**5 = 0. What is w?
-1, 0
Let p(s) = s - 2. Let y be p(4). Let v = -213 - -213. Suppose v + 0*u - 2/5*u**y = 0. What is u?
0
Let l(r) = 3*r - r**2 + 7 + 1 - 10*r. Let z be l(-8). Determine x so that 8/7*x**2 + z + 4/7*x**4 + 10/7*x**3 + 2/7*x = 0.
-1, -1/2, 0
Let m = -157 + 157. Factor 0*j**2 + m - 1/2*j + 1/2*j**3.
j*(j - 1)*(j + 1)/2
Let y be 1/(-3) + (-16)/(-3). Factor 7*b**4 - 27*b**3 - 22*b**2 + y*b**4 - 3*b**5 - 6*b + 3*b**4 + 43*b**2.
-3*b*(b - 2)*(b - 1)**3
Let l(q) be the first derivative of q**6/45 - q**5/10 + q**4/6 - q**3/9 - q**2 - 11. Let j(d) be the second derivative of l(d). Factor j(z).
2*(z - 1)**2*(4*z - 1)/3
Let t**2 - 15*t - 7*t**2 - 2*t**2 + 5*t**2 = 0. What is t?
-5, 0
Determine d, given that -9*d**2 - 36*d**2 - 5 - 5 - 25*d**3 - 184*d**4 - 35*d + 179*d**4 = 0.
-2, -1
Let d(y) = -y**3 - 12*y**2 + 3*y. Let r(a) = 6*a**2 - 2*a. Let b(x) = -4*d(x) - 10*r(x). Factor b(w).
4*w*(w - 2)*(w - 1)
Let j = -1/70 + 3/10. Find m such that 2/7*m**2 + j*m + 0 = 0.
-1, 0
Let s(j) be the second derivative of -j**4/72 - j**3/36 - 2*j. Factor s(c).
-c*(c + 1)/6
Let t(q) = -14*q**2 + 2*q. Let x be t(3). Let k be (-4)/x*-4*-48. Factor 12/5*c**2 + 2/5*c**3 + 2/5*c - 48/5*c**4 + k*c**5 + 0.
2*c*(c - 1)**2*(4*c + 1)**2/5
Let r = 164 - 1967/12. Let i(f) be the second derivative of 0*f**2 + 1/30*f**6 - 1/12*f**4 - 1/84*f**7 - 2*f + 0 + 0*f**5 + r*f**3. Factor i(v).
-v*(v - 1)**3*(v + 1)/2
Let h = 7 - 5. Determine n so that 2*n + 2*n + h*n**2 - 1 - 5*n = 0.
-1/2, 1
Determine p, given that -8/3 - 14/3*p - 7/3*p**2 - 1/3*p**3 = 0.
-4, -2, -1
Let t(l) be the second derivative of l**4/16 + l**3/8 - 3*l**2/4 - 27*l. Let t(g) = 0. What is g?
-2, 1
Let w(b) be the first derivative of -2*b**5/5 + b**4/2 - 7. Factor w(q).
-2*q**3*(q - 1)
Suppose 2*a - 9 + 1 = 0. Let p(v) be the first derivative of 1/9*v**3 + 0*v**2 + 0*v - 2 + 1/15*v**5 - 1/6*v**a. Factor p(y).
y**2*(y - 1)**2/3
Let t(j) be the second derivative of j**5/120 - 5*j. Factor t(v).
v**3/6
Let b(v) = -v**2 + v. Let z(g) = -g**2 + 1. Let f(s) = s**2 - s - 1. Let j be f(2). Let r(x) = j*b(x) + 2*z(x). Factor r(o).
-(o - 1)*(3*o + 2)
Let i = -4 - -2. Let p = 2 + i. Find s such that -2 - 2*s**4 + 3*s**2 + s**2 + p = 0.
-1, 1
Let f = 10 + -6. Suppose f*z - 4 - 8 = 0. Factor h - 3 + 3 + 4*h**2 - z*h**4 + 7*h**4 + h**5 + 6*h**3.
h*(h + 1)**4
Let k(y) be the third derivative of y**6/24 + 5*y**5/12 + 5*y**4/4 + 23*y**2. Factor k(p).
5*p*(p + 2)*(p + 3)
Let p = 137 - 2053/15. Suppose 0*z - 4/15*z**4 + p*z**3 + 0 + 2/15*z**5 + 0*z**2 = 0. What is z?
0, 1
Let s be 4 + (2 + -5 - -2). Let b(o) = -o**3 - 4*o**2 + 5*o - 4. Let q(v) = -v**3 - 3*v**2 + 4*v - 3. Let w = -3 + -1. Let d(l) = s*b(l) + w*q(l). Factor d(j).
j*(j - 1)*(j + 1)
Determine r so that 50*r**2 - r**4 - 5*r**2 + 20 + 55*r - 4*r**4 + 5*r**3 = 0.
-1, 4
Let g(u) be the second derivative of -u**4/6 + u**3 - 2*u**2 + 18*u. Factor g(a).
-2*(a - 2)*(a - 1)
Let d(a) be the first derivative of -a**5/10 - 2*a**4/9 - a**3/9 + 2*a - 3. Let l(x) be the first derivative of d(x). Solve l(p) = 0 for p.
-1, -1/3, 0
Let w = 243/4 + -60. Factor 0*t + 0 - w*t**2.
-3*t**2/4
Factor 10*p**2 + 19*p**3 - 8*p + 15*p**3 - 36*p**3.
-2*p*(p - 4)*(p - 1)
Let s(c) be the third derivative of -c**10/30240 - c**4/8 + 5*c**2. Let o(v) be the second derivative of s(v). Find f, given that o(f) = 0.
0
Suppose -2*h - 4 = 2*f - 3*h, 8 = 3*f + 2*h. Suppose f = -3*s + 8 + 1. Let -3 + c + c**2 + s = 0. What is c?
-1, 0
Let g be 95/20 + (-24)/(36/6). Determine j, given that -1/4*j**4 - 3/4*j + 1/2 - 1/4*j**2 + g*j**3 = 0.
-1, 1, 2
Let s(o) = -o**2 - 3*o + 2. Let d(k) = 5*k**2 + 16*k - 10. Let g(n) = -2*d(n) - 11*s(n). Determine w, given that g(w) = 0.
-2, 1
Let u be 2/(60/8 + -7). Suppose 0*v + 1/2*v**2 + 1/2*v**u - v**3 + 0 = 0. Calculate v.
0, 1
Let j(f) be the third derivative of 0*f - 1/18*f**6 - 8/45*f**5 + 7*f**2 - 2/9*f**4 + 0 - 2/315*f**7 + 0*f**3. Factor j(b).
-4*b*(b + 1)*(b + 2)**2/3
Let w = -20382/13 - -1569. Let q = w + 59/39. Factor -q*t**2 + 0 + 8/3*t + 2/3*t**3.
2*t*(t - 2)**2/3
Let f be 0/((-6)/(-3) - 1). Factor -3*m**5 + f*m**4 + 3*m**4 + m**2 + 3*m**3 - 4*m**2.
-3*m**2*(m - 1)**2*(m + 1)
Let i(s) be the first derivative of s**7/840 - s**5/40 + s**4/12 - 5*s**3/3 - 4. Let d(q) be the third derivative of i(q). Factor d(c).
(c - 1)**2*(c + 2)
Let x(q) be the first derivativ