f - 3*f**2 + 28*f - 2352 + 57*f = 0. What is f?
28
Let n = 4 + 7. Find a such that -1105*a**2 - 22*a - 18*a**3 + 3*a**5 + 3*a**4 - n*a - 9 + 1063*a**2 = 0.
-1, 3
Let d(a) be the first derivative of 0*a**2 - 2/5*a + 4 + 2/15*a**3. Solve d(y) = 0 for y.
-1, 1
Suppose 2/7*m**4 + 2/7*m**2 + 8/7*m**3 - 12/7*m + 0 = 0. Calculate m.
-3, -2, 0, 1
Suppose 46 = 7*b - 80. Suppose 5*y = -y + b. Factor -1/4*v**y - 1/4*v**4 + 1/4*v**2 + 1/4*v + 0.
-v*(v - 1)*(v + 1)**2/4
Let d be 253/(-132) + 2 + (0 - 0). Let b(l) be the second derivative of 1/2*l**2 + d*l**3 + 0 - 1/24*l**4 - 7*l. Factor b(m).
-(m - 2)*(m + 1)/2
Let r(t) = 36*t + 612. Let y be r(-17). Factor 2/11*d**4 + 0 - 2/11*d**3 + y*d**2 + 0*d.
2*d**3*(d - 1)/11
Determine o so that 12*o + 0 - 5*o**2 - 23*o + 25 + 31*o = 0.
-1, 5
Let q(i) be the third derivative of i**6/420 + i**5/5 - 15*i**4/7 + 184*i**3/21 + 147*i**2 + 2*i. Let q(b) = 0. What is b?
-46, 2
Let j(n) be the third derivative of -n**5/10 + n**4 - 5*n**3/2 - 15*n**2. Let k(h) = 7*h**2 - 25*h + 14. Let s(x) = 4*j(x) + 3*k(x). Solve s(g) = 0 for g.
1, 6
Let v(g) = -12*g**2 + 162*g + 164. Let w(b) = -19*b**2 + 242*b + 245. Let i(u) = 8*v(u) - 5*w(u). Factor i(c).
-(c - 87)*(c + 1)
Suppose -11*w = -3*w - 80. Suppose -9*r**3 - w + 6*r + 22*r - r - 84*r**2 + 32*r = 0. What is r?
-10, 1/3
Suppose d - 6*o = -2*o - 8, -52 = -4*d - 5*o. Factor v**2 - d*v**3 + 15*v**3 - 6*v**3.
v**2*(v + 1)
Let w(v) = -v**3 - v**2 - v. Suppose -3*i = 32 + 19. Let p = 13 + i. Let b(h) = 2*h**3 + 6*h + 4. Let m(k) = p*w(k) - b(k). Let m(y) = 0. Calculate y.
-2, -1, 1
Let y(j) be the third derivative of -j**8/1344 - j**7/120 - 7*j**6/240 - j**5/30 - 171*j**2. Determine m so that y(m) = 0.
-4, -2, -1, 0
Let o(x) be the third derivative of -1/120*x**6 + 0*x - 21*x**2 + 0*x**4 + 0*x**3 + 1/210*x**7 - 1/1008*x**8 + 1/180*x**5 + 0. Factor o(r).
-r**2*(r - 1)**3/3
Let q = 13526 + -13523. Find u such that -4/5*u**5 - u**4 + u**2 + 3/5*u**q + 0 + 1/5*u = 0.
-1, -1/4, 0, 1
Let g(i) = 3 - 2 + 2 - 3*i. Let a(n) = n**4 - n**2 + 5*n - 5. Let x(s) = -3*a(s) - 5*g(s). Factor x(m).
-3*m**2*(m - 1)*(m + 1)
Let c(g) be the first derivative of g**3/3 + 5*g**2/2 - 50*g - 353. Factor c(j).
(j - 5)*(j + 10)
Let z(a) = 2*a**2 - 11*a + 5. Let o be z(6). Let n be o/(-33) + (-7)/(-3). Find y such that -1 + 1 - 7*y**n + 5*y + 2*y**2 = 0.
0, 1
Suppose -2*u = -9*u - 7. Let r be -2 + (44/(-16))/u. Factor -9/4*d**4 - 3/2*d**3 + 3/4 + 3/2*d**2 - r*d**5 + 9/4*d.
-3*(d - 1)*(d + 1)**4/4
Let z(v) be the first derivative of -v**5/60 - 5*v**4/6 - 50*v**3/3 - 2*v**2 - v - 18. Let r(y) be the second derivative of z(y). Suppose r(f) = 0. Calculate f.
-10
Let q(o) = -5*o + o**3 + 4*o**3 + 4 - 4*o**3 - 3*o**2 + 0*o**2. Let c be q(4). Factor 0*m + 3/8*m**3 + 1/4*m**2 + c.
m**2*(3*m + 2)/8
Let x(y) be the first derivative of -y**5/80 - 7*y**4/48 - 11*y**3/24 - 5*y**2/8 + 26*y - 2. Let h(g) be the first derivative of x(g). Factor h(q).
-(q + 1)**2*(q + 5)/4
Let v(f) = -7*f**3 - 57*f**2 - 246*f - 193. Let m(w) = -8*w**3 - 56*w**2 - 244*w - 192. Let k(o) = -3*m(o) + 4*v(o). What is p in k(p) = 0?
-7, -1
Let n = -1589 + 1589. Let v(i) be the first derivative of -1/6*i**3 - 8 + n*i + 0*i**2 + 1/8*i**4. Solve v(u) = 0 for u.
0, 1
Factor 152/7*v + 48/7 + 10/7*v**3 + 12*v**2.
2*(v + 2)*(v + 6)*(5*v + 2)/7
Factor 5*c**3 - 5*c**4 - 7*c**4 - 16*c**2 + 19*c**3 + 4*c**5 - 4*c**4 + 4*c.
4*c*(c - 1)**4
Let p(b) be the first derivative of -4/3*b**3 - 2*b**2 + 0*b + 4. What is f in p(f) = 0?
-1, 0
Let q(c) be the third derivative of -c**5/21 - 2*c**4/7 - 8*c**3/21 + 3*c**2 - 5. Factor q(f).
-4*(f + 2)*(5*f + 2)/7
Let y(b) be the third derivative of 256*b**7/105 + 8*b**6/5 - b**4/6 - 419*b**2. Solve y(v) = 0 for v.
-1/4, 0, 1/8
Let h(u) be the second derivative of -u**7/70 - u**6/5 - 27*u**5/25 - 27*u**4/10 - 27*u**3/10 + 684*u + 2. Find s such that h(s) = 0.
-3, -1, 0
Let x(v) = v**5 + 2*v**4 + v**3 + v - 1. Let d(m) = m**5 + 212*m**4 - 4751*m**3 + 40854*m**2 - 68240*m + 31940. Let q(w) = -d(w) + 4*x(w). Factor q(r).
3*(r - 22)**3*(r - 1)**2
Let i(k) = 4*k**3. Let x be i(1). Let p(g) = g**2 - 1. Let f(b) = b**3 - 4*b**2 - b + 4. Let n(o) = x*p(o) + f(o). Find c such that n(c) = 0.
-1, 0, 1
Let y be (2/2)/((-5)/(-5)). Find w such that -y - 1 + w**2 + w**2 + 0*w**2 = 0.
-1, 1
Let l(t) be the second derivative of -t**9/26460 - t**8/5880 - t**7/4410 + 7*t**4/3 - t. Let h(w) be the third derivative of l(w). Factor h(k).
-4*k**2*(k + 1)**2/7
Find g such that -482*g**5 - 94*g**3 - 77*g**3 + 479*g**5 + 174*g**4 = 0.
0, 1, 57
Let i(s) be the third derivative of 1/10*s**6 + 0 + 17*s**2 + 0*s**3 + 0*s - 1/12*s**4 + 1/30*s**7 + 1/20*s**5. Factor i(y).
y*(y + 1)**2*(7*y - 2)
Suppose r + 14*r = -2*r. Determine g, given that 0*g - 3/5*g**2 + 3/5*g**3 + r = 0.
0, 1
Suppose -3*d + 5*d = -12. Let z be (d/(-7))/(3/14). Find y, given that -2*y**2 - y**2 + 2*y - 2*y**3 + y**4 + y**2 + y**z = 0.
-1, 0, 1
Let m(v) be the third derivative of -v**7/15120 - v**6/2160 + v**5/240 + v**4/4 + v**2. Let u(a) be the second derivative of m(a). Solve u(f) = 0 for f.
-3, 1
Let z = -2005 + 2005. Factor -2/17*h - 2/17*h**3 - 4/17*h**2 + z.
-2*h*(h + 1)**2/17
Let q(l) be the first derivative of 2/15*l**4 + 4 - 4*l - 1/20*l**5 + 0*l**2 - 2/15*l**3 + 1/150*l**6. Let o(u) be the first derivative of q(u). Factor o(t).
t*(t - 2)**2*(t - 1)/5
Find v, given that -139*v**4 - 900*v + 69*v**4 - 405 - 100*v**3 + 65*v**4 - 590*v**2 = 0.
-9, -1
Let k(a) = a**2 + 4*a - 16. Let h be k(-8). Factor 17*b**2 - b**4 - 2*b**3 - h*b**2 + b + b**3.
-b*(b - 1)*(b + 1)**2
Suppose 22 = 4*y - 10. Factor 16*z - 12*z - 13*z**2 + 12*z**3 + 20*z - 13*z**2 - 2*z**4 - y.
-2*(z - 2)**2*(z - 1)**2
Let z be -3*9948/18956 + (0 - -1). Let x = -2/677 - z. Determine q, given that 2*q + x - 18/7*q**2 = 0.
-2/9, 1
Let i(t) = t - 14. Let q be i(9). Let r be 6/(-10) - 18/q. Determine k so that -3*k**4 - 2*k**4 - 4*k**2 - 15*k**r + k**2 - 7*k**2 = 0.
-2, -1, 0
Determine n so that -78*n**2 - 501*n**3 - 25229 + 25229 + 39*n**4 = 0.
-2/13, 0, 13
Let n = -75/22 + 21/11. Let c = 9/4 + n. Factor 0*t - c*t**3 - 3/4*t**2 + 0.
-3*t**2*(t + 1)/4
Suppose -177/5*b**2 + 3/5*b**3 - 132 + 672/5*b = 0. What is b?
2, 55
Factor -3/5*y**2 - 6/5*y + 1/5*y**3 + 8/5.
(y - 4)*(y - 1)*(y + 2)/5
Let r(v) = -v**3 - 14*v**2 - 16*v - 11. Let p be r(-13). Factor g + g**2 + 0*g - p + 28.
g*(g + 1)
Let x(m) be the second derivative of -16*m**2 - 2/15*m**6 + 0 + 2*m**4 - 8/3*m**3 + 5*m + 1/5*m**5. Factor x(s).
-4*(s - 2)**2*(s + 1)*(s + 2)
Solve -3*x - 4*x**3 + 413*x**2 + 0*x + 139*x**2 + 3*x = 0 for x.
0, 138
Suppose -4*x - 4*z + 210 - 198 = 0, 2*x + 5*z = 15. Factor 0*o + 1/8*o**4 + x*o**3 - 1/4*o**2 + 1/8.
(o - 1)**2*(o + 1)**2/8
Let s = 63 - 89. Let b = -24 - s. Determine m, given that 4/9*m + 0 + 2/3*m**b + 2/9*m**3 = 0.
-2, -1, 0
Let b(w) be the first derivative of -3*w**4/4 - w**3 - w**2/2 - 3*w - 11. Let g(o) = o**3 - o + 1. Let r(c) = 3*b(c) + 6*g(c). What is d in r(d) = 0?
-1
Let w = -10452 - -10454. Solve 3/5 + 1/5*r**w + 4/5*r = 0 for r.
-3, -1
Let y be (3 - 8)*-3 - 3. Let r be 4/(-3)*(-45)/y. Suppose -r*g - 4*g + 3*g + 4*g**2 + 4*g**3 - 4 + 2*g = 0. Calculate g.
-1, 1
Factor -8 + 3 - 2 + 4*l**2 - 21 + 54*l.
2*(l + 14)*(2*l - 1)
Let r(p) be the third derivative of p**7/735 + p**6/70 + p**5/42 + 110*p**2. Factor r(t).
2*t**2*(t + 1)*(t + 5)/7
Let l be ((-295)/(-708))/(-2 - (-7)/3). Let f(w) be the second derivative of 0 - 4*w + 3/5*w**5 - l*w**4 + 1/2*w**3 + 0*w**2. Let f(v) = 0. What is v?
0, 1/4, 1
Let x = -35 - -52. Let a = x - 15. Factor 0*r**2 + r**2 + 0*r**a - r.
r*(r - 1)
Let y(z) be the third derivative of -19*z**6/240 - 3*z**5/5 - 5*z**4/4 + 4*z**3/3 + 187*z**2. Factor y(x).
-(x + 2)**2*(19*x - 4)/2
Let i(j) be the second derivative of j**5/30 - 35*j**4/18 + 32*j**3 + 108*j**2 + j - 10. Factor i(q).
2*(q - 18)**2*(q + 1)/3
Let f be -2 + (-46)/(-6) - 1/(-3). Suppose 2*q - 2*c = 3 - 9, 2*c = f. Factor 1/4*w**5 - w**4 + w**2 + q - w + 3/4*w**3.
w*(w - 2)**2*(w - 1)*(w + 1)/4
Let j(r) be the third derivative of r**7/210 - r**3/6 + 27*r**2. Let h(q) = -5*q**4 + 4*q**3 + q**2 - 4*q + 4. Let o(f) = h(f) + 4*j(f). Factor o(n).
-n*(n - 4)*(n - 1)*(n + 1)
Suppose 5*j - 3*j = -2*j. Let m(h) be the third derivative of 1/90*h**6 -