.
0, 1
Let w(n) be the first derivative of -n**3/9 + 169*n**2/3 - 28561*n/3 + 664. Suppose w(u) = 0. What is u?
169
Let z = -58 + 62. Factor 2*c**3 - 58*c + z - c**4 - 6*c**3 - 3*c**2 + 62*c.
-(c - 1)*(c + 1)*(c + 2)**2
Let b be (18/189)/(7/49). Find t such that -2/9*t**2 - 4/9*t + b = 0.
-3, 1
Factor 5/9*t - 1/3 + 2/9*t**2.
(t + 3)*(2*t - 1)/9
Solve 0*j + 0 - 21/8*j**3 + 9/4*j**2 + 0*j**4 + 3/8*j**5 = 0 for j.
-3, 0, 1, 2
Let g(n) be the second derivative of 10*n**7/21 + 3*n**6/2 - 5*n**5/2 - 175*n**4/12 - 20*n**3 - 10*n**2 + 385*n. Find t, given that g(t) = 0.
-2, -1, -1/4, 2
Let q(t) = -t**4 - t**3 + t**2 + t - 1. Let k(y) = y**5 - 29*y**4 + 223*y**3 + 861*y**2 + 932*y + 328. Let c(s) = -k(s) - 4*q(s). Factor c(f).
-(f - 18)**2*(f + 1)**3
Let v be 2/(-1) - 16/(-4). Suppose -4*q + 12 = r, -3*q = -v*r - 5*q + 12. Let g**4 + 6*g**r + 0*g**4 - 3*g**4 = 0. What is g?
0
Factor -28*a + 1/4*a**2 + 784.
(a - 56)**2/4
Factor -5 + 3/8*o**2 + 1/8*o**3 - 9/4*o.
(o - 4)*(o + 2)*(o + 5)/8
Let z(q) be the first derivative of -q**5/5 - q**4 - 2*q**3 - 2*q**2 - q + 468. What is v in z(v) = 0?
-1
Let w(v) = -17*v**3 - 4*v**2 - 5*v - 3. Let h be w(-2). Let s = h + -761/6. Factor 1/2*t**3 + 0 + s*t**5 + 2/3*t**4 - 2/3*t - 2/3*t**2.
t*(t - 1)*(t + 1)*(t + 2)**2/6
Let z = -116 + 114. Let b be 160/(-28) - (-8 - z). Factor 1/7*w**2 - 3/7*w + b.
(w - 2)*(w - 1)/7
Let l = 7735 - 7735. Factor -1/3*d**4 + 4/3*d**2 - 1/3*d**3 + 4/3*d + l.
-d*(d - 2)*(d + 1)*(d + 2)/3
Factor -37/4*b - 13/2*b**2 + b**3 + 1/4*b**5 + 2*b**4 - 7/2.
(b - 2)*(b + 1)**3*(b + 7)/4
Let q = 4 - 2. Suppose 3*z - 2*z = q. Solve -2*i**z - 8*i + 0*i - 4 + 4*i**2 - 5*i**2 = 0 for i.
-2, -2/3
Let f(v) be the first derivative of -21/16*v**4 + 0*v - 3/2*v**5 + 23 - 3/8*v**6 + 3/2*v**2 + v**3. Find i such that f(i) = 0.
-2, -1, 0, 2/3
Suppose -z - z = -12. Let x = -3 + z. Factor 0*o**2 + 6*o + 6*o**2 + x*o**2 + 3*o**3.
3*o*(o + 1)*(o + 2)
Let w(d) be the first derivative of 33*d**5/10 - 51*d**4/4 - 4*d**3 + 51*d**2/2 - 9*d/2 - 18. What is i in w(i) = 0?
-1, 1/11, 1, 3
Factor 4/15*n**3 - 4/15*n + 0*n**2 - 2/15 + 2/15*n**4.
2*(n - 1)*(n + 1)**3/15
Let t(a) be the second derivative of -2*a**6/45 + 2*a**5/15 - 4*a**3/9 + 2*a**2/3 - 337*a. Solve t(y) = 0.
-1, 1
Let o(m) be the second derivative of m**6/15 - m**5/3 - 5*m**4/6 + 10*m**3/3 - 8*m**2/3 - 14*m. Suppose o(b) = 0. What is b?
-2, 1/3, 1, 4
Suppose 151*h - 576 = -101*h + 180. Solve 1/2*i**h - 1/2*i**2 - 1/2*i + 0 + 1/2*i**4 = 0.
-1, 0, 1
Suppose -52*m + m = -102. Determine d, given that -2/9*d**m + 16/9*d - 32/9 = 0.
4
Factor -6/7*j**3 + 0 + 32/7*j**2 - 24/7*j - 2/7*j**4.
-2*j*(j - 2)*(j - 1)*(j + 6)/7
Let a be ((1/21)/(-1))/(20/(-70)). Factor 1/6*k**3 + 0*k + a*k**4 + 0 - 1/6*k**2 - 1/6*k**5.
-k**2*(k - 1)**2*(k + 1)/6
Let t = 23/315 + 761/2520. Factor -3/2*f - t*f**2 - 9/8.
-3*(f + 1)*(f + 3)/8
Let z(x) = -6*x**2 + 54*x + 4. Let r be z(9). Let j(u) be the third derivative of 2/9*u**r + 0*u + 8/9*u**3 + 5*u**2 + 1/45*u**5 + 0. Factor j(m).
4*(m + 2)**2/3
Let u(k) = 19*k**2 - 32*k - 36. Let x(p) = -7*p**2 + 11*p + 12. Let t(h) = -4*u(h) - 11*x(h). Let t(a) = 0. Calculate a.
-4, -3
Let m be 2*(3 + (2 - -2)). Suppose -5*h = 3*l + 5, h = -3*l - m + 1. Factor 3*c + c**2 + 1 - 3*c**2 + c**3 + 4*c**2 + c**h.
(c + 1)**3
Let l(a) be the third derivative of -a**6/30 + 29*a**5/5 - 308*a**4 - 3872*a**3/3 + 40*a**2 - a. Determine h, given that l(h) = 0.
-1, 44
Let c = 45 + 3. Let -c*o**2 + 162*o**3 + 0 + 16*o - 9*o**5 + 12*o**4 - 130*o**3 + 0 = 0. What is o?
-2, 0, 2/3, 2
Let c = 612 - 609. Factor -1/2*s**4 - 4*s + 3/2 + c*s**2 + 0*s**3.
-(s - 1)**3*(s + 3)/2
Let q = -513/2 + 246. Let m = q - -45/4. Let -3/2*v**4 + 3/2*v**2 + 3/4*v**5 + 0*v + 0 - m*v**3 = 0. What is v?
-1, 0, 1, 2
Let n(m) = -7*m - 3. Let d be n(-2). Let k = d + -9. Factor -2*y - 3*y - 4*y**4 + y**k + 5*y.
-y**2*(2*y - 1)*(2*y + 1)
Let k = -184 + 924/5. Determine h so that 2/5*h**4 - k*h**3 + 0 + 2/5*h**2 + 0*h = 0.
0, 1
Determine x, given that -32*x - x**2 - 3*x**2 + 3*x**2 - 256 + 0*x**2 = 0.
-16
Let p = -27509/27 - -1019. Let b = 19/54 + p. Determine z, given that -3/4*z**4 - b*z**3 + 1/4 + 1/2*z**2 - 1/4*z**5 + 3/4*z = 0.
-1, 1
Let n(k) be the second derivative of 1/60*k**4 + 0*k**3 + 0 + 1/100*k**5 + 0*k**2 + 14*k. Factor n(p).
p**2*(p + 1)/5
Let r = 5629 - 5627. Factor -2*j + 1/4*j**r + 4.
(j - 4)**2/4
Let x(a) = 5*a**2 - 5*a. Let c be x(3). Let m = c - 28. Factor -8*b + 8*b + 0*b + m*b - 3 + b**2.
(b - 1)*(b + 3)
Let b be 147 - 0/(0/(-3) - 2). Factor -68 + 15*q**2 + q**3 + 46 + b + 75*q.
(q + 5)**3
Let h(f) be the first derivative of -f**7/1050 + f**5/150 - f**3/30 + f**2 - 6*f + 8. Let k(z) be the second derivative of h(z). Factor k(n).
-(n - 1)**2*(n + 1)**2/5
Let v(w) be the first derivative of w**4/4 - 4*w**3/3 - 5*w**2/2 + 2*w + 1. Let t be v(5). Suppose -3*i + 8*i - 16 - 4*i**t + 11*i = 0. Calculate i.
2
Suppose -l + 0*t = 3*t - 8, -3*l = 3*t - 12. Factor 4/11 - 2/11*f - 4/11*f**l + 2/11*f**3.
2*(f - 2)*(f - 1)*(f + 1)/11
Let k(f) = -f**2 + 54*f - 366. Let y be k(8). Let v be (-32)/(-10) + 0/(-5). Factor v*x - 128/5*x**y - 2/15 + 1024/15*x**3.
2*(8*x - 1)**3/15
Let r = 38777 + -38774. Let 0*i + 0 + 0*i**2 + 2/5*i**5 + 0*i**4 - 2/5*i**r = 0. Calculate i.
-1, 0, 1
Let a(v) = -17*v**2 + 736*v + 737. Let d(b) = -6*b**2 + 246*b + 246. Let u(r) = -3*a(r) + 8*d(r). Let u(z) = 0. Calculate z.
-1, 81
Let x(q) = -7*q - 35. Let b be (-5)/(-2)*(-6 + 8 + -4). Let r be x(b). Factor -z + 4*z**2 - 5/4*z**3 + r - 7/4*z**4.
-z*(z - 1)*(z + 2)*(7*z - 2)/4
Let q(k) = k**2 - 86 - 79 - k**3 + 165. Let i(d) = 26*d**3 - 74*d**2 - 18*d. Let w(z) = -i(z) + q(z). Find j, given that w(j) = 0.
-2/9, 0, 3
Let w(s) be the second derivative of 0 + 0*s**3 + 1/30*s**5 - 1/63*s**7 + 1/45*s**6 + 16*s + 0*s**2 - 1/18*s**4. Factor w(o).
-2*o**2*(o - 1)**2*(o + 1)/3
Let q(w) be the third derivative of w**6/540 - w**5/20 + 2*w**4/9 - 11*w**3/6 - 24*w**2. Let b(o) be the first derivative of q(o). Find p such that b(p) = 0.
1, 8
Let g(p) be the first derivative of 2/3*p**3 + 1/4*p**4 + 2 - 8*p - 2*p**2. Solve g(r) = 0.
-2, 2
Let i(v) = -v**2 - v + 2. Let s = -13 - -13. Let r be i(s). Factor -r*h**2 - 8/5 + 16/5*h + 2/5*h**3.
2*(h - 2)**2*(h - 1)/5
Let f(n) be the second derivative of -n**7/5040 - n**6/480 - n**4/2 + 2*n**2 - 35*n. Let i(j) be the third derivative of f(j). Solve i(y) = 0.
-3, 0
Let k(i) = i**3 + 25*i**2 + 31*i + 9. Let p be k(-23). Let d = 2484/7 - p. Factor d + 8/7*s + 2/7*s**2.
2*(s + 1)*(s + 3)/7
Let j(i) be the third derivative of 0 + 1/130*i**5 + 0*i**3 + 1/780*i**6 + 0*i - 13*i**2 - 1/78*i**4 + 1/2184*i**8 - 1/455*i**7. Suppose j(f) = 0. Calculate f.
-1, 0, 1, 2
Let k = 9727 - 9725. Factor 0 + h**k - 2/3*h - 1/3*h**3.
-h*(h - 2)*(h - 1)/3
Let g be (-130)/308 + (-2 - 64/(-28)). Let u = 17/44 + g. Factor -1/2*d**2 + 1/2 + u*d**3 - 1/4*d.
(d - 2)*(d - 1)*(d + 1)/4
Let p(m) be the second derivative of -m**5/5 + 22*m**4/3 - 335*m. Solve p(c) = 0 for c.
0, 22
Let f = -103799/6 - -17300. Suppose -7/3*w + 49/6 + f*w**2 = 0. Calculate w.
7
Let x(a) be the second derivative of a**7/15 - 16*a**6/75 - 166*a**5/25 + 391*a**4/15 - 539*a**3/15 + 98*a**2/5 - 36*a. Let x(u) = 0. What is u?
-7, 2/7, 1, 7
Let r(d) be the second derivative of d**4/36 - 25*d**3/18 + 4*d**2 - 80*d - 2. Factor r(b).
(b - 24)*(b - 1)/3
Let j(p) be the first derivative of -5/3*p**3 + 37 - 5/2*p**6 + 0*p + p**5 - 5*p**2 + 25/4*p**4. Find c, given that j(c) = 0.
-1, -2/3, 0, 1
Let c be -18 + (3 - 2) + 3. Let n be 4/c*(-6 + -1). Factor 10*i - 7*i + 0*i - 9*i**n.
-3*i*(3*i - 1)
Solve -102*y**2 - 166*y**2 + 24*y**2 - 1080*y**3 + 78*y + 2*y + 1092*y**3 = 0 for y.
0, 1/3, 20
Let t**4 - 2/3 + 7/3*t - 7/3*t**3 - 1/3*t**2 = 0. Calculate t.
-1, 1/3, 1, 2
Let b = -36 - -38. Find x, given that -7*x**2 + 3*x**3 + 5*x**2 + 5*x**b = 0.
-1, 0
Let p(t) be the first derivative of -t**7/700 + t**6/225 - t**5/300 + 7*t**3/3 + 10. Let v(m) be the third derivative of p(m). Let v(a) = 0. Calculate a.
0, 1/3, 1
Let a(i) = -28*i - 640. Let f be a(-23). Factor -10648/7*m**3 - 29282/7*m**f - 88/7*m - 1452/7*m**2 - 2/7.
-2*(11*m + 1)**4/7
Let g(b) = 3*b**2 + 149*b + 98. Let v be g(-49). Let i(u) be the second derivative of 0 + 5*u + 0*u**2 + v*u**3 + 5/6*u**4 + 1/4*u**5.