ctor 4*c**3 - 2*c**3 + 19 + 30*c**2 + 21 + 3*c**r + 60*c.
5*(c + 2)**3
Let w(i) = 3*i**4 - 5*i**3 + 8*i**2 + 5*i. Suppose 14 + 6 = -4*a. Let o(p) = -p**4 + p**3 - p. Let m(f) = a*o(f) - w(f). Let m(z) = 0. What is z?
-2, 0, 2
Determine i so that -17/2*i**2 + 37/2*i - 1/2*i**3 - 19/2 = 0.
-19, 1
Let q = 1016 + -1016. Suppose 4*r - 13 + 5 = 0. Let 2/5*f**r + 1/5*f**4 + q*f + 3/5*f**3 + 0 = 0. What is f?
-2, -1, 0
Suppose -2*k + 11 = 23*s - 18*s, 3*s - 7 = -k. Factor -10/7*o**4 - 20/7*o**2 + 10/7*o - 2/7 + 20/7*o**s + 2/7*o**5.
2*(o - 1)**5/7
Suppose 4*s = -4 + 16. Solve -3*w + 35*w**s + 4*w**4 + w - 35*w**3 - 4*w**2 + 2*w**5 = 0 for w.
-1, 0, 1
Let k be (2/(-1) - -2) + (-11)/(55/(-36)). Determine t, given that 16/5*t**3 - k*t**2 + 24/5*t - 4/5 = 0.
1/4, 1
Let a(d) be the second derivative of d**5/10 + 13*d**4/6 + 32*d**3/3 + 20*d**2 - 387*d. What is h in a(h) = 0?
-10, -2, -1
Suppose -47*b - 156 = -156. Factor -2/11*l**4 + 4/11*l**2 + b - 2/11*l**3 + 0*l.
-2*l**2*(l - 1)*(l + 2)/11
Let b be ((-200)/(-120))/((-2)/((-48)/20)). Factor 0*x**3 - 2/3*x**b + 1/3*x**5 - 1/3*x + 2/3*x**4 + 0.
x*(x - 1)*(x + 1)**3/3
Let d be (-91)/(-52)*(-2)/(-98). Let y(t) be the second derivative of 0 + d*t**4 + 3/14*t**2 - 1/7*t**3 - 5*t. Factor y(b).
3*(b - 1)**2/7
Let h(b) be the second derivative of b**6/40 + 3*b**5/40 - b**4/16 - b**3/4 + 2*b - 3. Factor h(c).
3*c*(c - 1)*(c + 1)*(c + 2)/4
Let u(n) be the third derivative of n**7/70 + 13*n**6/40 + 23*n**5/20 + 11*n**4/8 - 612*n**2. Solve u(i) = 0.
-11, -1, 0
Let x(c) = 6*c**4 - c**3 - 3*c**2 + 18*c + 14. Let g(y) = 5*y**4 - y**3 - 2*y**2 + 16*y + 12. Let v(t) = -7*g(t) + 6*x(t). Factor v(h).
h*(h - 2)*(h + 1)*(h + 2)
Let f(u) be the second derivative of u**5/30 + u**4/2 + 3*u**3 + 5*u**2/2 + 32*u. Let p(s) be the first derivative of f(s). Solve p(i) = 0 for i.
-3
Suppose 68*n + 8 = 72*n. Suppose 4*i - 10 = -n*x, -5*x - i = -0*i - 16. Solve -6/5*r**2 - 4/5*r**x - 4/5*r - 1/5 - 1/5*r**4 = 0.
-1
Let n = 22 + -20. Find q such that -n + q + 7*q - 4*q**2 + 5*q**4 + q**2 - q - 7*q**3 = 0.
-1, 2/5, 1
Suppose -13*h - 18 + 70 = 0. What is z in 2*z**3 + 2*z**h - z**3 + z**3 - 4*z**2 = 0?
-2, 0, 1
Let n(k) = -25*k**2 - 19*k + 14. Let q(l) = l**2 - 2. Let o(s) = 3*n(s) + 24*q(s). Factor o(y).
-3*(y + 1)*(17*y + 2)
Suppose 5*j - 20 = -0*j, 4*j = x - 29. Factor 2*s + 21*s - 5*s**2 + 7*s - x.
-5*(s - 3)**2
Suppose 3*n - 5*u = 72, -2*n - n = 5*u - 42. Suppose -4*m + n = 7. Determine k, given that -16/7 + 4/7*k + 16/7*k**2 - 4/7*k**m = 0.
-1, 1, 4
Suppose -5*v = 26*n - 2*n - 87, 5*v = 5*n. Let -l**n + 0*l + 8/3*l**4 - 2/3*l**2 - l**5 + 0 = 0. What is l?
-1/3, 0, 1, 2
Let l be 135/(-225) + 52/90*(-546)/(-28). Find t, given that 16/3*t - l + 8/3*t**2 - 4/3*t**3 = 0.
-2, 2
Suppose -5*a - 133 = 4*s, -2*s - 44 = 2*a + 10. Let k be (-3 - 1) + a/(-6). Solve -1/2*p + k*p**2 + 1/3 = 0 for p.
1, 2
Let l be (19/(1539/(-108)))/(4*15/(-18)). Factor 0 + 1/5*c**3 + l*c**2 + 0*c.
c**2*(c + 2)/5
Let l(g) = -2*g**2 - 11*g + 36. Let t(k) = k**2 - k - 1. Let b(c) = l(c) + 3*t(c). Suppose b(s) = 0. Calculate s.
3, 11
Let s(d) be the third derivative of -d**7/70 + 3*d**6/40 + 21*d**5/5 + 34*d**4 + 96*d**3 - 3*d**2 - 50. Suppose s(z) = 0. Calculate z.
-4, -1, 12
Let n(z) be the first derivative of -3*z**4/20 + 2*z**3 + 36*z**2/5 - 135. Factor n(b).
-3*b*(b - 12)*(b + 2)/5
Let c be (-22)/(-8) - (-55)/220. Determine z, given that -3*z**4 + 3/2*z**5 + 3/2*z - c - 3*z**3 + 6*z**2 = 0.
-1, 1, 2
Let o(r) be the first derivative of 3*r**5/5 + 3*r**4/2 - 4*r**3 - 12*r**2 + 13. Suppose o(k) = 0. What is k?
-2, 0, 2
Let f be 95/(-10) - -5 - -7. Let p(x) be the first derivative of 1 - 55/16*x**4 - 75/8*x**2 + 10*x**3 + f*x. Factor p(n).
-5*(n - 1)**2*(11*n - 2)/4
Determine r so that -4*r**3 - 18*r + 1/3*r**4 + 0 + 15*r**2 = 0.
0, 3, 6
Factor 1058*c**2 - 531*c**2 + 25*c - 526*c**2 + 24.
(c + 1)*(c + 24)
Let l = -6651/5 + 1332. Factor 2/5*j + 13/5*j**4 - 1/5*j**2 - l*j**3 + 0 - j**5.
-j*(j - 1)**3*(5*j + 2)/5
Determine q, given that 8/5*q**2 - 8/5*q**5 + 28/5*q**4 - 28/5*q**3 + 0 + 0*q = 0.
0, 1/2, 1, 2
Factor 1788*u + 5*u**4 - 61*u**3 + 2645 + 3110*u**2 - 179*u**3 - 7308*u.
5*(u - 23)**2*(u - 1)**2
Let k = -90 - -95. Factor 3*l**3 + l**2 - l**k - 2*l - l**4 + 1045 - 1045.
-l*(l - 1)**2*(l + 1)*(l + 2)
Solve -70*h**2 - 5*h**5 + 20*h**4 + 7*h - 13 + 78*h - 17 = 0 for h.
-2, 1, 3
Let l(n) be the first derivative of n**6/60 - n**5/20 + n**3/6 - n**2/4 + 13*n + 10. Let x(k) be the first derivative of l(k). Solve x(a) = 0 for a.
-1, 1
Factor -30*p**2 + 27*p**2 - 30*p - 69*p - 96.
-3*(p + 1)*(p + 32)
Let s = -29 - -21. Let w = -8 - s. Factor w*c**2 - 1/2*c**3 + 3/2*c - 1.
-(c - 1)**2*(c + 2)/2
Let f(y) = 12*y**4 - 55*y**3 + 77*y**2 - 16*y - 9. Let q(l) = -12*l**4 + 54*l**3 - 78*l**2 + 14*l + 10. Let v(n) = 4*f(n) + 3*q(n). Factor v(w).
2*(w - 3)*(w - 1)**2*(6*w + 1)
Let l be (-1 - (-2)/(-4))/(-11 + (-780)/(-80)). Suppose 2*g**3 - 2/5 - l*g**2 + 8/5*g**4 - 2*g = 0. Calculate g.
-1, -1/4, 1
Let g = 25 - 19. Suppose -3*j - 5*o - g = -4*j, 3*o = 2*j - 12. Solve 12*l - 11 - 9*l**2 + 13 - j = 0 for l.
2/3
Let b(w) = -4*w**3 - 232*w**2 + 6276*w + 6492. Let s(m) = 3*m**3 + 231*m**2 - 6275*m - 6493. Let k(h) = -5*b(h) - 6*s(h). Solve k(r) = 0 for r.
-1, 57
Let q(u) be the third derivative of 0*u**3 + 1/180*u**6 + 0*u**4 + 0*u**5 + 0*u + 1/630*u**7 - 1/1008*u**8 + 15*u**2 + 0. Factor q(d).
-d**3*(d - 2)*(d + 1)/3
Let c(v) be the second derivative of -v**8/168 - v**7/168 + 19*v**4/6 + 37*v. Let n(k) be the third derivative of c(k). Factor n(t).
-5*t**2*(8*t + 3)
Suppose -4*y + 8 = 4*b, 4*y = 2*b - 52 + 42. Solve -2/3*k + 0 + 8/9*k**2 - 2/9*k**b = 0.
0, 1, 3
Let j(p) = p**4 + p**3 - 3*p**2 + 2*p + 1. Let q(u) = -21*u**4 - 146*u**3 - 327*u**2 - 112*u - 6. Let t(k) = -6*j(k) - q(k). Factor t(l).
5*l*(l + 4)*(l + 5)*(3*l + 1)
Let c(f) be the first derivative of f**5/90 + f**4/54 - 4*f**3/27 - 4*f**2/9 - 32*f + 48. Let y(z) be the first derivative of c(z). What is v in y(v) = 0?
-2, -1, 2
Let i(h) be the third derivative of -h**8/1344 - h**7/504 + h**6/36 + h**5/6 + 5*h**4/12 - 9*h**2. Let t(f) be the second derivative of i(f). Factor t(w).
-5*(w - 2)*(w + 1)*(w + 2)
Suppose 136 = 8*a - 8. Let 9*b + a*b**2 - b - 14*b**2 = 0. What is b?
-2, 0
Suppose -10 = -4*d - d. Let -24*i + 24*i**2 + 12 - 4 + 26*i**d - 16*i = 0. What is i?
2/5
Let y(a) = 66*a - 56. Let h be y(6). Let q = h - 2719/8. Factor 3/8*c + q*c**3 - 5/8*c**2 + 9/8.
(c - 3)**2*(c + 1)/8
Factor 7/9*a**2 + 1/3 + 10/9*a.
(a + 1)*(7*a + 3)/9
Suppose 34 = -4*g + 26, 5*i - 2*g - 14 = 0. Find r such that -2/7*r**i + 0 - 4/7*r = 0.
-2, 0
Let j(w) = 26*w**3 + 34*w**2 - 218*w - 38. Let l(k) = k**3 + k**2 + k - 1. Let d(r) = -j(r) - 10*l(r). Factor d(i).
-4*(i - 2)*(i + 3)*(9*i + 2)
Let v(m) = m**3 - 3*m. Let i(f) = -10*f**3 + 60*f**2 - 210*f + 270. Let n(o) = i(o) + 5*v(o). Solve n(w) = 0.
3, 6
Determine y so that -95*y + 21*y**3 + 260*y**2 - 16*y**3 - 70 - 190*y**4 + 25*y**5 + 31*y**3 + 28*y**3 + 6*y**3 = 0.
-1, -2/5, 1, 7
Let n(o) be the third derivative of -o**5/150 - o**4/2 + 19*o**2. Factor n(d).
-2*d*(d + 30)/5
Let y(j) be the second derivative of j**6/45 + j**5/2 + 13*j**4/9 + j + 88. Factor y(p).
2*p**2*(p + 2)*(p + 13)/3
Let n be (7 + -8)*(-5 - 0). What is f in -9*f**3 - f**5 + 10*f**3 - 3*f**n - 9*f**3 - 12*f**4 + 8*f**2 + 12*f + 4 = 0?
-1, 1
Let o(u) = -8*u**4 + 14*u**3 - 10*u**2 - 14*u + 9. Let n(w) = 6*w**4 - 14*w**3 + 10*w**2 + 14*w - 10. Let v(j) = -3*n(j) - 2*o(j). Factor v(b).
-2*(b - 6)*(b - 1)**2*(b + 1)
Let h be -12*(22/(-4) + 5). Let u be -1 + h/(54/21). Factor -1/3*s**5 - 7/3*s + 8/3*s**3 - u + 2/3*s**2 + 2/3*s**4.
-(s - 4)*(s - 1)*(s + 1)**3/3
Let z(q) be the first derivative of -q**4/20 - 2*q**3/5 + 9*q**2/10 + 14*q/5 - 150. Factor z(j).
-(j - 2)*(j + 1)*(j + 7)/5
Let z(d) be the third derivative of -5*d**5/9 - 5*d**4/18 - d**3/18 - 6*d**2 + 5. Factor z(j).
-(10*j + 1)**2/3
Let p(i) be the first derivative of 4/15*i**3 + 1/15*i**6 - 21 - 2/5*i**4 + 0*i**5 + 3/5*i**2 - 4/5*i. Solve p(r) = 0.
-2, -1, 1
Factor -32/7 - 2/7*y**2 + 16/7*y.
-2*(y - 4)**2/7
Factor 17*q**3 - 86*q**5 + 7*q**3 + 173*q**5 + 26*q**4 - 85*q**5.
2*q**3*(q + 1)*(q + 12)
Let t(p) be the first derivative of 8/15*p**3 + 4/5*p**2 + 2/5*p - 11. Dete