111/2.
-3*(s - 37)*(s + 1)/2
Let t = -23 - -27. Find y such that -t - 9*y + 3*y**2 + 4 = 0.
0, 3
Let s = -97 - -100. Let i(m) = -14*m**5 + 10*m**4 - 18*m**3 - 2*m**2. Let z(q) = -5*q**5 + 3*q**4 - 6*q**3 - q**2. Let k(u) = s*i(u) - 8*z(u). Factor k(n).
-2*n**2*(n - 1)**3
Let b(d) = 2*d**2 - d. Let p(i) = -4*i**3 + 68*i**2 - 36*i - 36. Let r(f) = -24*b(f) + p(f). Solve r(w) = 0.
-1, 3
Let s(j) = 7 + 9*j + 32*j**2 - 279*j**3 + 292*j**3 + 7*j**2 + 11*j**4. Let r(k) = 5*k**4 + 7*k**3 + 19*k**2 + 5*k + 3. Let o(y) = 7*r(y) - 3*s(y). Factor o(a).
2*a*(a + 1)*(a + 2)**2
Suppose 5*a - 193 + 171 = -t, a = t + 2. Factor 1/4*b**t - 1 + 0*b.
(b - 2)*(b + 2)/4
Let a(l) = -l. Let c(m) = -160*m**2 - 93*m - 5. Let d(p) = -3*a(p) + c(p). Determine x, given that d(x) = 0.
-1/2, -1/16
Let f be (-306)/72*6/(-51). Suppose f*l - 1/2 + l**2 = 0. Calculate l.
-1, 1/2
Let b(u) be the second derivative of u**7/168 + u**6/120 - 13*u**5/80 - 25*u**4/48 - u**3/2 + 124*u. Factor b(s).
s*(s - 4)*(s + 1)**2*(s + 3)/4
Let j(f) be the third derivative of f**7/70 - f**6/25 - 69*f**5/100 - 19*f**4/10 - 2*f**3 - 4*f**2 + f. Solve j(b) = 0.
-2, -1, -2/5, 5
Let s(w) be the first derivative of -5*w**4/12 - 5*w**3/6 + 4*w + 6. Let g(h) be the first derivative of s(h). Solve g(z) = 0 for z.
-1, 0
Let m be 57/11 + (-2)/11. Find r, given that 7*r**2 + 2*r - 11*r**2 - 7*r - m + 5*r**3 + 9*r**2 = 0.
-1, 1
Let j be -18 + 9 + 28 + -19. Find v such that j + 0*v - 3/5*v**2 - 1/5*v**3 = 0.
-3, 0
Let z(n) be the third derivative of -n**6/120 - 113*n**5/60 - 406*n**4/3 - 1568*n**3/3 - 255*n**2. Factor z(b).
-(b + 1)*(b + 56)**2
Let t(y) be the second derivative of -1/8*y**4 + 0 - 24*y + 1/12*y**3 + 1/120*y**5 + 1/60*y**6 + 1/6*y**2. Factor t(f).
(f - 1)**2*(f + 2)*(3*f + 1)/6
Let z(v) be the second derivative of -v**6/2520 - v**5/840 + v**4/28 + 5*v**3/3 - 14*v. Let b(t) be the second derivative of z(t). Factor b(n).
-(n - 2)*(n + 3)/7
Let z(c) = -16*c**2 - 91*c - 1859. Let d(m) = -3*m**2 - m - 2. Let g(w) = -5*d(w) + z(w). Solve g(x) = 0.
-43
Suppose 3*c + 27 = 4*x - 0*c, x - 3*c = 0. Let o be (x/6)/(2/4). Solve 0*j - 4*j + 4*j**3 - 3 + j + 3*j**2 - j**o = 0 for j.
-1, 1
Let g(f) be the first derivative of -f**4/12 - 5*f**3/9 + f**2/6 + 5*f/3 + 109. Find k such that g(k) = 0.
-5, -1, 1
Let t(j) be the third derivative of -289*j**8/672 + 17*j**7/14 - 157*j**6/240 - j**5/2 - j**4/12 - j**2 + 23. Factor t(u).
-u*(u - 1)**2*(17*u + 2)**2/2
Let p(o) be the second derivative of -o**6/30 - o**5/4 + 47*o**4/12 - 13*o**3/2 - 45*o**2 - 23*o. Factor p(v).
-(v - 3)**2*(v + 1)*(v + 10)
Determine q so that -5*q**5 + 10648/5 + 328*q**4 + 105028/5*q + 251746/5*q**2 - 35641/5*q**3 = 0.
-1/5, 22
Suppose -m + 27 + 6 = 0. Find l, given that m + l**2 - 4*l - 70 + 33 + l**3 = 0.
-2, -1, 2
Solve 5/4*x**3 - 135/4*x**2 + 0 + 0*x = 0 for x.
0, 27
Let x(s) be the second derivative of s**5/15 + s**4/60 - s**3/5 + 7*s**2 + 11*s. Let p(o) be the first derivative of x(o). Suppose p(f) = 0. Calculate f.
-3/5, 1/2
Solve -75 - 1/3*j**2 - 10*j = 0 for j.
-15
Let 0 + 10*m**2 - 36/5*m**3 - 12/5*m - 18/5*m**4 = 0. What is m?
-3, 0, 1/3, 2/3
Let f(a) be the first derivative of 8 + a - 1/33*a**4 + 1/33*a**3 + 2/11*a**2 - 1/110*a**5. Let s(t) be the first derivative of f(t). Factor s(i).
-2*(i - 1)*(i + 1)*(i + 2)/11
Suppose 3*u - t = 14, 5*u = 2*t + 2 + 20. Let c = u - 2. Factor 83 + 12*w**3 + 4*w**c + 4*w + 12*w**2 - 83.
4*w*(w + 1)**3
Let k(v) be the third derivative of v**5/20 + 25*v**4/8 + 12*v**3 + v**2 - 34. Find c, given that k(c) = 0.
-24, -1
Let i(c) = -c**2 + 5*c + 27. Let y be i(-3). Factor -2*w**y - 64*w + 155 + 17*w**2 - 2*w**3 - 45*w**2 - 203.
-4*(w + 2)**2*(w + 3)
Let v(y) = -12*y**3 - 6*y**2 + 132*y - 165. Let l(n) = -n**4 + n**3 + n**2 - n - 1. Let b(k) = -3*l(k) + v(k). Factor b(r).
3*(r - 3)**2*(r - 2)*(r + 3)
Let v = 23 - 7. Let l(w) = w**3 - 15*w**2 - 16*w + 4. Let r be l(v). Solve 0*y + 8/5*y**2 - 2/5 - 4/5*y**5 - 6/5*y**r + 4/5*y**3 = 0.
-1, 1/2, 1
Let j be 0/(-5 + 5 + -2). Let x(n) be the second derivative of -1/6*n**4 + 0*n**2 + 0*n**5 + j + 7*n + 1/15*n**6 + 0*n**3. Factor x(d).
2*d**2*(d - 1)*(d + 1)
Let 2/11*r**3 + 74/11*r**2 - 722/11 + 646/11*r = 0. Calculate r.
-19, 1
Let g(d) = -3*d**3 - 5*d**2 - 3*d - 4. Let y be g(-3). Solve 32*p**3 - 4*p**3 - 26*p**2 - 38*p**2 + y*p - 8 + 3*p = 0.
2/7, 1
Let j(y) be the third derivative of 0 - 26/35*y**7 + 0*y**6 + 35*y**2 + 0*y**3 + 4/15*y**5 + 0*y**4 - 5/12*y**8 + 0*y. Solve j(f) = 0.
-1, -2/5, 0, 2/7
Let t(x) be the second derivative of 6*x + 2*x**4 + 0*x**2 + 2 + 6*x**3 + 1/5*x**5. Factor t(n).
4*n*(n + 3)**2
Let q = -502 + 507. Let f(h) be the second derivative of 0*h**2 - 1/84*h**7 + 0*h**3 + 0 - 1/8*h**q + 1/12*h**4 + 1/15*h**6 + 3*h. Factor f(s).
-s**2*(s - 2)*(s - 1)**2/2
Determine x, given that 4*x**3 - 2*x**4 + 4*x - 4*x**4 + 12*x**2 - 5*x**2 + 5*x**4 + 14*x**2 - 28 = 0.
-2, 1, 7
Let y(g) be the second derivative of -g**5/150 - g**4/90 + 4*g**3/45 + 4*g**2/15 - 74*g. Determine r so that y(r) = 0.
-2, -1, 2
Let c = 26605/7977 + -5/2659. Find w such that 0 + 55/3*w**2 - c*w = 0.
0, 2/11
Let n(k) be the third derivative of -2*k**7/105 - 41*k**6/30 + 14*k**5/5 + 49*k**2 + 1. Let n(m) = 0. Calculate m.
-42, 0, 1
Let f = 792 - 10286/13. Let b = f + -44/91. Factor -24/7*o - b*o**3 + 12/7*o**2 + 16/7.
-2*(o - 2)**3/7
Let j be 4/4 - 52/(-36) - -2. Let w = 334/63 - j. Solve 2*y**4 + 0 - w*y**5 + 4/7*y - 6/7*y**3 - 6/7*y**2 = 0.
-2/3, 0, 1
Let y(v) = -3*v**3 + 98*v**2 - 60*v - 124. Let x be y(32). Factor 2/3*m**x + 2 + 8*m**2 - 20/3*m - 4*m**3.
2*(m - 3)*(m - 1)**3/3
Factor 5/8*z**2 - 1/8 - 1/2*z.
(z - 1)*(5*z + 1)/8
Let f = -1397 - -1399. Factor 18/13 + 12/13*s + 2/13*s**f.
2*(s + 3)**2/13
Find f such that -8/11 + 6/11*f**2 + 0*f - 2/11*f**3 = 0.
-1, 2
Let k(g) be the first derivative of g**5/5 - 2*g**4 + 3*g**3 + 9*g**2 + 20. Factor k(i).
i*(i - 6)*(i - 3)*(i + 1)
Suppose 4*i = b + 17, 2*i = 4*i - 10. Suppose 2 - 6 = -b*a + 2*n, 4*a + 2*n + 4 = 0. Determine m, given that 0*m**2 + 1/7*m**3 + 0*m + a = 0.
0
Let 0 + 1/4*u**3 - 3/4*u**2 - 9/2*u = 0. What is u?
-3, 0, 6
Suppose -4*o + 2 = w - 0, 3*w + 4*o = 22. Suppose 7*d = 12*d - w. Determine n so that -38/3*n**3 + 14/3*n**5 - 16*n + 6*n**4 - 82/3*n**d - 8/3 = 0.
-1, -2/7, 2
Let t(z) be the second derivative of -z**4/4 + z**3/6 - 3*z**2 - z. Let u(r) = -50 - r**2 - 22 + 69. Let g(c) = 2*t(c) - 5*u(c). Factor g(n).
-(n - 3)*(n + 1)
Let v = 3/31349 + 3134423/4984491. Let j = v + 2/53. Suppose 2/3 + 2/3*q**3 - 2/3*q - j*q**2 = 0. Calculate q.
-1, 1
Let y(t) be the second derivative of -1/84*t**4 + 14*t - 14*t**2 + 2 + 2/3*t**3. Factor y(b).
-(b - 14)**2/7
Let i be ((-6)/(-33))/(3/(-2) + 2). Suppose 11*h + 28 - 50 = 0. Determine u so that 2/11*u**3 + 8/11*u**h + 10/11*u + i = 0.
-2, -1
Let g(p) be the first derivative of 6*p**2 - 9 + 4/3*p**3 + 8*p. Factor g(d).
4*(d + 1)*(d + 2)
Let i = 150 + -149. Let o be 1*i/3*(7 - -2). Determine b so that -3/4*b**5 + 1 + 0*b + 7/4*b**4 + 3/4*b**o - 11/4*b**2 = 0.
-1, -2/3, 1, 2
Let w(p) be the second derivative of 0 - 10/3*p**3 + 9*p + 0*p**2 + 5/12*p**4. Find o such that w(o) = 0.
0, 4
Let b be (-12)/(-27) + (-76)/1539*9. Factor 0*j**2 + 0*j**4 + 0*j**3 + 4/7*j**5 + b*j + 0.
4*j**5/7
Let m(n) = n**3 - 10*n**2 + 21*n - 6. Let k(w) = w**3 - 9*w**2 + 19*w - 7. Let i(y) = -6*k(y) + 4*m(y). Factor i(f).
-2*(f - 3)**2*(f - 1)
What is t in -65*t**4 + 7*t**2 + 57*t**2 + 25*t**5 + 6*t**3 + 23*t - 55*t = 0?
-1, 0, 4/5, 2
Let -1/3*d**4 + 84*d - 109/3*d**2 - 196/3 + 6*d**3 = 0. Calculate d.
2, 7
Let x be 608/84*6/4. Let s(g) = g**3 - 11*g**2 + g - 7. Let k be s(11). Find m such that -26/7*m + 4/7 + 44/7*m**k - 10/7*m**5 + 64/7*m**2 - x*m**3 = 0.
2/5, 1
Let m(n) = -19*n**2 + 252*n + 14641. Let u(t) = -23*t**2 + 254*t + 14641. Let d(b) = 6*m(b) - 5*u(b). Factor d(j).
(j + 121)**2
Let x(d) be the first derivative of -4*d**3/3 + 128*d**2 - 252*d + 381. Factor x(r).
-4*(r - 63)*(r - 1)
Factor 5/8*b**4 - 89/4*b**3 - 432 - 972*b + 261*b**2.
(b - 12)**3*(5*b + 2)/8
Factor -513/5*b**2 - 201/5*b**3 - 3/5*b**5 - 648/5*b - 39/5*b**4 - 324/5.
-3*(b + 2)**2*(b + 3)**3/5
Let a(o) = o**3 + 5*o**2 + o - 10. Let u be a(-3). Suppose -z - 5*f + 10 = 2*z, -5*f = u*z - 10. Factor z - 2/11*d**3 + 4/11*d - 2/11*d