(p - 1)*(p + 1)/2
Let j be (20/8)/((-4)/(-8)). Suppose 0 = -i - j, 0 = 5*h - 0*i - i - 30. Determine n, given that 0 + 7*n**2 - h*n**2 + 0 = 0.
0
Let n(i) = -i**3 + 5*i**2 + 5*i + 6. Suppose -6*x + 1 = -4*q - x, 5*x = 5*q - 5. Let d be n(q). Find y, given that d*y + 2/5*y**2 - 2/5 = 0.
-1, 1
Let u(y) be the first derivative of y**4/18 - 2*y**3/3 + 14*y**2/9 + 370. Factor u(w).
2*w*(w - 7)*(w - 2)/9
Let v = -30 - -29. Let c be (v - 1/(-4))*4/(-6). Find f, given that f**3 - 1/2*f**5 - 1/2 + f**2 - c*f - 1/2*f**4 = 0.
-1, 1
Let g(f) be the second derivative of f**5/10 + 3*f**4/4 - 11*f**3/2 + 7*f**2 + 2*f + 1. Factor g(c).
(c - 2)*(c + 7)*(2*c - 1)
Let u = 6680/171 + -738/19. Find k, given that 0 + 2/9*k + 0*k**2 - u*k**3 = 0.
-1, 0, 1
Let z(n) = n**2 - 13*n - 6. Let v be -2 + 32/(4 + -2). Let u be z(v). Find h, given that h**3 + u*h**2 + 8*h + 8*h**2 + 3*h**3 + 2*h**3 = 0.
-2, -2/3, 0
Suppose -3*b + 4*b = -2, 0 = 2*q + 4*b. Let p be 24/q - (0 - -2). Factor -2*f**2 + 0*f**3 - 8 + 7 - 3*f**4 - 3*f + f**5 + 2*f**3 + 6*f**p.
(f - 1)*(f + 1)**4
Let n(i) be the first derivative of 11/6*i**3 - 1/12*i**6 + 22 + 0*i + 9/8*i**4 + i**2 + 1/10*i**5. Factor n(h).
-h*(h - 4)*(h + 1)**3/2
Let z = 1937/3 + -645. Let f(b) be the first derivative of -2 + 2*b**2 + 2*b + z*b**3. Determine u, given that f(u) = 0.
-1
Determine h, given that 9*h**5 - 57*h + 27 + 45*h**3 - 43 - 75*h**2 + 3*h**5 + 34 + 57*h**4 = 0.
-3, -2, -1, 1/4, 1
Let -2540 + 530*d**3 + 2648*d**2 + 3875 + 2489 + 34*d**4 + 2*d**5 + 6496*d + 2448 + 18*d**4 = 0. What is d?
-7, -4
Let q(c) be the third derivative of 0 - 1/60*c**6 + 0*c**3 - c**2 + 0*c - 1/105*c**7 + 1/30*c**5 + 1/12*c**4. Factor q(y).
-2*y*(y - 1)*(y + 1)**2
Let l be 5/3 - (30/(-9) - -5). Let q(a) be the second derivative of 4*a - 1/50*a**6 + 0*a**2 + 0 + l*a**4 - 9/100*a**5 + 2/5*a**3. Factor q(v).
-3*v*(v - 1)*(v + 2)**2/5
Let x(n) = -65 - n**2 + 64 - n**2. Let u(q) = -4*q**2 - 1. Let r(w) = -6*u(w) + 10*x(w). Factor r(v).
4*(v - 1)*(v + 1)
Let a be 4 + (5 - 207/115). Factor -a*g - 2/5*g**2 - 162/5.
-2*(g + 9)**2/5
Suppose -2*i + 14 = -46. Let x(b) = -11 + i - 13 - 4*b - b**2. Let m(n) = -4*n**2 - 12*n + 19. Let y(z) = 6*m(z) - 21*x(z). Factor y(g).
-3*(g - 2)**2
Factor 49/5*c**4 - 16*c**2 - 12/5*c + 0 - 119/5*c**3.
c*(c - 3)*(7*c + 2)**2/5
Let t(r) be the first derivative of r**7/56 + r**6/10 + 3*r**5/16 + r**4/8 + 5*r + 21. Let p(m) be the first derivative of t(m). Suppose p(h) = 0. Calculate h.
-2, -1, 0
Let i = -881 + 883. What is m in -3/5*m + 0 - 3/5*m**i = 0?
-1, 0
Let f(h) be the second derivative of -3/110*h**5 + 1/33*h**4 + 0 + 1/165*h**6 + 0*h**2 + 0*h**3 - 42*h. Let f(i) = 0. What is i?
0, 1, 2
Suppose 0 = -3*q - 3, 3*p + q = -q + 73. Suppose -p*z = 30*z - 57*z. Factor -w + w**3 + 1/2*w**2 - 1/2*w**4 + z.
-w*(w - 2)*(w - 1)*(w + 1)/2
Let x(c) be the second derivative of 1/9*c**3 + 0*c**4 + 0 + 0*c**2 + 20*c - 1/30*c**5. Determine o, given that x(o) = 0.
-1, 0, 1
Let c = -1241 + 8699/7. Find g, given that -2*g**3 + 8/7*g**4 + 2*g - c*g**2 + 4/7 = 0.
-1, -1/4, 1, 2
Find u, given that 2/3*u**2 - u**4 - 4/3*u**3 + 4/3*u + 1/3 = 0.
-1, -1/3, 1
Let t(d) = -4*d**2 - 21*d - 12. Let n(s) = -12*s**2 - 64*s - 36. Suppose -16 = 3*u - 2*u. Let c(l) = u*t(l) + 5*n(l). Let c(w) = 0. What is w?
-3, -1
Let c(r) = -8*r**4 - 3*r**3 + r**2 + 3*r - 1. Let d(n) = 42*n**4 + 14*n**3 - 4*n**2 - 14*n + 6. Let w(q) = 11*c(q) + 2*d(q). Let w(k) = 0. Calculate k.
-1, -1/4, 1
Suppose 0 = -x + 3*u + 9 - 4, 2 = 2*u. Let n be x + (-8)/4 + -4. Factor -1/2 + 1/6*j**n - 1/3*j.
(j - 3)*(j + 1)/6
Let y(h) be the third derivative of -1/20*h**5 + 0*h**3 - 1/240*h**6 - 5/48*h**4 + 0*h + 0 - 9*h**2. Find m, given that y(m) = 0.
-5, -1, 0
Suppose -4*u - 3*w + 4*w + 153 = 0, 2*u - 4*w = 94. Suppose -u + 7 = -3*s. Suppose -1 + 6 + s*v**3 - 4*v**3 + 14*v + 16*v**2 - 1 = 0. What is v?
-1, -2/3
Let x = -241/110 + 123/22. Factor -2 - 3/5*q**2 + x*q.
-(q - 5)*(3*q - 2)/5
Let n(o) be the third derivative of o**5/360 - 7*o**4/144 + o**3/3 - 65*o**2. Factor n(q).
(q - 4)*(q - 3)/6
Factor -35*i**3 + 69*i**3 - 8*i**2 - 30*i**3.
4*i**2*(i - 2)
Suppose r + 3 - 7 = 0. Factor -7*v**3 - 59*v**3 - 10*v + 45*v**2 + 12*v**3 + 55*v**r - 21*v**3 - 15*v**5.
-5*v*(v - 1)**3*(3*v - 2)
Suppose t - 6*t = 4*n - 4713, -t + n + 948 = 0. Let g be (-9)/(t/(-20)) - 1/(-7). Factor -x**2 + 2/3*x + 0 + g*x**3.
x*(x - 2)*(x - 1)/3
Suppose 0 = 26*k - 27*k + 3. Let v(h) be the first derivative of h**2 - h - 2 - 1/3*h**k. Let v(w) = 0. Calculate w.
1
Factor -45*j**3 + 35*j**2 + 22*j**3 + 18*j**3 - 35 + 5*j.
-5*(j - 7)*(j - 1)*(j + 1)
Let w(q) = -7*q**2 - 23*q - 90. Let z(u) = 10*u**2 + 35*u + 135. Let p(l) = 7*w(l) + 5*z(l). Factor p(x).
(x + 5)*(x + 9)
Suppose 15*f - 72 = -6*f - 15*f. Find k such that -2*k**3 - 3/2 + k**f + 2*k + 1/2*k**4 = 0.
-1, 1, 3
Let o(w) be the first derivative of w**3/21 + 51*w**2/14 + 50*w/7 + 17. Factor o(m).
(m + 1)*(m + 50)/7
Let z(p) = 4*p**2 - 5*p - 3. Let h be z(5). Let f = 106 - h. Factor 4*l**2 - 36*l**3 + 2 + 2*l + 2 + f*l**3 - 8*l**2.
-2*(l - 1)*(l + 1)*(l + 2)
Let x = 60509/8 - 7562. Factor x*m + 3/4 + 1/8*m**3 + m**2.
(m + 1)**2*(m + 6)/8
Let a(i) be the third derivative of 0*i**3 + 16*i**2 + 0 - 1/30*i**5 + 0*i**4 + 0*i. Solve a(q) = 0 for q.
0
Let c(r) be the second derivative of r**4/8 + 5*r**3/16 + 3*r**2/16 - 3*r - 6. Suppose c(q) = 0. Calculate q.
-1, -1/4
Let x = 677/2002 + -15/286. Determine n so that 6/7*n - 4/7 - x*n**2 = 0.
1, 2
Let v be 7 + (-732)/108 + 32/18. Let r(x) be the second derivative of -1/42*x**7 + 0*x**3 + 0*x**v - 1/20*x**5 + 0 + 6*x + 0*x**4 + 1/15*x**6. Factor r(m).
-m**3*(m - 1)**2
Let j be (-22)/(-3) - 10/(-15). Let a = 2 + j. Factor 5*v + a + 13*v**2 - 5*v + 12*v - 6 + v**4 + 6*v**3.
(v + 1)**2*(v + 2)**2
Let o(j) be the third derivative of j**8/1344 - 5*j**7/504 + j**6/18 - j**5/6 - 11*j**4/24 - 7*j**2. Let v(c) be the second derivative of o(c). Factor v(m).
5*(m - 2)**2*(m - 1)
Let w(o) be the second derivative of 1/4*o**4 + 0*o**2 - 1/14*o**7 + 0*o**3 - o + 0 - 1/10*o**6 + 3/20*o**5. Suppose w(c) = 0. Calculate c.
-1, 0, 1
Let d = 9513 - 9509. Let -2/11*c + 2/11*c**3 - 2/11*c**2 + 0 + 2/11*c**d = 0. What is c?
-1, 0, 1
Let h be 3*4/(-960)*16/(-12). Let f(m) be the second derivative of 1/18*m**3 + 0 + 1/18*m**4 + m + 0*m**2 + h*m**5. Factor f(w).
w*(w + 1)**2/3
Let j = 863/3 - 287. Let v(c) be the first derivative of -j*c + 1/9*c**3 + 4 + 1/6*c**2. Factor v(p).
(p - 1)*(p + 2)/3
Solve 17 - 23 + 8 + 1072*m**2 + 92*m - 14*m**2 = 0.
-1/23
Let r(w) be the second derivative of -1/18*w**4 + 0*w**2 + 29*w + 0*w**3 + 0 + 1/252*w**7 + 3/40*w**5 - 1/30*w**6. Determine z, given that r(z) = 0.
0, 1, 4
Let r(y) = 2*y**2 + y - 2. Let s(u) = 11*u**2 - 12*u - 48. Let o(g) = 5*r(g) - s(g). Factor o(k).
-(k - 19)*(k + 2)
Let v(z) be the second derivative of -z**4/6 - 12*z**3 - 35*z**2 - 433*z. What is h in v(h) = 0?
-35, -1
Let d = -252 - -258. Suppose 5*o = -25, 26 = 3*f - 10*o + d*o. Factor 2/9*y**5 + 2/3*y**4 + 0*y**f + 0 + 4/9*y**3 + 0*y.
2*y**3*(y + 1)*(y + 2)/9
Let t(y) be the third derivative of y**6/60 - 7*y**5/45 - 47*y**4/36 - 14*y**3/9 + 177*y**2. Factor t(n).
2*(n - 7)*(n + 2)*(3*n + 1)/3
Let x(i) be the second derivative of -i**6/90 + i**5/30 + i**4/3 - 5*i**3/6 + 25*i. Let d(u) be the second derivative of x(u). Let d(z) = 0. Calculate z.
-1, 2
Let u(x) = 5*x**3 + 3*x**2 - 30*x - 29. Let a(y) = 24*y**3 + 14*y**2 - 148*y - 146. Let o(m) = -3*a(m) + 14*u(m). What is r in o(r) = 0?
-2, 4
Let a(j) be the first derivative of -j**3/18 + 13*j**2/3 - 183. Factor a(s).
-s*(s - 52)/6
Let x be -2 + (80/(-45) + 0)/((-8)/12). Let m = -6 - -8. Determine s so that -1/3 + x*s**m + 7/6*s = 0.
-2, 1/4
Let y(n) be the first derivative of 3*n**8/280 - 11*n**7/210 + 19*n**6/405 - 2*n**5/135 - 2*n**3 + 10. Let m(u) be the third derivative of y(u). Solve m(o) = 0.
0, 2/9, 2
Let f(b) be the first derivative of 1/8*b + 3/32*b**4 - 3/16*b**2 - 1/24*b**3 - 46. Solve f(p) = 0 for p.
-1, 1/3, 1
Let r(h) be the first derivative of 2/21*h**3 - 6/7*h**2 + 0*h - 21. Find a, given that r(a) = 0.
0, 6
Solve 2*d**4 + 70*d**4 + 35*d**5 - 120*d + 4*d**4 - 20 - 205*d**2 - 31*d**4 - 95*d**3 = 0 for d.
-1, -2/7, 2
Let l = 8 + -8. Let q be 2 - 1 - (l + -2). Factor 2*w**2 + 0*w