- 4*z - 12. Let r(n) = -2*n**2 - 9*n - 25. Let x(k) = c*i(k) - 4*r(k). Factor x(d).
(d + 4)**2
Let h be 6 + -2 + 6 + -5. Suppose -2*a + 10 = -h*q, 2*q + a - 5 = -q. Let 2/3*u**2 - 2/3*u**3 + 0 + q*u = 0. What is u?
0, 1
Let z be -2 + (3 - 0 - 1/1). Factor 5*t**4 + 4*t**5 + z*t**4 - 9*t**4.
4*t**4*(t - 1)
Let a = -13/8 + 55/24. Factor -4/7 + a*y - 2/21*y**2.
-2*(y - 6)*(y - 1)/21
Let f = -39 - -18. Let w = -16 - f. Factor -14*s**4 + 7*s**5 - s**5 - 2*s**2 + w*s**3 + 5*s**3.
2*s**2*(s - 1)**2*(3*s - 1)
Suppose -5*t = 5*l + 10, 3*t - 6*t = 4*l + 11. Suppose 0 = -3*g + 3*w - t, 0 = g + 3*g - 5*w + 8. Factor -87*v**3 - 2*v**5 + 88*v**g + v**5.
-v**3*(v - 1)*(v + 1)
Suppose -4*p + 0*p - 25 = -3*w, 5*w - 11 = -p. Suppose w*x - 3*x = x. Factor x + 1/3*b + 1/3*b**2.
b*(b + 1)/3
Suppose 16 = c - 0. Let b(q) = -q**2 + 16*q + 3. Let d be b(c). Factor 0*w - 2/7*w**2 + 2/7*w**d + 0.
2*w**2*(w - 1)/7
Let b(c) be the first derivative of 3/160*c**5 - 1/16*c**4 + c**3 - 1/480*c**6 + 0*c**2 - 6 + 0*c. Let t(a) be the third derivative of b(a). Factor t(h).
-3*(h - 2)*(h - 1)/4
Let l be 4 - (0 + 3/(-3)). Suppose r**2 + 27*r**4 - 18*r**5 + 6*r**l - 18*r**3 + 2*r**2 = 0. What is r?
0, 1/4, 1
Suppose 15 = 11*t - 6*t. Factor 10*f**4 + 60*f + 4*f**t + 87*f**2 + 10 + 44*f**3 + 2 - f**4.
3*(f + 1)*(f + 2)**2*(3*f + 1)
Suppose 86*m - 35*m - 6*m - 90 = 0. What is z in m*z + 2/5*z**2 + 12/5 = 0?
-3, -2
Let n(u) = 8*u**3 - 101*u**2 + 5*u. Let g(l) = 4*l**3 - 51*l**2 + 3*l. Let p(h) = 5*g(h) - 3*n(h). Find z such that p(z) = 0.
0, 12
Let a(k) = -2. Let p(w) = -11 - 10*w - 17 - 28*w**2 + 26*w**2 - 4*w. Let f(u) = -8*a(u) + p(u). Find x such that f(x) = 0.
-6, -1
Find m, given that -10/3*m**2 + 12*m - 6 = 0.
3/5, 3
Let v(j) be the third derivative of 0*j**3 + 0 + 0*j - 1/60*j**5 - 5/336*j**8 + 16*j**2 + 1/12*j**4 + 13/210*j**7 - 3/40*j**6. Factor v(d).
-d*(d - 1)**3*(5*d + 2)
Let c(r) be the third derivative of r**7/1260 - 13*r**5/360 + r**4/12 + 93*r**2. Determine w so that c(w) = 0.
-4, 0, 1, 3
Let x(d) be the third derivative of -d**7/70 - 77*d**6/20 - 5929*d**5/20 - 12*d**2 - 6. Solve x(g) = 0 for g.
-77, 0
Let s(t) = -3*t**4 + 5*t**3 + 7*t**2 - 13*t. Let p(d) = -6*d**4 + 11*d**3 + 13*d**2 - 25*d. Let x(g) = -4*p(g) + 7*s(g). Factor x(n).
3*n*(n - 3)*(n - 1)*(n + 1)
Let h(g) be the first derivative of 0*g**4 + 4*g + 0*g**3 + 0*g**2 - 1/10*g**5 + 2. Let z(w) be the first derivative of h(w). Find d, given that z(d) = 0.
0
Factor 5*a**2 + 17*a - 103*a - 63*a - 235*a - 151*a.
5*a*(a - 107)
Suppose -7 = -2*c - 5*q - 19, -2*c = -3*q - 20. Factor 0*j + 0 - 1/4*j**c + j**3 + 0*j**2.
-j**3*(j - 4)/4
Let t = 46754 + -46752. Factor 1/11*r**4 + 29/11*r**t + 39/11*r + 18/11 + 9/11*r**3.
(r + 1)*(r + 2)*(r + 3)**2/11
Suppose -7*u + u + 12 = 0. Let t be (25/1)/5 + (-6)/u. Suppose 24/5*l**t - 2/5*l**3 - 96/5*l + 128/5 = 0. Calculate l.
4
Let u = 287 - 287. Let h(n) be the second derivative of 1/21*n**7 - 1/12*n**4 - 4*n + 1/6*n**3 + 0 + 1/30*n**6 - 3/20*n**5 + u*n**2. Find f such that h(f) = 0.
-1, 0, 1/2, 1
Let r = -68 + 70. Factor 16*o**3 - 130*o - 57*o**2 + 153*o**2 - 10*o + 36 + 32*o**r.
4*(o + 9)*(2*o - 1)**2
Let p = 7535/9 - 837. Let f(x) = -2*x - 4. Let a be f(-3). Solve p*h - 2/9 + 4/9*h**a + 2/9*h**5 - 2/9*h**4 - 4/9*h**3 = 0.
-1, 1
Factor -4*q**2 - 8*q**2 + 8*q**2 + 116*q - 1682 + 2*q**2.
-2*(q - 29)**2
Let b(v) = -5*v**2 - 35*v + 95. Let d(x) = -5*x**2 - 34*x + 94. Let o(u) = -6*b(u) + 5*d(u). Solve o(k) = 0 for k.
-10, 2
Find f such that 0*f - 4/5*f**2 + 16/5 = 0.
-2, 2
Let a = 18 + -13. Let n = 481 - 479. Let 4*r - 11*r**2 + 3*r**a - 9*r**5 + 8*r**4 + 3*r**n + 2*r**5 = 0. What is r?
-1, 0, 1
Suppose 345*n = 362*n - 85. Factor -2/5*k**n - 2/5*k**4 + 0*k - 6/5*k**2 + 0 + 2*k**3.
-2*k**2*(k - 1)**2*(k + 3)/5
Solve 1/9*i**5 + 26/9*i + 0 + 13/9*i**4 - 37/9*i**2 - 1/3*i**3 = 0 for i.
-13, -2, 0, 1
Let c = -467 + 472. Let n(u) be the second derivative of -1/5*u**6 + 1/2*u**4 + 1/21*u**7 + 0 + 3*u + 0*u**2 - 2/3*u**3 + 1/10*u**c. Factor n(m).
2*m*(m - 2)*(m - 1)**2*(m + 1)
Factor -3*u**4 + 0*u**3 - 28*u**3 + 0*u**4 - 36*u**2 + 4*u**3.
-3*u**2*(u + 2)*(u + 6)
Let v(b) be the third derivative of 0*b + 4/3*b**3 + 1/30*b**6 + 0 + 0*b**5 - 10*b**2 - 1/2*b**4. Factor v(l).
4*(l - 1)**2*(l + 2)
Let k(f) be the second derivative of -f**5/60 + f**4/12 + f**3/2 + 5*f**2/6 - 73*f + 3. Find o, given that k(o) = 0.
-1, 5
Factor 0*j + j + 180*j**2 - 181*j**2.
-j*(j - 1)
Suppose -4*s = 20, r - 4*s - 18 = 2*r. Suppose 10 = -r*u + 7*u - 3*f, 3*u - f = 6. Factor -1/4*a - 1/4*a**u + 0.
-a*(a + 1)/4
Let o be 5895/1179*((-2)/25)/(-1). Factor 4/5 - 4/5*u**2 + o*u**3 - 2/5*u.
2*(u - 2)*(u - 1)*(u + 1)/5
Let u(r) be the first derivative of -4*r**3/3 + 22*r**2 - 72*r + 146. Determine b, given that u(b) = 0.
2, 9
Let n(j) = -3*j**2 + 8*j - 3. Let b be n(6). Let s be (27/b)/((-2)/4). Find i such that -s - 10/7*i**2 - 2/7*i**3 - 2*i = 0.
-3, -1
Let c(m) be the second derivative of -1/2*m**5 + 2*m**2 - 1/5*m**6 + 0 + 15*m + 5/3*m**3 + 1/6*m**4. Find q such that c(q) = 0.
-1, -2/3, 1
Factor -29/5*l - 2/5*l**3 + 0 - 31/5*l**2.
-l*(l + 1)*(2*l + 29)/5
Suppose 5*s - 10 = 5*g, -3*g + 3*s = -2*g + 12. Suppose 0 = -g*c - 17 + 32. Factor 0*j - 9/4*j**c + 15/4*j**4 + 1/4*j**2 + 0 - 7/4*j**3.
-j**2*(j - 1)*(3*j - 1)**2/4
Let b = 5946 - 5943. Solve 0 + 4/3*x**2 - 2/3*x**b - 2/3*x = 0.
0, 1
Factor -4 - 50*i + 18*i**2 - 10*i**2 + 52*i - 4 - 2*i**3.
-2*(i - 4)*(i - 1)*(i + 1)
Let y(r) be the first derivative of r**4/24 - 2*r**3/9 - r**2/12 + 2*r/3 - 112. Solve y(i) = 0 for i.
-1, 1, 4
Let o(v) = 6*v - 18. Let u be o(6). Let q be (72/(-63))/(u/(-14)). Factor -2/9*d**4 - 2/9 - 4/3*d**2 - 8/9*d**3 - q*d.
-2*(d + 1)**4/9
Let w(a) = -a**4 - a**3 + a + 1. Let p(s) = 2*s - 17*s - 21*s**3 + 2*s**2 - 12*s**4 + s**2 + 30*s + 15. Let x(b) = p(b) - 15*w(b). Find u, given that x(u) = 0.
0, 1
Let r(q) = -q**3 + q**2 + q + 1. Let k = 68 - 45. Let u = 25 - k. Let x(w) = 5*w**3 - 7*w**2 - 5*w - 1. Let t(h) = u*r(h) + 2*x(h). Factor t(a).
4*a*(a - 2)*(2*a + 1)
Let o = 864/7 + -120. Factor 30/7 + 3/7*m**3 + o*m**2 + 51/7*m.
3*(m + 1)*(m + 2)*(m + 5)/7
Factor 52*z**2 - 5*z**3 + 24*z - 105*z + 4*z**3 - 2*z**3 - 16*z**2.
-3*z*(z - 9)*(z - 3)
Let n = 31 - 27. Factor 4*x**4 - 3*x**3 + x**4 - 9*x**2 + 6 + 3*x + x**n - 3.
3*(x - 1)**2*(x + 1)*(2*x + 1)
Let s be 4/10*((-1 - 43) + -1). Let j be 2*(s/8)/(-9). Solve -1/4*w - 1/4*w**3 + 0 - j*w**2 = 0.
-1, 0
Let k(x) = x**2 - 8*x + 10. Let n be k(7). Let z = 11020 - 11017. Solve 3/4*s**3 + z*s**4 - n*s**2 + 0 - 3/4*s = 0.
-1, -1/4, 0, 1
Let d(u) = 0*u - 13*u**5 + 42*u**4 + 7*u + 2*u - 2*u**5 - 30*u**3. Let y(c) = c**4 - c**3 + c**2 + c. Let z(b) = d(b) - 3*y(b). Solve z(m) = 0 for m.
-2/5, 0, 1
Let a(r) be the second derivative of -1/18*r**4 + 0*r**2 + 0 - 2*r + 1/6*r**3 - 1/90*r**5 - 1/1080*r**6. Let h(s) be the second derivative of a(s). Factor h(f).
-(f + 2)**2/3
Let -76/7 + 1/7*u**2 - 15/7*u = 0. Calculate u.
-4, 19
Let q(g) be the first derivative of 25*g**4/8 + 65*g**3/3 + 129*g**2/4 + 18*g - 281. Let q(o) = 0. Calculate o.
-4, -3/5
Factor -4/3*x**2 - 17/3*x - 4/3.
-(x + 4)*(4*x + 1)/3
Factor 26/9 - 70/3*g - 32/9*g**3 + 48*g**2.
-2*(g - 13)*(4*g - 1)**2/9
Solve 20824*h**3 + 0*h**2 - 12*h**2 - 3*h**5 - 20851*h**3 - 18*h**4 = 0 for h.
-4, -1, 0
Let y(u) = -9*u**2 - 75*u - 22. Let j be y(-8). Factor -11/7*c**3 + 11/7*c - 2/7 + 2/7*c**j.
-(c - 1)*(c + 1)*(11*c - 2)/7
Let h(o) = 24*o**2 + 93*o - 8. Let k be h(-4). What is r in -8/11*r**3 - 4/11*r - 2/11*r**k + 0 - 10/11*r**2 = 0?
-2, -1, 0
Let o be 103/((-9)/21 + (-60)/(-42)). Let s = -103 + o. Suppose -1/6*q + s - 1/6*q**2 = 0. Calculate q.
-1, 0
Let c = -1/165 + 56/165. Let n be (-22)/99*(-2 - 0 - 1). Factor 0 + n*q + c*q**2.
q*(q + 2)/3
Let a(j) be the first derivative of j**6/15 + 16*j**5/25 + 8*j**4/5 - 26. Suppose a(m) = 0. What is m?
-4, 0
Let a(g) be the third derivative of -g**6/180 + g**4/12 + 5*g**3/2 - 19*g**2. Let f(j) be the first derivative of a(j). Suppose f(z) = 0. What is z?
-1, 1
Suppose 0 = -5*v + 61 - 11. Let y = v - 1. Find w, given that -10*w**4 + 17*w**3 + w - 2*w + 25*w**2 - 22*w**3 - y*w = 0.
-2, 0, 1/2, 1
Let w = 1921/9 + -14803/36. Let h = -197 - w. Solve 3/2*v**4 + 3/4*v**3 - 3/2*v**2 + 0*v - h*v**5 + 0 = 0 for v.
-1, 0, 1