Let q(b) = -b + 1. Let r(j) = y*q(j) + 2*l(j). Determine n so that r(n) = 0.
-1, 4
Find z such that 7027337*z**4 + 2704891*z**2 - 74082976*z + 11332204*z**2 + 5274923*z**2 - 2*z**5 + 73034632 - 267110*z**3 - 7026075*z**4 = 0.
2, 209
Let c(d) be the third derivative of -d**6/960 - d**5/20 - 21*d**4/64 + 24*d**2 - d - 24. Factor c(g).
-g*(g + 3)*(g + 21)/8
Let g(z) be the second derivative of -8*z**7/21 - 92*z**6/5 - 273*z**5/20 - 17*z**4/6 + 1801*z - 1. Find w such that g(w) = 0.
-34, -1/4, 0
Suppose -a + 1229 = 4*y, -3873 = -4*a + 5*y + 1064. Let m = a + -1233. Factor -12/5*l**3 + 18/5*l + m + 3/5*l**4 + 3/5*l**2.
3*l*(l - 3)*(l - 2)*(l + 1)/5
Let q(p) be the first derivative of -p**6/24 - 127*p**5/10 - 16129*p**4/16 - 245. Factor q(h).
-h**3*(h + 127)**2/4
Let n(h) be the second derivative of h**5/5 + 22*h**4/3 + 262*h**3/3 + 220*h**2 - 3*h - 1821. Factor n(p).
4*(p + 1)*(p + 10)*(p + 11)
Let m be -4 - -2 - 7/(-2). Suppose 4*q - k = 1, k - 17 = -2636*q + 2634*q. Find d such that -3/2*d + 3/2*d**q - 3 - m*d**4 + 9/2*d**2 = 0.
-1, 1, 2
Suppose 37 = 5*h + 2*k, -1 = -2*k + 1. Suppose -h + 1 = -2*j. Factor -18*m + 5 + j*m**2 - 1 + 11.
3*(m - 5)*(m - 1)
Let u(b) be the first derivative of -b**7/4200 - b**6/1800 + b**5/100 - 2*b**3/3 - 6*b**2 - 1. Let k(o) be the third derivative of u(o). Factor k(j).
-j*(j - 2)*(j + 3)/5
Let g be 422/700 + (969/(-85))/19. Let i(p) be the third derivative of -1/25*p**5 + 0*p**3 + 0*p + 0 - 1/30*p**4 - g*p**7 + 16*p**2 - 11/600*p**6. Factor i(l).
-l*(l + 1)*(l + 2)*(3*l + 2)/5
Suppose 28*k**2 - 10*k**3 - 65 + 4*k + 61 - 18*k = 0. Calculate k.
-1/5, 1, 2
Factor -1/5*u**2 + 18*u - 89/5.
-(u - 89)*(u - 1)/5
Suppose 53*l = -9*l + 3348. Suppose l = 26*c + c. Factor 2/3*s**4 + 1/9*s**5 + 16/9*s - 8/3*s**c + 1/9*s**3 + 0.
s*(s - 1)**2*(s + 4)**2/9
Solve -5*o - 220 + 5/4*o**3 + 55*o**2 = 0 for o.
-44, -2, 2
Find o, given that -33 + 29*o**3 + 183*o**2 + 25*o**3 - 4*o**4 + 38 + 216*o + 79 + 7*o**4 = 0.
-14, -2, -1
Let m = -127 - -15. Let j be (-3)/(6/21 - (-186)/m). Factor -2/11*x**2 - 72/11 - j*x.
-2*(x + 6)**2/11
Let j(a) be the second derivative of -39/20*a**4 - 399/10*a**3 - 4 - 3/100*a**5 + 2*a - 1083/10*a**2. Factor j(d).
-3*(d + 1)*(d + 19)**2/5
Let b = -213734 + 213734. Determine g so that 2/5*g**2 + b - 36/5*g = 0.
0, 18
Let a be 5708/16 + 1/4. Let p be (-6)/(-7) + 1598/a. Solve -4/3*m**2 - 16/3*m - p = 0.
-2
Let y(x) be the first derivative of x**6/21 + 12*x**5/35 + 13*x**4/14 + 8*x**3/7 + 4*x**2/7 + 694. Find m, given that y(m) = 0.
-2, -1, 0
Suppose -4 = 38*n - 80. Let d(l) be the third derivative of 12*l**n + 0 - 1/20*l**5 + 0*l - 1/2*l**3 - 1/4*l**4. Solve d(r) = 0 for r.
-1
Let d = -998079/5 + 199617. Factor 0 + 3/5*z**4 + d*z**2 - 3*z**3 + 24/5*z.
3*z*(z - 4)*(z - 2)*(z + 1)/5
Let g be (-8*(-5)/35)/((-3)/(-21)). Suppose -13*i**3 + 12*i**2 - 51*i**4 - g*i**3 - 47*i**4 + 36*i + 101*i**4 = 0. Calculate i.
-1, 0, 2, 6
Suppose 0 = -4*o + 36 - 24. Let -16*x + 41*x**2 + 7*x**5 - 13*x**o - 9*x**4 + 6*x**3 - 8*x - 12*x**3 + 4 = 0. What is x?
-2, 2/7, 1
Let d = 368403/22318 + -78/11159. Factor 3/4*t**2 + 39/4*t + d.
3*(t + 2)*(t + 11)/4
Let u = -858 - -875. Let l be 17 - -11 - u - 7/1. Factor 0*f + 0 + 4/13*f**2 + 2/13*f**l - 6/13*f**3.
2*f**2*(f - 2)*(f - 1)/13
Suppose -39 - 161 = -4*p. Let f = p + 29. Factor 2*x**3 + 4*x - f*x**2 + 0*x + 73*x**2.
2*x*(x - 2)*(x - 1)
Let c(p) be the first derivative of p**4/24 + 19*p**3/3 + 335*p**2/12 + 37*p + 1838. Factor c(v).
(v + 1)*(v + 2)*(v + 111)/6
Let g = 231 - 229. Factor l**2 + 5*l**g - 2 - 4*l**2.
2*(l - 1)*(l + 1)
Factor -163/3*l + 7/3*l**3 + 0 - 52*l**2.
l*(l + 1)*(7*l - 163)/3
Let b(i) be the second derivative of -i**5/15 + 2*i**4/3 - 8*i**3/3 - 5*i**2 - 17*i + 2. Let u(c) be the first derivative of b(c). Let u(k) = 0. What is k?
2
Let v(n) be the second derivative of -76*n - 1/40*n**6 + 5/48*n**4 + 0*n**2 + 0 - 1/4*n**3 + 1/10*n**5. Let v(z) = 0. What is z?
-1, 0, 2/3, 3
Let c(d) be the third derivative of d**7/210 + 3*d**6/40 - d**5/5 - 5*d**4/6 - 881*d**2. Let c(b) = 0. Calculate b.
-10, -1, 0, 2
Let c(t) be the first derivative of -5/6*t**3 - 21/8*t**2 - 54 + 3/16*t**4 + 18*t. Factor c(x).
(x - 3)**2*(3*x + 8)/4
Let i = 295215 + -60227. Let a = 3997458/17 - i. Factor 66/17*w - 2/17 + a*w**3 - 726/17*w**2.
2*(11*w - 1)**3/17
Let n(f) be the third derivative of 23*f**5/90 - 5*f**4/9 - f**3/3 - 74*f**2 - 2. Factor n(d).
2*(d - 1)*(23*d + 3)/3
Let v(l) = -6*l - 116. Let t be v(-20). Let k(w) be the second derivative of 15/2*w**2 + 0 - 10*w + w**3 + 1/20*w**t. Solve k(m) = 0.
-5
Let u(s) be the third derivative of s**8/1176 - 4*s**7/147 + 11*s**6/140 + 31*s**5/105 - 37*s**4/21 + 24*s**3/7 + s**2 - 19*s - 10. Find p such that u(p) = 0.
-2, 1, 2, 18
Solve 5*k**3 - 160 - 66*k**2 - 13*k**2 + 6*k**2 - 22*k**2 + 250*k = 0.
1, 2, 16
Let y(o) be the first derivative of 2*o**5/55 + 7*o**4/22 - 18*o**3/11 + 29*o**2/11 - 20*o/11 - 2817. Factor y(w).
2*(w - 1)**3*(w + 10)/11
Solve -41 - 17*s**2 + 761*s - 257*s + 21*s**2 + 409 + 132 = 0.
-125, -1
Let w(u) be the first derivative of -u**5/45 + 7*u**4/3 - 2098*u**3/27 + 2146*u**2/3 + 15059*u/9 + 9786. Find i such that w(i) = 0.
-1, 11, 37
Let i(x) = -2*x**3 + 4*x**2 + 6*x - 8. Let f = 127 - 124. Let b(a) = -25*a**3 + 3*a**2 + 19*a**f - 5 + 5*a**3 + 4*a. Let y(r) = 8*b(r) - 5*i(r). Factor y(d).
2*d*(d + 1)**2
Let q(m) be the second derivative of 3*m**5/20 + 9*m**4 + 162*m**3 - 8616*m. Factor q(d).
3*d*(d + 18)**2
Find f, given that -2/5*f**3 + 0 + 0*f + 4/5*f**2 = 0.
0, 2
Let j(q) be the second derivative of -q**5/70 + 71*q**4/42 + 232*q**3/21 - 740*q**2/7 + 73*q. Factor j(s).
-2*(s - 74)*(s - 2)*(s + 5)/7
Let s(i) be the third derivative of 9/40*i**5 - 1/240*i**6 + 85*i**2 + 19/16*i**4 + 0*i + 29/12*i**3 + 0. Factor s(r).
-(r - 29)*(r + 1)**2/2
Let v(r) = r**2 + 2*r - 7. Suppose -18 = -8*k + 6*k. Let w(t) = -4*t**2 - 7*t + 29. Let g(f) = k*v(f) + 2*w(f). Factor g(d).
(d - 1)*(d + 5)
Let i = -32 - -45. Let h = i + -10. Factor -3*t**h - 3*t**2 + 8 - 1 + 6*t - 7.
-3*t*(t - 1)*(t + 2)
Let k(a) = 4*a - 3460*a**2 + 8*a + 7*a**3 + 3433*a**2 + 8. Let f(m) = m**3 + m**2 - 2. Let n(x) = 2*f(x) + k(x). Suppose n(g) = 0. Calculate g.
-2/9, 1, 2
Let z(s) be the first derivative of 5*s**5 + 5*s**4/2 - 55*s**3/3 - 20*s**2 - 640. Solve z(w) = 0.
-1, 0, 8/5
Factor -83*a + 22*a - 20*a**3 + 33*a + 69*a**2 - 2*a**4 - 115*a**2.
-2*a*(a + 1)*(a + 2)*(a + 7)
Let y(v) = 3*v**2 - 25*v - 16. Let o be y(9). Determine k so that 10*k**3 + 10*k**2 + 5*k**5 - 32*k + 17*k + 5 + 0*k**o - 15*k**4 = 0.
-1, 1
Suppose -2*b + 96 = b. Let w be 4 + 28/(-6) + b/12. Factor -5*n**5 - 22*n**4 + n**5 - 4*n - 6*n**2 - 12*n**w - 30*n**3 - 2*n**5.
-2*n*(n + 1)**3*(3*n + 2)
Let p(n) be the first derivative of -4/5*n**5 - 676*n - 472/3*n**3 + 624*n**2 - 24*n**4 + 50. Suppose p(i) = 0. Calculate i.
-13, 1
Let t(i) be the third derivative of -17*i**2 + 2 + 1/108*i**5 + 0*i - 1/27*i**4 - 2/27*i**3. Let t(r) = 0. Calculate r.
-2/5, 2
Let k(q) = -7*q**2 + q. Let n be k(1). Let u(h) = 4*h + 29. Let w be u(n). Let w*z**3 - 27*z + 72*z + 35*z + 40*z**2 = 0. Calculate z.
-4, 0
Determine y so that 0 + 3/5*y**4 + 12/5*y - 12/5*y**2 - 3/5*y**3 = 0.
-2, 0, 1, 2
Let s(p) be the second derivative of -p**6/2 + 12*p**5/5 - 9*p**4/2 + 4*p**3 - 3*p**2/2 - 4890*p. Factor s(t).
-3*(t - 1)**3*(5*t - 1)
Factor -1545*w**2 - 200*w + 250*w**3 + 1840*w + 621 + 2819 - 5*w**4.
-5*(w - 43)*(w - 4)**2*(w + 1)
Let u(x) be the second derivative of -6*x**3 - 56*x + 1/3*x**4 + 0 + 16*x**2. Factor u(k).
4*(k - 8)*(k - 1)
Let 894*u**4 + 3*u**5 - 1298*u - 896*u**3 + 611*u + 687*u - u**5 = 0. Calculate u.
-448, 0, 1
Let k(u) be the first derivative of -u**4/22 + 2*u**3/3 + 276*u**2/11 - 3679. Factor k(f).
-2*f*(f - 23)*(f + 12)/11
Let s = -442844 - -885691/2. Factor 15/2 - 9*z + s*z**2.
3*(z - 5)*(z - 1)/2
Let i(u) = 4*u**2 - 14*u - 1. Let s be i(4). Suppose 2*a = s*a - 20. Factor 2*d**a + 0*d**5 - 3*d**5 + d**5 + 0*d**5 + 4*d**3.
-2*d**3*(d - 2)*(d + 1)
Suppose 4*y = -3*k - 15, 94 = -115*y + 116*y - 5*k. Factor y*w**2 + 3/4*w**5 + 0 + 39/4*w**3 + 3*w + 9/2*w**4.
3*w*(w + 1)**2*(w + 2)**2/4
Let r(u) be the third derivative of u**8/672 + 2*u**7/105 - u**6/60 - 43*u**5/60 - 15*u**4/16 + 21*u**3/2 - 577*u**2. Let r(n) = 0