e 17/34*(-160)/(-200). Factor 2/5*s**2 + 2/15*s**4 - i*s**3 + 0 - 2/15*s.
2*s*(s - 1)**3/15
Let s = 3804 + -15211/4. Let m(p) be the first derivative of 15/2*p**2 + 10*p - s*p**4 + 0*p**3 + 20. Factor m(l).
-5*(l - 2)*(l + 1)**2
Factor 4531*u**2 - 3*u**3 - 87*u**2 + 6939 + 2501*u**2 - 13881*u.
-3*(u - 2313)*(u - 1)**2
Suppose 2*t + 154 = 2*g, -3*t + 4*g = -g + 229. Let x be 65/t + 5/6. Factor -2/3*f**4 - 2/3*f**3 + 0*f + x*f**2 + 0.
-2*f**3*(f + 1)/3
Let u(g) = g**2 + 89*g + 286. Let s(y) = 3*y**2 + 274*y + 859. Let l(i) = -2*s(i) + 7*u(i). Factor l(k).
(k + 4)*(k + 71)
Let k be ((-1)/(-411))/((-10659)/(-3555) + -3). Let r = 8/137 - k. Factor 3*w + r*w**2 - 9/2.
3*(w - 1)*(w + 3)/2
Let g = -3 + 5. Let 6*i**3 + 590*i - 618*i - g*i**3 + 24 = 0. What is i?
-3, 1, 2
Let v(m) be the second derivative of -1/6*m**3 + 0*m**2 - 1/36*m**4 + 1/240*m**5 + 27*m + 0. Factor v(i).
i*(i - 6)*(i + 2)/12
Let j = 15601/26677 - 51/3811. Solve -8/7*s + 4/7*s**2 + j = 0.
1
Let z(k) be the third derivative of k**8/560 + k**7/280 - 37*k**3/2 + 101*k**2. Let y(s) be the first derivative of z(s). Solve y(j) = 0 for j.
-1, 0
Let g(i) = 5*i**5 + 78*i**4 - 3*i**3 - 2500*i**2 + 12. Let a(j) = -j**4 + j**3 - 4. Let r(k) = -3*a(k) - g(k). Factor r(q).
-5*q**2*(q - 5)*(q + 10)**2
Suppose -h + 2*h - 4*l = 26, -5*h - 5*l = -5. Let c be -1 + (h - (0 + 2)). Determine o, given that -881*o**3 + 3*o**2 + 876*o**c - 25*o + 17*o**2 + 10 = 0.
1, 2
Factor -33*p**2 - 432 + 216*p + 3/2*p**3.
3*(p - 12)*(p - 6)*(p - 4)/2
Let l be (-13560)/5876 + (-10)/(390/(-207)). Factor -4/3*r**2 + 8/9*r - 2/9*r**l + 1/9*r**4 + 32/9.
(r - 4)*(r - 2)*(r + 2)**2/9
Let v(m) be the second derivative of -m**6/180 - 31*m**5/120 - 55*m**4/12 - 344*m**3/9 - 416*m**2/3 + 10562*m - 1. What is g in v(g) = 0?
-13, -8, -2
Determine p so that 98/3*p**3 - 4*p**2 + 0 + 0*p = 0.
0, 6/49
Let g(b) be the first derivative of -b**5/180 + 17*b**4/24 - 25*b**3/9 - 37*b**2/2 + b + 28. Let l(u) be the second derivative of g(u). Factor l(z).
-(z - 50)*(z - 1)/3
Let a(q) be the second derivative of -q**6/90 + q**5/3 - 83*q**4/36 + 62*q**3/9 - 10*q**2 + 842*q. Factor a(m).
-(m - 15)*(m - 2)**2*(m - 1)/3
Let x(k) be the second derivative of -k**7/504 - 5*k**6/144 - k**5/4 + 31*k**4/12 - k**2/2 + 17*k + 1. Let c(u) be the third derivative of x(u). Factor c(z).
-5*(z + 2)*(z + 3)
Let b(g) = -g**3 - 5*g**2 - 8*g - 3. Let j be b(-3). Solve 40*m**2 - 21*m**2 + 3*m**4 + 21*m**j - m**2 = 0.
-6, -1, 0
Let q(k) be the first derivative of -k**4/36 - 88*k**3/9 + 265*k**2/18 + 7482. Factor q(a).
-a*(a - 1)*(a + 265)/9
Let o be 0 - ((-4)/(-6)*6 + -10). Suppose 0 = -2*p + o, w + p = 6*w - 192. Factor -45*s**2 - 20 + 0*s**4 + 8 - 3*s**4 + 21*s**3 + w*s.
-3*(s - 4)*(s - 1)**3
Let x = 23315/134 + -174. Let j = 203/268 + x. What is l in j*l**2 + 3/4 + 3/2*l = 0?
-1
Suppose -6 = n - 2. Let j be (18/(-4) - -4)/(2/n). Find p, given that -8*p - 729*p**3 - j + 0*p - 19*p - 380*p**2 + 137*p**2 = 0.
-1/9
What is k in -11/3*k**4 + 726*k + 0 + 728/3*k**3 - 4037*k**2 = 0?
0, 2/11, 33
Suppose 2*d - 4*c - 16 = 0, 0*d - c = -4*d + 18. Let h = 3 - 1. Factor 28*a**d - 2 + 2 + h*a**5 - 22*a**4.
2*a**4*(a + 3)
Let r(t) = -t**2 - 38*t + 132. Let c be r(-41). Suppose 0 = -3*i - c + 15. Find p such that 0 + 1/2*p**3 + 1/2*p**i - p = 0.
-2, 0, 1
Let a(d) be the second derivative of d**7/315 - d**6/60 - 13*d**5/90 + 5*d**4/12 - 53*d**2 + 61*d. Let f(c) be the first derivative of a(c). Factor f(k).
2*k*(k - 5)*(k - 1)*(k + 3)/3
Determine k, given that -1704*k**3 + 21*k**2 + k**5 + 1703*k**3 - 16*k**4 - 5*k**4 = 0.
-1, 0, 1, 21
Let t = -768 - -241. Let l be t/(-62) + (1 - 9). What is r in -l*r**3 + 0 + 6*r**2 - 18*r = 0?
0, 6
Suppose -5*o = 3*l - l - 20, l + 16 = 4*o. Suppose -3*r - 2 = 2*s, 5*r - 4*s - 3 - 1 = l. Factor r - 1/4*h**2 - 1/4*h.
-h*(h + 1)/4
Let y(w) = -3*w**2 + 15*w + 84. Let l(b) = 10*b**2 - 94*b - 252. Let u(t) = 2*l(t) + 7*y(t). Determine m so that u(m) = 0.
-84, 1
Let o = -8482/7 - -42376/35. Let d = -166/315 - o. Solve 10/3*n**2 + 14/9*n**4 - 38/9*n**3 - d - 2/9*n = 0.
-2/7, 1
Let t be 18/(-80)*70/(-294). Let x(l) be the third derivative of 1/280*l**6 + 11*l**2 + 0 + 0*l + 0*l**3 - 1/70*l**5 - t*l**4. Factor x(y).
3*y*(y - 3)*(y + 1)/7
Let -128/3*y**2 - 1376/3*y - 3698/3 = 0. What is y?
-43/8
Let i(z) be the third derivative of -z**8/1400 - z**7/1400 + 35*z**3/3 - 3*z**2. Let n(b) be the first derivative of i(b). Factor n(t).
-3*t**3*(2*t + 1)/5
Let t(c) be the third derivative of -c**7/1680 - c**6/480 + c**5/32 - 2*c**2 - 50. Let t(o) = 0. What is o?
-5, 0, 3
Suppose -994 = -391*l - 84*l + 1381. Determine w, given that -66/5*w**2 - 6/5 + 12/5*w**3 - 39/5*w + 72/5*w**4 + 27/5*w**l = 0.
-2, -1, -1/3, 1
Suppose 154*c**2 - 983*c - 994*c + 2949*c - 72 - 32*c**4 + 59*c**3 + 3*c**5 - 984*c = 0. What is c?
-1, 2/3, 6
Let y be ((-44)/((-2464)/126))/(3 - (0 + 0)). Suppose -3/8*s**4 + 3/4*s**3 - y*s + 27/8*s**2 - 3 = 0. What is s?
-2, -1, 1, 4
Suppose -3*g - 10*f + 12 = -13*f, g = 5*f + 4. Let p be (63/14)/(2*(g - 2)). Find t such that -3/8*t**5 - 9/8*t**4 - 3/8*t + 9/4*t**2 - p + 3/4*t**3 = 0.
-3, -1, 1
Suppose 20*o - 15*o - 4*b = 12, 0 = 3*o + b - 14. Solve k**2 + 4/3*k**3 + 0 - 4/3*k**5 + 0*k - k**o = 0.
-1, -3/4, 0, 1
Solve 7*m**4 + 11*m**4 - 87*m + 42*m + 160*m**3 - 109 + 95*m**3 + 270*m**2 + 31 = 0 for m.
-13, -1, -2/3, 1/2
Let l(z) be the first derivative of -z**4/2 - 34*z**3/3 - 79*z**2 - 126*z - 3051. Factor l(k).
-2*(k + 1)*(k + 7)*(k + 9)
Let i(d) = -8*d**3 - 12*d**2 + 956*d - 936. Let m(q) = 2*q**3 - 2*q**2. Let u(v) = -i(v) - 2*m(v). Factor u(p).
4*(p - 13)*(p - 1)*(p + 18)
Let t(s) be the second derivative of s**6/15 - 4*s**5/5 - 41*s**4/2 - 94*s**3/3 + 224*s**2 + 1320*s - 3. Determine m so that t(m) = 0.
-7, -2, 1, 16
Let w(k) = -k**3 - 10*k**2 + 10*k - 6. Let b be w(-11). Let v be ((-3)/(9/b))/((-13)/117). Factor -i**3 + v*i**2 - 10 - 4*i**3 + 5*i + 0*i - 5*i**4.
-5*(i - 1)**2*(i + 1)*(i + 2)
Let u(r) be the second derivative of -r**6/6 - 7*r**5/2 + 5*r**4/3 + 140*r**3/3 - 7*r - 807. Let u(c) = 0. What is c?
-14, -2, 0, 2
Let h(b) be the third derivative of 23/51*b**4 - 11*b**2 + 0*b - 16/51*b**3 - 217/1020*b**6 + 0 - 2/17*b**5 - 7/255*b**7. Let h(m) = 0. Calculate m.
-4, -1, 2/7
Let x(p) be the third derivative of -p**6/480 - p**5/120 + 133*p**4/32 - 125*p**2 + 2*p - 2. Factor x(q).
-q*(q - 19)*(q + 21)/4
Suppose -15*n + 32 = 2. Solve -30*a + 24*a**2 - 21 - 19 - 49*a**2 + 20*a**n = 0 for a.
-4, -2
Let q be (-14816)/(-6880) + 32/688. Solve 0 - 24/5*w**2 + q*w**5 - 4/5*w + 24/5*w**4 - 7/5*w**3 = 0 for w.
-2, -1, -2/11, 0, 1
Let m(f) be the first derivative of -f**6/1440 + 7*f**5/80 - 147*f**4/32 - 67*f**3/3 - 2*f - 98. Let q(i) be the third derivative of m(i). Factor q(u).
-(u - 21)**2/4
Let v(p) = -46*p**3 + 28*p**2 - 86*p - 6. Let q(d) = 2*d**3 - d**2 + 4*d. Let t(g) = -44*q(g) - 2*v(g). Solve t(h) = 0 for h.
-1, 1, 3
Find a, given that -45*a**4 - 4*a**5 + a**5 + 310*a**3 + 299*a**3 + 594*a + 439*a**3 - 963*a**2 - 631*a**3 = 0.
-22, 0, 1, 3
Let d = 1099511/8796216 + 2/1099527. Suppose 7/8*q**2 + 2*q + d*q**3 + 3/2 = 0. What is q?
-3, -2
Let u(k) be the third derivative of k**7/1365 - k**6/780 - k**5/65 + 105*k**2 + 1. Solve u(y) = 0 for y.
-2, 0, 3
Let u(b) = -7*b**2 + 33*b + 4. Let z(n) = -85*n**2 + 395*n + 50. Let h(c) = -3*c - 94. Let v be h(-32). Let k(x) = v*z(x) - 25*u(x). Factor k(s).
5*s*(s - 7)
Factor 410040*l**2 + 189700*l**3 - 4244832/7 - 124848/7*l + 24500*l**4.
4*(l - 1)*(35*l + 102)**3/7
Let p(d) be the first derivative of 5*d**8/1512 - d**7/315 - d**6/270 - 8*d**2 - 2*d - 40. Let y(j) be the second derivative of p(j). Solve y(l) = 0 for l.
-2/5, 0, 1
Let m(x) be the third derivative of 1/12*x**4 + 0*x - 56*x**2 + 0*x**3 + 0 + 1/420*x**7 - 1/80*x**6 + 0*x**5. Determine g so that m(g) = 0.
-1, 0, 2
Suppose 28*m - 194 = -54. Let v(o) = 2*o**2 + 1. Let s(k) = 20*k**3 + 46*k**2 - 8*k + 5. Let n(i) = m*v(i) - s(i). Solve n(t) = 0.
-2, 0, 1/5
Suppose -23/3*g**4 - 361/3*g**2 + 1/3*g**5 + 163/3*g**3 + 320/3*g - 100/3 = 0. Calculate g.
1, 10
Suppose -32 + 2 = -10*u. Determine l so that l**2 - 17*l**4 - l**4 + 7*l**2 + 14*l**u - 4*l**2 = 0.
-2/9, 0, 1
Factor -2/3*j**3 + 1040/3 - 14/3*j**2 + 236/3*j.
-2*(j - 10)*(j + 4)*(j + 13)/3
Let x be