4*i**2 - 5049*i**4 + 10103*i**4 - 5050*i**4 = 0.
-1, 0, 1, 2
Let a(k) = 2*k**2 + 185*k - 131. Let q(d) = d**2 + 89*d - 66. Let l(h) = -3*a(h) + 7*q(h). Let l(f) = 0. What is f?
-69, 1
Solve 44 - 264*i**2 + 132*i**2 - 18*i + 130*i**2 = 0.
-11, 2
Let h = -155/174 - -71/58. Factor -8/3*n + 5/3*n**2 - h*n**3 + 4/3.
-(n - 2)**2*(n - 1)/3
Let k = -444088/9 - -49344. Factor k + 2/9*y**2 + 8/9*y.
2*(y + 2)**2/9
Let l(p) = -p**2 - 11*p - 15. Suppose q = -k - 5 + 2, 0 = -5*q + k - 39. Let d be l(q). Factor 12 - 18*v - 2 - 5*v**2 + d*v.
-5*(v - 1)*(v + 2)
Let r(t) be the second derivative of t**7/28 - t**6/5 + 3*t**5/8 - t**4/4 - 167*t. Determine p so that r(p) = 0.
0, 1, 2
Let b be ((-6)/15)/((-4)/10). Let u be (-15)/(-7) - b/7. Determine m, given that m + 3/2 - 1/2*m**u = 0.
-1, 3
Let v(g) = -2*g**2 - 27*g - 18. Let m(p) = p - 6. Let j(y) = m(y) + v(y). Determine x so that j(x) = 0.
-12, -1
Let x(v) = 10*v**4 + 265*v**3 - 520*v**2 + 725*v - 155. Let m(l) = -l**4 - 24*l**3 + 47*l**2 - 66*l + 14. Let t(c) = 65*m(c) + 6*x(c). Factor t(i).
-5*(i - 2)**2*(i - 1)**2
Let y(n) be the second derivative of n**4/12 - 7*n**3/6 - 4*n**2 - 399*n. Suppose y(l) = 0. Calculate l.
-1, 8
Let d be 840/430 - 16/(-344). Let t(w) be the third derivative of 0*w + 2/39*w**3 + 8*w**d + 2/195*w**5 + 1/780*w**6 + 0 + 5/156*w**4. Factor t(a).
2*(a + 1)**2*(a + 2)/13
Let t(o) = -4*o**4 + 15*o**3 + 80*o**2 - 87*o - 274. Let l(z) = z**4 - 4*z**3 - 20*z**2 + 22*z + 68. Let h(v) = -9*l(v) - 2*t(v). Factor h(b).
-(b - 8)*(b - 2)*(b + 2)**2
Let g(l) be the second derivative of l**5/20 - 5*l**4/24 - l**3/3 - 8*l**2 - 4*l. Let s(m) be the first derivative of g(m). Suppose s(x) = 0. What is x?
-1/3, 2
Let b(f) be the second derivative of -f**6/720 + f**5/60 - f**4/12 - 13*f**3/6 + 7*f. Let n(g) be the second derivative of b(g). Factor n(d).
-(d - 2)**2/2
Let -144/5 + 416/5*i - 84*i**2 - 12/5*i**4 + 164/5*i**3 - 4/5*i**5 = 0. What is i?
-9, 1, 2
Let z(w) be the third derivative of -w**7/420 + w**6/15 - 29*w**5/120 + 7*w**4/24 + 2*w**2 - 65. Solve z(k) = 0.
0, 1, 14
Let c(z) be the third derivative of -z**7/2940 + z**6/315 - z**5/140 + 7*z**3/3 - 19*z**2. Let w(h) be the first derivative of c(h). Factor w(r).
-2*r*(r - 3)*(r - 1)/7
Let d be (-4)/(12/(-27)) + -1 - 0. Determine b, given that -b**4 - 17*b - d*b**3 + 2*b**3 - b**2 + 2*b**4 + 23*b = 0.
-1, 0, 1, 6
Let o = -2 - -4. Suppose 31*l + 107 = 200. Factor -1/2*w**2 - 2/3 - 5/6*w**l + o*w.
-(w - 1)*(w + 2)*(5*w - 2)/6
Suppose 20*f + 5*f = 0. Let y(m) be the third derivative of f*m**3 + 1/60*m**5 - 3*m**2 - 1/360*m**6 + 0 - 1/36*m**4 + 0*m. Determine i so that y(i) = 0.
0, 1, 2
Let d be (-10)/(-6)*264/110. Let q(a) be the third derivative of -1/960*a**6 + 0*a + 1/240*a**5 + 0 + 0*a**3 - 7*a**2 + 0*a**d. Let q(o) = 0. What is o?
0, 2
Let q be 72/(-54)*(-6)/4. Factor 27*z + z**q - 77*z + 125 + 4*z**2.
5*(z - 5)**2
Factor -98*p**2 + 39*p**3 - 39 - 15 + 141*p - 3*p**4 - 25*p**2.
-3*(p - 9)*(p - 2)*(p - 1)**2
Suppose 0 = -5*c + 13 + 2. Factor 24 + 140*v**2 + 50*v**4 + 97*v**2 + 152*v + 81*v**2 + 240*v**c.
2*(v + 1)*(v + 3)*(5*v + 2)**2
Let -155*h - 4*h**4 + 195*h**3 - 3*h**4 + 44 + 32*h**4 - 14 + 20*h**4 + 125*h**2 = 0. Calculate h.
-3, -2, 1/3
Suppose -19 = 90*x - 89*x - 3*g, 11 = -5*x + 3*g. Factor -3/5*a**x + 6/5 + 3/5*a.
-3*(a - 2)*(a + 1)/5
Let n(p) be the third derivative of p**8/2352 - p**7/735 - p**6/280 - 75*p**2. Factor n(y).
y**3*(y - 3)*(y + 1)/7
Suppose 5*j = 4*y + 49, j + 3*y + y - 5 = 0. Find u, given that -j*u - 7*u**3 + 10*u + 6*u**3 - u**2 + u**4 = 0.
-1, 0, 1
Let t(s) be the first derivative of -s**4/21 + 3*s + 11. Let c(h) be the first derivative of t(h). Factor c(q).
-4*q**2/7
Let z be (-3)/15 + (-3504)/105. Let u = 34 + z. Suppose -3/7*c**4 - 3/7*c**5 + 0*c + 3/7*c**3 + u*c**2 + 0 = 0. What is c?
-1, 0, 1
Let o = -1/6891 + 833816/34455. Let -1/5*z**2 + 22/5*z - o = 0. Calculate z.
11
Determine v so that 27/8*v**3 + 3/2*v - 3/8*v**5 + 3/8*v**4 + 33/8*v**2 + 0 = 0.
-1, 0, 4
Solve -2/3*l + 6*l**2 + 2/3*l**3 - 6 = 0 for l.
-9, -1, 1
Let i(t) be the first derivative of -3*t**5/5 + 9*t**4/4 + 6*t**3 - 42*t**2 + 72*t + 37. Suppose i(k) = 0. Calculate k.
-3, 2
Let p = -5063/3 - -1688. Find t, given that 1/3*t - p*t**3 + 1/3*t**2 - 1/3 = 0.
-1, 1
Suppose 4*q + 0*q = 8. Let 0 - 15 + q*t**2 + 3 - 2*t + 0*t = 0. What is t?
-2, 3
Let s(f) be the second derivative of f**4/78 + 4*f**3/39 + 3*f**2/13 - 6*f - 4. Factor s(c).
2*(c + 1)*(c + 3)/13
Let f(s) = s**3 + s**2 + 3*s. Let q(o) = 7*o**3 - 12*o**2 + 99*o. Let w(n) = 6*f(n) - q(n). Suppose w(x) = 0. Calculate x.
0, 9
Suppose 0 = 17*d - 18*d + 15. Suppose -3*b = 3*f - d, 2*f = 5*f - 3. Suppose 4*o**3 + o**2 - 1/2*o - 9*o**b + 0 + 9/2*o**5 = 0. Calculate o.
-1/3, 0, 1/3, 1
Determine s, given that 58*s**4 + 162*s**5 - 174*s**5 - 3*s**4 + 37*s**4 + 32*s**3 = 0.
-1/3, 0, 8
Let y(h) be the third derivative of -392*h**7/15 - 196*h**6/5 - 126*h**5/5 - 9*h**4 - 27*h**3/14 - 61*h**2. Factor y(a).
-(14*a + 3)**4/7
Suppose -5*c - 104 = 3*c. Let y be c*(-6)/234*15*1. Factor -1/2*o**2 + 1/4*o**4 - 1/2*o**3 + 1/4*o**y + 1/4 + 1/4*o.
(o - 1)**2*(o + 1)**3/4
Let z = 3475/3 - 1157. Factor 1/6*i**2 - z*i + 8/3.
(i - 4)**2/6
Let v(g) be the second derivative of g**9/45360 + g**8/3360 + g**7/840 - g**4/12 + 4*g**3/3 - 37*g. Let q(z) be the third derivative of v(z). Factor q(b).
b**2*(b + 3)**2/3
Let p(r) be the first derivative of -15/4*r**4 + 15/2*r**2 + 7 + 20*r + r**5 - 25/3*r**3. Determine v so that p(v) = 0.
-1, 1, 4
Let d = -21 + 26. Let k be 21/(-90) + 2/d. Factor -k*t**2 + 1/6*t + 0.
-t*(t - 1)/6
Suppose 25*m - 28*m + 6 = 0. Factor 4/5*y + y**m + 0.
y*(5*y + 4)/5
Let c be -1*1*(-1)/(-1). Let m be ((-12)/(-36))/(c/(-6)). Factor 4*o - 4*o**4 + 4 + 8*o**4 + 4*o**5 + 51*o**2 - 8*o**3 - 59*o**m.
4*(o - 1)**2*(o + 1)**3
Let w(t) be the first derivative of -9 + 3/5*t**5 + 0*t**2 + 0*t + t**3 - 3/2*t**4. Determine z, given that w(z) = 0.
0, 1
Let y(t) be the second derivative of t**7/1050 - 7*t**6/300 + 49*t**5/300 - 5*t**2 + 18*t - 1. Let q(u) be the first derivative of y(u). Factor q(p).
p**2*(p - 7)**2/5
Factor -1/7*c**3 - 1/7*c**5 - 2/7*c**4 + 0 + 0*c**2 + 0*c.
-c**3*(c + 1)**2/7
Let l(h) = 4*h**2 - 3*h + 2. Let x be l(1). Suppose -5*s**2 + 5*s**4 + 2*s**2 + 7*s**x + 6*s**2 + s**5 = 0. What is s?
-3, -1, 0
Let f = 3518 - 38690/11. Determine s, given that -2/11*s**3 - 4/11*s**2 + f*s + 16/11 = 0.
-2, 2
Let f(n) be the first derivative of -154*n**6/3 - 584*n**5/5 + 20*n**4 + 32*n**3/3 + 76. Find g such that f(g) = 0.
-2, -2/11, 0, 2/7
Let n(l) be the third derivative of l**6/720 - 9*l**5/40 + 243*l**4/16 - 2187*l**3/4 - 166*l**2. Factor n(h).
(h - 27)**3/6
Let s(z) = z**2 + 173*z + 7936. Let v(k) = k**2 + 172*k + 7939. Let h(d) = 6*s(d) - 5*v(d). Factor h(j).
(j + 89)**2
Let p = -1447 + 1454. Let s(f) be the second derivative of p*f + 1/48*f**4 + 0*f**2 + 0 + 1/12*f**3. Solve s(w) = 0 for w.
-2, 0
Let p = 206788/7 + -29540. What is q in p + 10/7*q + 2/7*q**2 = 0?
-4, -1
Let z be (27/6 - 4)*2 - -2. Factor -450*a**2 + 4*a**5 - 216 - 3*a**5 + 625*a + 91*a - 20*a**4 + 145*a**z - 176*a.
(a - 6)**3*(a - 1)**2
Find l such that -69*l**5 - 4708*l**3 - 2176*l + 5*l**5 - 1133*l**4 + 2381*l**4 + 240 + 5964*l**2 = 0.
1/4, 2, 15
Let a(t) be the second derivative of -4*t + 7/26*t**4 + 19/39*t**3 + 9/130*t**5 + 2 + 1/195*t**6 + 6/13*t**2. Suppose a(z) = 0. What is z?
-6, -1
Let i be 3/(15/(-10))*-1. Factor -30 - 357*r + 179*r - 5*r**i + 153*r.
-5*(r + 2)*(r + 3)
Let s(k) be the first derivative of -k**6/360 + k**5/45 - k**4/18 - 4*k**2 - 24. Let n(l) be the second derivative of s(l). Factor n(p).
-p*(p - 2)**2/3
Suppose 3*d + 1 = -2*n - 9, -24 = -4*n + 5*d. Let j be n + 3 + ((-189)/(-6))/(-9). Factor -j*m - m**2 + 1/2*m**3 + 1.
(m - 2)*(m - 1)*(m + 1)/2
Let a(r) be the first derivative of -2*r**3/21 + 10*r**2/7 - 18*r/7 + 5. Solve a(b) = 0 for b.
1, 9
Let u(h) be the third derivative of -h**8/4032 + h**7/336 - h**5/60 + 17*h**4/24 - 35*h**2. Let v(o) be the third derivative of u(o). Factor v(z).
-5*z*(z - 3)
Solve -9/2*j**2 - 15/2*j - 7/2 - 1/2*j**3 = 0.
-7, -1
Suppose 9*w = 5*w + 32. Suppose 4*a = -w + 16. Factor 0*m**3 + 1/4*m**4 - 3/4*m**a - 1/2*m + 0.
m*(m - 2)*(m + 1)**2/4
Let h be (2 + 42/(-12))/(3/(-4)). Let z