or 28/9 + 2/9*q**w + 2*q.
2*(q + 2)*(q + 7)/9
Let i(z) be the third derivative of 109*z**2 + 0 + 1/10*z**4 + 1/150*z**5 + 0*z + 8/15*z**3. Determine s, given that i(s) = 0.
-4, -2
Factor 0 + 3*s**3 + 24/5*s**2 - 3/5*s**4 - 144/5*s.
-3*s*(s - 4)**2*(s + 3)/5
Let q = -64 - -68. Factor -4*r + 21*r - 35*r**3 - 18*r**4 + 3*r**q + 3*r.
-5*r*(r + 1)*(r + 2)*(3*r - 2)
Let r(p) be the third derivative of 204*p**2 + 45/8*p**4 + 0*p - 1/12*p**5 + 70/3*p**3 + 0. Suppose r(t) = 0. What is t?
-1, 28
Let a(q) be the second derivative of 5*q**4/12 + 5*q**3/2 - 175*q**2 + 1300*q. What is y in a(y) = 0?
-10, 7
Suppose -662*b + 478*b + 552 = 0. Factor -1/3*l**4 + 32/3 - 20*l + 2*l**b + 23/3*l**2.
-(l - 8)*(l - 1)**2*(l + 4)/3
Let b(i) = 5*i**3 + 137*i**2 + 2723*i + 15135. Let a(m) = -6*m**3 - 138*m**2 - 2722*m - 15134. Let s(t) = -3*a(t) - 4*b(t). Determine z so that s(z) = 0.
-29, -9
Factor 0*v**2 - 273 - 549/2*v + 3/2*v**3.
3*(v - 14)*(v + 1)*(v + 13)/2
Suppose -1 = -w - 5. Let k(b) = -2*b - 2. Let s be k(w). Factor 346*j**3 + s*j**4 + 3*j**4 + 3*j**2 - 355*j**3 - 3*j**5.
-3*j**2*(j - 1)**3
Let f(g) be the first derivative of 2*g**3/21 + 25*g**2/7 + 48*g/7 + 803. What is j in f(j) = 0?
-24, -1
Factor -40/3 + 1364/3*x - 136/3*x**2.
-4*(x - 10)*(34*x - 1)/3
Let m be 11*(-180)/1782 + 13/9. Factor -m*x**2 + 0 + 4/3*x.
-x*(x - 4)/3
Suppose 0 = -30*f + 34*f. Let j be 8 - (-48)/(-8) - (-432 + f). Factor 438*q**2 + 51 - 6*q - 15 - j*q**2 - 18*q.
4*(q - 3)**2
Let p(o) be the third derivative of o**5/12 - 395*o**4/24 + 250*o**3 + 386*o**2 + o + 3. Let p(i) = 0. Calculate i.
4, 75
Let v be (32/(-12))/(1/(-15)). Suppose v = 8*b - 0*b. Find d such that -5*d - 24*d**4 + 4*d**3 + 5*d + 12*d**4 + 8*d**b = 0.
0, 1/2, 1
Let s(m) be the third derivative of -m**8/112 + 9*m**7/35 - 4*m**6/5 - 14*m**2. Determine q so that s(q) = 0.
0, 2, 16
Let j = 824 + -824. Suppose 15*c - 2*k = 12*c + 212, 5*c + 4*k - 346 = j. Find y, given that -71*y**2 - c*y**3 - 49/2*y**4 - 9/2 - 30*y = 0.
-1, -3/7
Let o(i) be the first derivative of 6*i**5/5 - 1105*i**4 + 811064*i**3/3 + 543906*i**2 + 272322*i - 7381. Determine d so that o(d) = 0.
-1, -1/3, 369
Let z(o) be the first derivative of 21/4*o**2 - 1/4*o**3 + 265 - 36*o. Factor z(g).
-3*(g - 8)*(g - 6)/4
Let v = 46835 + -46833. What is a in 3/4*a**5 + 12*a + 75/4*a**v + 21/4*a**4 + 57/4*a**3 + 3 = 0?
-2, -1
Let b(d) be the third derivative of 3*d**6/16 - 46*d**5/15 + 379*d**4/48 - 14*d**3/3 + d**2 - 39*d - 27. Factor b(p).
(p - 7)*(p - 1)*(45*p - 8)/2
Let k = -661 + 663. Suppose k*a = -40*t + 43*t - 5, -5*t = a - 30. Suppose 272/9*f - 4/9*f**t - 64/9 - 133/9*f**3 - 43/9*f**4 - 28/9*f**2 = 0. What is f?
-4, 1/4, 1
Let m(o) = -15*o**3 + 63*o**2 + 4*o + 4. Let n(q) = -61*q**3 + 246*q**2 + 15*q + 17. Let r(b) = 17*m(b) - 4*n(b). Factor r(c).
-c*(c - 8)*(11*c + 1)
Let s = 206 + -200. Suppose -17*v + 8*v - s*v + 5*v**5 + 40*v**2 + 0*v**3 - 30*v**3 = 0. What is v?
-3, 0, 1
Factor 460*p**2 + 914*p + 55470 - 12739*p - 681*p**3 + 676*p**3.
-5*(p - 43)**2*(p - 6)
Let z(o) be the second derivative of -o**8/560 + o**7/210 + o**6/360 - o**5/60 - 6*o**3 + 58*o. Let a(x) be the second derivative of z(x). Factor a(f).
-f*(f - 1)**2*(3*f + 2)
Let p(r) = -22*r**3 + 725*r**2 - 13. Let h(i) = -10*i**3 + 362*i**2 - 6. Let z(f) = 13*h(f) - 6*p(f). Factor z(u).
2*u**2*(u + 178)
Let a = 2009/148 - 49/37. Let d = -43/4 + a. Factor d*h**5 + 0 - 9*h**3 + 0*h + 3/2*h**4 + 0*h**2.
3*h**3*(h - 2)*(h + 3)/2
Suppose -41/8*r + 21/4 - 1/8*r**2 = 0. Calculate r.
-42, 1
Let q(f) be the second derivative of f**6/20 - 111*f**5/40 + 17*f**4/4 + 18*f**3 + 3*f - 223. Factor q(h).
3*h*(h - 36)*(h - 2)*(h + 1)/2
Let k(w) be the second derivative of w**4/24 + 31*w**3/3 + 61*w**2 + 19*w - 16. Factor k(x).
(x + 2)*(x + 122)/2
Let t(o) = o**2 + 3*o + 3. Let i be t(-2). Let q be (-3)/(-1) + i + 0. Factor -12*n**2 - 16/3*n - 32/3*n**3 - 10/3*n**q - 2/3.
-2*(n + 1)**3*(5*n + 1)/3
Suppose -s + 3*i + 22 = 8*i, 0 = 2*s + 5*i - 24. Factor -540*d**3 - 58*d - 162*d**4 + 39*d**5 + 42*d**5 - 38*d - 408*d**s.
3*d*(d - 4)*(3*d + 2)**3
Let o be 56/35*(50/(-15))/((-80)/30). What is u in 56/3*u - 392/3 - 2/3*u**o = 0?
14
Factor 214/5*o + 32/3 + 968/15*o**2 + 2/15*o**5 + 652/15*o**3 + 56/5*o**4.
2*(o + 1)**4*(o + 80)/15
Let i be 94/329*(-1 - (-8 - 0)). Let -25*f**3 - 12*f - 10*f**2 + 0*f**2 - 42*f**4 + 70*f**i - 26*f**3 = 0. Calculate f.
-2, 0, 2/7, 1/2
Let z = -92 + 95. Suppose 4*n + 2*v - 100 = 0, 3*n - z*v + 36 = 120. Factor 5*h**3 + n*h**2 - 8*h + 1793 - 15*h**3 - 1801.
-2*(h - 2)*(h - 1)*(5*h + 2)
Let k(f) be the third derivative of f**5/60 - 17*f**4/4 - 103*f**3/6 - f**2 - 478. Factor k(w).
(w - 103)*(w + 1)
Factor -7*a + 260*a**2 + 28*a**4 + 13*a**3 + 78*a**3 + 63*a + 141*a**3.
4*a*(a + 1)*(a + 7)*(7*a + 2)
Let v = 24 + -12. Let u = v + -9. Factor -7*a + 0*a**u - 2*a**3 - 8*a**3 - 25*a**2 + 17*a + 25*a**4.
5*a*(a - 1)*(a + 1)*(5*a - 2)
Let m be 10/20*-8 - 537. Let v = 541 + m. Factor 2/5*o**2 + 0*o + v.
2*o**2/5
Let c(i) be the third derivative of -i**6/30 + i**5/6 - i**4/6 - 646*i**2. Determine b, given that c(b) = 0.
0, 1/2, 2
Let h(u) be the first derivative of u**7/420 + 7*u**6/36 + 67*u**5/60 + 11*u**4/4 - 238*u**3/3 + 159. Let q(t) be the third derivative of h(t). Factor q(n).
2*(n + 1)**2*(n + 33)
Let s = 133/709 + -222/4963. Let -s*z**3 + 5/7*z**2 + 8/7*z - 48/7 = 0. Calculate z.
-3, 4
Solve 113 - 66*g - g**2 + 89 + 83*g - 32 + 100 = 0 for g.
-10, 27
Let m(u) be the first derivative of -1/12*u**4 - 147/2*u**2 - 14 + 14/3*u**3 + 0*u. Let m(s) = 0. Calculate s.
0, 21
Let u(x) = -2*x + 2. Let t(r) = 4*r**3 - r**2 + r + 1. Let p be t(-1). Let a be u(p). Solve 7*k + a*k**2 + 8*k**3 - 28*k - 12*k + k + 16 - 4*k**4 = 0 for k.
-2, 1, 2
Let j(h) be the first derivative of -61*h**4/2 + 1102*h**3/3 - 872*h**2 + 56*h + 12935. Determine d so that j(d) = 0.
2/61, 2, 7
Suppose 50/11*l**2 - 24/11*l - 28/11*l**3 + 2/11*l**4 + 0 = 0. Calculate l.
0, 1, 12
Suppose 0 - 1/5*f**2 + 341/5*f = 0. Calculate f.
0, 341
Let g(m) be the second derivative of m**5/5 + 41*m**4 - 166*m**3 + 250*m**2 - 192*m + 1. Factor g(w).
4*(w - 1)**2*(w + 125)
Suppose 0 = -76*s - 40 - 492. Let h be ((-3678)/32)/(s - 143/(-26)). Find t, given that 757/8*t**2 - 7/4*t**5 - 345/8*t + 165/8*t**4 - h*t**3 + 25/4 = 0.
2/7, 1/2, 1, 5
Let p(b) = 6*b**3 - 2*b**2 + 1. Suppose -10*v = -9 - 1. Let q be p(v). Determine k, given that 16*k**3 - q*k**2 - 5*k**3 + 55*k - 57*k + 15*k**5 + 29*k**4 = 0.
-1, -1/3, 0, 2/5
Let d(m) = -3*m**2 - 1589*m - 1592. Let k(j) = -22*j**2 - 11121*j - 11144. Let n(z) = -15*d(z) + 2*k(z). Factor n(s).
(s + 1)*(s + 1592)
Let b be (1 - 2)*(-1 + -4). Let k(v) = -v**3 + 3*v**2 + 9*v + 8. Let c be k(b). Solve -150*j**3 + 71*j**c - 3*j**4 + 70*j**3 - 6*j**2 = 0 for j.
-2, -1, 0
Let t(s) be the second derivative of s**4/66 + 8*s**3/33 - 84*s**2/11 - 1524*s. Suppose t(i) = 0. What is i?
-14, 6
Let n(d) be the second derivative of -d**6/50 - 4653*d**5/100 - 120435*d**4/4 - 120125*d**3/2 - 7*d - 126. Determine k so that n(k) = 0.
-775, -1, 0
Let g(w) be the third derivative of 0*w**3 - 7/60*w**5 - 8*w**2 + 1/120*w**6 + 0 + 0*w + 0*w**4. Determine b, given that g(b) = 0.
0, 7
Let d(n) = -10*n**2 - 8*n**2 + 37*n**2 - 8*n**2 - 13*n**2 - 8*n + 4. Let v(g) = 4*g**2 + 17*g - 5. Let q(b) = -5*d(b) - 3*v(b). Find j such that q(j) = 0.
-5, -1/2
Let j be (21 + -585)*(-2)/4. Find m such that -j*m - 1336 - 2761 - 3*m**2 - 3274 + 744 = 0.
-47
Let p(z) be the first derivative of 14*z**6/15 + z**5 - 16*z**4/3 + 8*z**3/3 + 219*z - 91. Let d(q) be the first derivative of p(q). Solve d(v) = 0.
-2, 0, 2/7, 1
Let z be -1366*(8 - 29308/3664). Let o = 2/229 - z. Factor 3/2*n + 0 + o*n**2.
3*n*(n + 1)/2
Determine h so that -3/5*h**4 - 164*h**2 - 708/5*h + 361/5*h**3 + 0 = 0.
-2/3, 0, 3, 118
Let i(z) be the first derivative of -2*z**3/27 + 42*z**2 - 681. Factor i(u).
-2*u*(u - 378)/9
Let g(s) be the second derivative of s**7/147 + s**6/105 - 11*s**5/70 + s**4/6 + 10*s**3/21 - 8*s**2/7 - 3*s. Find y, given that g(y) = 0.
-4, -1, 1, 2
Let d be ((-6)/28)/((-58557)/(-262)). Let c = d + 1045/2086. Determine o, given that 3/2*o**3 + o**2 - 6*o + 4 - c*o**4 = 0.
-2, 1, 2
Let g(r) = 13*r**3 + 769*r**2 + 49151*r - 49925. Let x(c) = 213*c**3 + 12303*c**2 + 786417*c -