2*p(t). Determine g so that y(g) = 0.
3, 30
Let d(y) be the third derivative of -y**6/48 - 205*y**5/6 + 1546*y**2 - 2. Factor d(x).
-5*x**2*(x + 820)/2
Let t(u) be the third derivative of 2*u**7/735 + 66*u**6/35 + 494*u**5 + 156674*u**4/3 - 672182*u**3 + 1175*u**2. What is h in t(h) = 0?
-133, 3
Suppose -1210 = -110*c - 770. Let r(b) be the third derivative of -7/2*b**c - 1/15*b**5 - 16*b**2 + 0*b + 12*b**3 + 0 + 1/6*b**6 - 2/105*b**7. Factor r(d).
-4*(d - 3)**2*(d - 1)*(d + 2)
Let s = -1 + 3. Let m = 18278 + -54818/3. Factor 2/3*n**3 + m*n - 10/3*n**s - 8/3.
2*(n - 2)**2*(n - 1)/3
Let z = -2283 + 2288. Let g(t) be the second derivative of 10/3*t**3 + 11/4*t**4 + 0 + 2*t**2 + 11/10*t**z - 4*t + 1/6*t**6. Let g(v) = 0. Calculate v.
-2, -1, -2/5
Let p = -3223 - -1513. Let l = -1707 - p. Suppose -3/4*f + 3/4*f**l - 3/8*f**4 + 3/8*f**2 + 0 = 0. What is f?
-1, 0, 1, 2
Let u(z) be the first derivative of 20 - 2/27*z**3 + 0*z**2 + 8/9*z. Factor u(o).
-2*(o - 2)*(o + 2)/9
Let p(g) be the third derivative of g**7/210 - g**6/20 - 3*g**5/20 + 7*g**4/12 - 2184*g**2. Factor p(k).
k*(k - 7)*(k - 1)*(k + 2)
Let r(f) = 2*f**2 + 82*f - 82. Let m be 3/5 + 168/(-30). Let l(q) = 3*q**2 + 165*q - 163. Let c(g) = m*r(g) + 2*l(g). Find o, given that c(o) = 0.
-21, 1
Factor 26/9*n**4 + 0 - 80/9*n**3 + 0*n + 8*n**2 - 2/9*n**5.
-2*n**2*(n - 9)*(n - 2)**2/9
Let m(a) = -27*a**2 - 326*a - 22. Let q(s) = 2. Let i(f) = -3*m(f) + 3*q(f). Factor i(l).
3*(l + 12)*(27*l + 2)
Let r(m) be the first derivative of -2*m**5/35 + 3*m**4/14 + 8*m**3/3 - 60*m**2/7 - 360. Factor r(i).
-2*i*(i - 6)*(i - 2)*(i + 5)/7
Suppose -110/3*i**2 - 36 + 217/3*i + 1/3*i**3 = 0. Calculate i.
1, 108
Let r be 2/4 + (-950)/(-180). Let l(m) = -7*m**2 - 41*m + 58. Let b be l(-7). Factor 2 - 2/9*n**4 - 4/3*n**3 + 16/3*n**b - r*n.
-2*(n - 1)**3*(n + 9)/9
Suppose 4*v - 4*p + 5*p - 18 = 0, 3*p + 2 = 2*v. Factor 10*t**3 + 242*t**2 - 242*t**2 + 3*t**v - t**3.
3*t**3*(t + 3)
Suppose 0 = -5*o - u - 3455, 7*o = 3*o - 2*u - 2770. Let j = o - -1383/2. Factor 0*w**2 + 0*w + 1/2*w**5 + 0 + w**3 - j*w**4.
w**3*(w - 2)*(w - 1)/2
Let r be (-43)/211 - (12 - (-183)/(-15)). Let o = r + 38008/7385. Suppose -6/7 - o*i**2 + 15/7*i**3 + 27/7*i = 0. What is i?
2/5, 1
Let u = 3082 - 2920. Suppose -2*l - 5*m - 15 = -0*l, -2*m = 4*l + 6. Suppose 178*w**2 - u*w**2 + 4*w**3 + 0*w + l*w = 0. Calculate w.
-4, 0
Suppose -49*n + 299*n - 68*n - 118*n + 2*n**2 = 0. What is n?
-32, 0
Let z be (12 - (-266)/(-21))*(30/9)/(-10). Factor 2/9*y + 0 + z*y**2.
2*y*(y + 1)/9
Let y(z) be the second derivative of z**5/110 - 4*z**4/33 - 3*z**3/11 + 8*z - 90. Factor y(s).
2*s*(s - 9)*(s + 1)/11
Let j be ((-150)/(-315))/(((-39)/351)/((-10)/25)). Solve -4/7*u**3 + j*u**2 + 0 - 8/7*u = 0.
0, 1, 2
Let s(u) be the second derivative of u**6/15 - 9*u**5/10 + 7*u**4/6 + 3*u**3 - 8*u**2 - 445*u. Factor s(q).
2*(q - 8)*(q - 1)**2*(q + 1)
Let h(w) be the third derivative of 11/270*w**5 + 0*w**4 + 12*w**2 + 0*w**3 + 0 - 1/540*w**6 + 0*w. Factor h(u).
-2*u**2*(u - 11)/9
Let h be 2/(-10) - (-231)/55. Factor -16*p**2 + 4*p**2 + 56*p + 107 + h*p**4 - 139 + 4*p**3 - 20*p**3.
4*(p - 4)*(p - 1)**2*(p + 2)
Let d(x) = x**3 - 8*x**2 + 19*x - 37. Let p be d(6). Let q be p + 0 - (-11 + 344/24). Factor 0*u - 1/3*u**4 + 1/3*u**5 + 0 - q*u**3 - u**2.
u**2*(u - 3)*(u + 1)**2/3
Let v(p) be the third derivative of -1/60*p**5 + 39*p**2 + p + 0 + 17/3*p**3 - 5/8*p**4. Factor v(k).
-(k - 2)*(k + 17)
Let i(t) = 29*t**2 + 1901*t - 1908. Let z(h) = 11*h**2 + 634*h - 637. Let v(p) = -4*i(p) + 11*z(p). Solve v(m) = 0.
1, 125
Suppose 15*h = 438 - 183. Let i(x) be the first derivative of h + 2/5*x + 1/10*x**2 - 1/15*x**3. What is f in i(f) = 0?
-1, 2
Let p(u) be the second derivative of u**5/60 + 11*u**4/36 + 2*u**3 + 6*u**2 - 6*u + 88. Factor p(d).
(d + 2)*(d + 3)*(d + 6)/3
Let v be 693/1540*112/126. Let 8/5*m + 6/5*m**4 - 6/5*m**2 - 2*m**3 + v*m**5 + 0 = 0. Calculate m.
-4, -1, 0, 1
Let h be (7 + 135/(-18))*-380. What is s in 35*s - h*s**2 - 184*s**2 + 369*s**2 = 0?
0, 7
Let l be (76/(-42) + 136/204)*420/(-120). Factor 40/7*n + 24/7*n**3 - 12/7 - 48/7*n**2 - 4/7*n**l.
-4*(n - 3)*(n - 1)**3/7
Let x = -179174/18665 + -2/3733. Let z = x - -346/35. Suppose z*a + 6/7*a**3 - 6/7*a**2 - 2/7*a**4 + 0 = 0. What is a?
0, 1
Let n(x) be the first derivative of 2*x**3/3 + 2628*x**2 + 3453192*x + 3486. Factor n(a).
2*(a + 1314)**2
Let i be 13 + (-43)/(-1)*(-12)/(-60) + -8. Suppose -648/5 - 506/5*k**2 + i*k**3 - 1224/5*k - 2/5*k**4 = 0. What is k?
-1, 18
Let q(a) = 2*a**2 + 6*a + 2. Let p(u) = -7207*u**2 + 7044*u - 1732. Let h(j) = -p(j) - 2*q(j). Factor h(x).
3*(49*x - 24)**2
Let s be 165/132 - ((-18)/(-8))/(-3). Suppose 5*a = -s*y + 33 - 22, -5*y + 13 = -2*a. Factor 5/3*z**5 - 1/3*z - 4/3*z**y - 8/3*z**4 + 10/3*z**2 - 2/3.
(z - 1)**3*(z + 1)*(5*z + 2)/3
Let i be 7 + (1140/76 - (-5)/(40/(-162))). Factor 61/2*j**2 + 131/4*j + 15/2*j**3 - i*j**4 - 1/4*j**5 + 45/4.
-(j - 5)*(j + 1)**3*(j + 9)/4
Suppose 67*p = -19*p + 69402. Let y = p - 5643/7. Factor 6/7 + 6/7*t - y*t**3 - 6/7*t**2.
-6*(t - 1)*(t + 1)**2/7
Let v(h) be the first derivative of 6*h**2 + 8/5*h**5 - 5*h**4 + 0*h - 16/3*h**3 - 1. Determine g, given that v(g) = 0.
-1, 0, 1/2, 3
Let o(y) be the third derivative of y**6/24 - 64*y**5/3 + 3805*y**4/24 - 1265*y**3/3 + 3871*y**2. Determine l so that o(l) = 0.
1, 2, 253
Let v be 72/(-63)*644/(-184). Determine i, given that -8*i + 44/7*i**3 - 92/7*i**2 + 0 + 8/7*i**v = 0.
-7, -1/2, 0, 2
Let t(n) be the first derivative of 11*n**4/6 + 304*n**3/9 - 193*n**2/3 + 20*n + 6103. Let t(r) = 0. Calculate r.
-15, 2/11, 1
Let c(p) = 76*p - 56. Let u = -1335 + 1336. Let r be c(u). Factor 4/5*j**4 + 48/5*j**3 + 48*j + r + 184/5*j**2.
4*(j + 1)**2*(j + 5)**2/5
Let k = 9/28 + 117/28. Let w = 103/14 - 48/7. Find q, given that -k*q**4 - 21/2*q**3 - 13/2*q**2 + w*q + 1 = 0.
-1, -2/3, 1/3
Suppose -38 = 2*s - 21*s. Factor -137*c**4 + 0*c**3 + 133*c**4 + 12*c**s + 8*c**3.
-4*c**2*(c - 3)*(c + 1)
Suppose -5*v + 4 = -2*v - 5*u, -5*u = 4*v + 18. Let z be (-2)/(-4)*(-11 - -9)/v. Solve 3/4 + z*p - 1/4*p**2 = 0.
-1, 3
Suppose 19*d**3 + 49*d**5 - 39*d**3 - 12*d**2 - 60*d**3 - 119*d**4 + 65709 - 65709 = 0. What is d?
-2/7, 0, 3
Let f be (-637)/(-65) - 4/(-20). Let h(y) = y**3 - 11*y**2 + 14*y - 38. Let l be h(f). Factor -3/4*o**3 - 3/2*o**l + 3/2 + 3/4*o.
-3*(o - 1)*(o + 1)*(o + 2)/4
Let w(n) be the second derivative of -n**7/6 - 5*n**6/2 + 29*n**5/20 + 25*n**4/4 - 11*n**3/3 - 2*n - 156. Solve w(i) = 0.
-11, -1, 0, 2/7, 1
Let i(n) be the third derivative of -n**8/560 - 121*n**7/35 - 122109*n**6/50 - 32969027*n**5/50 - 65450827*n**4/40 + 21*n**2 - 48*n. Factor i(u).
-3*u*(u + 1)*(u + 403)**3/5
Let a be 0/2 - (360/20 + -15) - -5. Let w(f) be the third derivative of 3/7*f**3 - 1/210*f**5 + 0 + f**a + 0*f + 2/21*f**4. Determine b, given that w(b) = 0.
-1, 9
Solve 37123*f - 1600*f**2 + 5717*f + 6*f**3 + 583*f**2 + 21675 = 0.
-1/2, 85
Let w be (-8)/(-6)*(-357)/35*-5. Let s = 71 - w. Factor -6*i**4 - 2*i + i**5 - 8*i - 6*i**5 - 45*i**s + 31*i**4 + 35*i**2.
-5*i*(i - 2)*(i - 1)**3
Let v = 125829/2 + -62913. Let 12 + 9*z - v*z**3 - 9/2*z**2 = 0. Calculate z.
-4, -1, 2
Suppose 2353*m = 4927*m - 2471*m. Solve 26/7*a**4 + m + 8/7*a**5 + 2/7*a + 30/7*a**3 + 2*a**2 = 0.
-1, -1/4, 0
What is g in -366*g**4 + 382*g**4 - 380*g**3 - 100*g - 389*g**2 - 107*g**2 = 0?
-1, -1/4, 0, 25
Let u be ((-207790)/52892)/((-44)/42). Factor u*l**2 + 15/8*l**4 + 3/8*l**5 + 3/8 + 15/4*l**3 + 15/8*l.
3*(l + 1)**5/8
Let x(c) be the third derivative of c**8/8400 + c**7/1050 - c**6/1800 - c**5/150 - 9*c**3 + 24*c**2. Let w(y) be the first derivative of x(y). Factor w(m).
m*(m - 1)*(m + 1)*(m + 4)/5
Let b be (-1 - 11 - -4) + 168/18. Let c(q) be the third derivative of 0*q + b*q**3 + 1/3*q**4 + 0 - 32*q**2 - 1/10*q**5. Let c(g) = 0. What is g?
-2/3, 2
Suppose -6*u + u - g = -139, 19 = u - 2*g. Let n = -23 + u. What is s in 0*s**2 + n - 6*s + 0*s**2 - 4*s**2 + 6*s**2 = 0?
1, 2
Suppose 0 = -5*s - 25, -15*q + 2*s = -11*q - 26. Factor 10/7*y - 2/7*y**2 + q.
-2*(y - 7)*(y + 2)/7
Let n(d) be the first derivative of 2*d**4/33 + d**3/33 - 56*d - 87. Let i(u) be the first derivative of n(u). Let i(y) = 0. What is y?
-1/4, 0
Let m(x) be the first derivative of -2*x**5/5 - 19*x**4 