c*p + 33. Find y such that -35*y**4 + 3*y**5 - 3*y**2 + 9*y**2 - p*y**2 + 12*y**5 + 25*y**3 = 0.
0, 1/3, 1
Let j be ((-492)/(-1107)*(0 - -3))/((-2)/(-8)). Factor j*a**2 - 2*a - 4/3 - 2*a**3.
-2*(a - 2)*(a - 1)*(3*a + 1)/3
Let o = 5662/1127 + -178/49. Suppose 2/23*t**2 + 16/23*t + o = 0. What is t?
-4
Let a(w) be the second derivative of -w**5 + 110*w**4/3 - 395*w**3/2 + 855*w**2/2 - 151*w. Factor a(t).
-5*(t - 19)*(2*t - 3)**2
Let d(w) = 8*w**3 - 14*w**2 + 10*w + 44. Let f(i) = -i**3 + i - 2. Let q = 38 + -44. Let l(g) = q*f(g) - d(g). Solve l(c) = 0.
-1, 4
Let s be ((-24)/(-20))/((-237)/60 - -4). Let 68/5*v - s - 4/5*v**2 = 0. Calculate v.
2, 15
Let z = 36564/13 + -182508/65. Solve -z - 66/5*n - 51/5*n**2 + 3*n**4 + 3/5*n**5 + 3/5*n**3 = 0 for n.
-4, -1, 2
Factor -254 + 852*l - 90 - 1198*l**2 + 156*l**3 + 4*l**4 + 530*l**2.
4*(l - 2)*(l - 1)**2*(l + 43)
Let w(q) be the second derivative of -q**5/5 - 26*q**4/3 - 112*q**3 - 7772*q. Factor w(b).
-4*b*(b + 12)*(b + 14)
Let c(z) = -16*z**2 - 5584*z - 5548. Let g(v) = -2*v**2 - 6*v - 2. Let p(i) = c(i) - 10*g(i). Factor p(m).
4*(m - 1382)*(m + 1)
Let o = -7001/30 - -3568/15. Factor -6*m**2 + 0 + 3/2*m**3 + o*m.
3*m*(m - 3)*(m - 1)/2
Find d such that -40 - 748/5*d**2 - 192/5*d**4 - 4832/5*d**3 + 1292/5*d = 0.
-25, -2/3, 1/4
Suppose 0 = 3601*s - 3620*s. Let r(u) be the third derivative of s*u - 1/4*u**3 - 1/120*u**5 + 13*u**2 + 0 - 1/12*u**4. Factor r(c).
-(c + 1)*(c + 3)/2
Let a be 2 - (-30)/14*420/(-80). Let l = -35/4 - a. Factor 0*n + l*n**2 + 0.
n**2/2
Let q = 46 + -350. Let v = q + 1536/5. Let -v - 12*x + 16/5*x**2 = 0. Calculate x.
-1/4, 4
Suppose 15*i = 2 - 2. Suppose -5*t - 2*t - 2*t = i. Factor t + 4*k**2 + 0 + 2*k**3 - 2*k - 3 - 1.
2*(k - 1)*(k + 1)*(k + 2)
Let g = -391 - 86. Let n = -475 - g. Factor -u**n + 1 - 3/2*u.
-(u + 2)*(2*u - 1)/2
Let m(b) = -29*b**3 - 29*b**2 + 40*b. Let q(g) be the second derivative of 7*g**5/20 + 7*g**4/12 - 5*g**3/3 - 50*g. Let w(h) = 2*m(h) + 9*q(h). Factor w(p).
5*p*(p - 1)*(p + 2)
Solve -4*j**3 + 3*j**3 + 29000*j - 83366 - 130492 + 0*j**3 - 134621*j + 652*j**2 = 0.
-2, 327
Let z(x) = x**4 - x**3 + x**2 - x. Let d(w) = 3*w**3 - 2*w**2 - w. Suppose -17*i - 16 = -33*i. Let n(g) = i*d(g) - z(g). Factor n(p).
-p**2*(p - 3)*(p - 1)
Let k(o) = 13*o**2 + 839*o - 390. Let t be k(-65). Factor i + 1/3*i**2 + t - i**3 - 1/3*i**4.
-i*(i - 1)*(i + 1)*(i + 3)/3
Let s(f) be the third derivative of 112*f**7/15 - 266*f**6/5 + 3361*f**5/30 - 19*f**4 + 4*f**3/3 - 79*f**2. Factor s(p).
2*(p - 2)**2*(28*p - 1)**2
Let w = 10937/1311 - 4/437. Let u(m) be the first derivative of 13 + 15/2*m**2 + 10*m - w*m**3. Factor u(r).
-5*(r - 1)*(5*r + 2)
Let z(k) be the second derivative of 14 - 1/6*k**4 + 1/40*k**5 - 1/12*k**3 + k**2 - k. Factor z(p).
(p - 4)*(p - 1)*(p + 1)/2
Let v(x) = 0*x**4 + 6*x - 3*x**4 + 17*x**2 + 12*x**2 + 20*x**3. Let w(q) = q**3 + 3955*q - 1976*q - 1979*q + q**4. Let c(f) = v(f) - w(f). Factor c(a).
-a*(a - 6)*(a + 1)*(4*a + 1)
Suppose q**5 + 30*q**4 + 217*q + 3483*q**2 + 53 - 162 + 77*q**4 - 3481*q**2 - 218*q**3 = 0. What is q?
-109, -1, 1
Let w be 11*(-27)/(594/(-4)). Let i(t) be the first derivative of 2/7*t**4 + 0*t - 2/7*t**w + 4/21*t**3 + 15. Factor i(m).
4*m*(m + 1)*(2*m - 1)/7
Let h(m) be the second derivative of m**7/21 + 614*m**6/15 + 12484*m**5 + 4117528*m**4/3 - 34458032*m**3/3 + 34967264*m**2 + 8*m - 597. Factor h(i).
2*(i - 2)**2*(i + 206)**3
Suppose -32*n - 2*n + 884 = 0. Factor -32*z**4 + 37*z**4 - n*z**4 + 9*z**2 + 12*z**3.
-3*z**2*(z - 1)*(7*z + 3)
Let r(v) = v**3 - 15*v**2 + 45*v + 28. Let f be r(5). Let d(l) be the third derivative of 0*l + 0 + 5*l**f + 5/24*l**4 - 1/12*l**5 - l**2. Factor d(y).
-5*(y - 3)*(y + 2)
Suppose 226 + 114 = 26*m + 42*m. Let k(w) be the second derivative of -7*w + 0 + 26/3*w**3 - 2/15*w**6 + 7/3*w**4 - 1/5*w**m + 12*w**2. Solve k(s) = 0.
-2, -1, 3
Factor 1/3*j**2 + 1530*j + 1755675.
(j + 2295)**2/3
Suppose -6050/7 + 220/7*j - 2/7*j**2 = 0. What is j?
55
Let r(p) = p**3 - 3*p**2 - 3*p + 6. Let d be r(3). Let c(w) = -22*w + 121. Let f = 346 + -349. Let o(k) = k**2. Let q(s) = d*o(s) + f*c(s). Factor q(j).
-3*(j - 11)**2
Suppose 0 + 2/9*x**3 + 0*x - 68*x**2 = 0. What is x?
0, 306
Let u = 467/150 + -121/75. Let h(p) be the first derivative of u*p**2 + 4*p**3 - 12*p - 10 - 3/4*p**4. Factor h(n).
-3*(n - 4)*(n - 1)*(n + 1)
Let k(a) = -16*a + 287. Let m be k(18). Let i be m*5/(-10)*4. Factor 10/3*b + 1 + 1/3*b**4 + 4*b**i + 2*b**3.
(b + 1)**3*(b + 3)/3
Let s(d) = 31*d**2 + 383*d + 4980. Let a(h) = 7*h**2 + 96*h + 1245. Let r(v) = 18*a(v) - 4*s(v). Factor r(y).
2*(y + 15)*(y + 83)
Suppose 6*g = 11 + 1. Factor -i - 62*i**2 + 64*i**g + 2*i**3 - 3*i**3.
-i*(i - 1)**2
Let z(q) be the second derivative of q**6/5 - 163*q**5/30 + q**4 - 2485*q. Factor z(x).
2*x**2*(x - 18)*(9*x - 1)/3
Suppose -16*z - 120 = -318 + 166. Factor 4 - 1/3*j**z - 1/3*j.
-(j - 3)*(j + 4)/3
Let a(g) be the first derivative of -3*g**4/4 + 22*g**3 + 69*g**2/2 + 974. Let a(c) = 0. What is c?
-1, 0, 23
Suppose 6*p = 45 + 63. Suppose -4*o = -14 - p. Factor 4*g**4 + 18*g**3 + 100*g**2 - 76*g**2 + o*g + 0*g**3.
2*g*(g + 2)**2*(2*g + 1)
Let i be 154/385 + 19*(-4)/192. Let d(j) be the third derivative of -1/48*j**4 + 0 + 0*j - 21*j**2 - i*j**5 - 1/24*j**3. Solve d(q) = 0.
-1
Suppose -148/5*p**2 - 14*p**3 + 224/5*p**4 + 0*p + 0 - 6/5*p**5 = 0. What is p?
-2/3, 0, 1, 37
Suppose 357*g - 558 = 360*g. Let c = g - -186. Factor c - 1/3*s**2 + 0*s.
-s**2/3
Let k(u) be the first derivative of -11/6*u**2 + 2*u - 246 + 1/6*u**4 - 1/3*u**3. Determine h so that k(h) = 0.
-2, 1/2, 3
Let q(l) be the first derivative of -14*l**5/5 + 37*l**4 - 568*l**3/21 + 40*l**2/7 - 5748. Factor q(u).
-2*u*(u - 10)*(7*u - 2)**2/7
Let 920*d - 70*d**2 + 0*d**3 - 78*d**2 + 29445 + 4*d**3 - 28257 + 116*d = 0. Calculate d.
-1, 11, 27
Let y = -277567 + 277569. Factor 0*b - 36/5*b**y + 0 - 34/5*b**3 + 2/5*b**4.
2*b**2*(b - 18)*(b + 1)/5
Let p(w) = w + 1. Let k be p(-12). Let u be (k - -10)*(-1 + 1). Suppose -4*o + 2*o + 10*o**3 - 8*o**3 + 3 - 4*o**2 + o**4 + u*o**4 = 0. Calculate o.
-3, -1, 1
Let k be 9/(-504)*(-70)/30. Let l(i) be the third derivative of -1/6*i**4 + 0 - 1/210*i**7 - k*i**6 - 2/15*i**5 - 7*i**2 + 0*i**3 + 0*i. Factor l(b).
-b*(b + 1)*(b + 2)**2
Let i = -240 + 243. Solve 237*g**2 + 16*g - 76*g**4 + 125*g**i - 172*g**2 - 149*g**2 + 12*g**5 + 7*g**3 = 0.
0, 1/3, 1, 4
Determine y so that 960*y - 136*y + 4*y**3 + 968*y + 148*y**2 + 7056 = 0.
-14, -9
Let q be (((-90465)/333)/163)/(17/(-12) + 1). Suppose -4*b + 0 + 8 = 0. Factor -1/5*g**b + 1/5*g**3 + 1/5*g**q - 1/5*g + 0.
g*(g - 1)*(g + 1)**2/5
Let a(u) be the first derivative of -u**4 - 46*u**3/3 - 5*u**2 + 132*u - 696. Let a(m) = 0. What is m?
-11, -2, 3/2
Suppose 0 = -16*x - 70 - 10. Let g be -6*(x/(-15) + -1). Factor -4/7*y**3 + 4/7*y**g + 20/7*y - 8/7 - 12/7*y**2.
4*(y - 1)**3*(y + 2)/7
Let k(v) be the third derivative of -4/3*v**3 + 0*v + 2/15*v**5 - 1/30*v**6 + 1/6*v**4 + 0 + 43*v**2. Factor k(o).
-4*(o - 2)*(o - 1)*(o + 1)
Let f(o) = -o + 2. Let a be ((-1)/(-3))/(12/(-36)). Let q be f(a). Solve q - 8 + 5 + 3*r**2 = 0.
0
Let g(q) = -2*q**3 + 140*q**2 + 172*q - 2128. Let b be g(71). Solve 0 - 2/7*a**3 + 8/7*a - 6/7*a**b = 0 for a.
-4, 0, 1
Let b(f) be the second derivative of f**5/60 - 7*f**4/4 - 32*f**3/9 + 241*f + 2. Determine p so that b(p) = 0.
-1, 0, 64
Let y = -267528 + 2407762/9. Find h such that -10/9 - 2/9*h**3 + y*h**2 + 2/9*h = 0.
-1, 1, 5
Factor -5/8*h**3 - 1/8*h**4 + 0*h - 1/2*h**2 + 0.
-h**2*(h + 1)*(h + 4)/8
Let y(a) be the second derivative of 247*a**7/210 + 991*a**6/150 + 10*a**5 + a**4/5 - a + 689. Find h, given that y(h) = 0.
-2, -3/247, 0
Let r = -13/415 + 1051/7055. Let b(h) be the first derivative of -12 - 2/51*h**3 + r*h**2 - 2/17*h. Factor b(t).
-2*(t - 1)**2/17
Let c(k) be the first derivative of 1/2*k**3 - 27/2*k + 3/8*k**4 - 2 - 27/4*k**2. Find s, given that c(s) = 0.
-3, -1, 3
Let o(m) = -2*m**2 - 38*m + 616. Let n(v) = -8*v**2 - 140*v + 2464. Let l(d) = 6*n(d) - 26*o(d). Factor l(w).
4*(w - 7)*(w + 44)
Let k(w) be the first derivative of -w**4/18 - 490*w**3/27 + 493*w**2/9 - 494*w/9 + 3733. Factor k(a).
-2*(a - 1)**2*(a + 247)/9
Factor -55/2*x**2 + 20*x + 50 + 5/2*x**3.
5*(x - 10)*(x - 2)*(x + 1)/2
Factor -