Factor z*r - 3607*r**2 - 26*r + 64*r**3 + 12*r**4 - 32 + 3667*r**2.
4*(r + 1)**2*(r + 4)*(3*r - 2)
Let r = -376925 - -1507707/4. Suppose 0*g - 15 = -5*g. Factor -4*b**2 - 1/4*b**4 + 0 - g*b - r*b**3.
-b*(b + 2)**2*(b + 3)/4
Let b be (42/(-20) - (-25 + 23))/((-46)/345). Determine m so that -3/8*m**2 + 3/8*m + b = 0.
-1, 2
Let t(b) be the third derivative of 0*b + 5/24*b**4 - 2/105*b**7 + 75*b**2 + 1/30*b**5 + 0 - 1/336*b**8 - 1/30*b**6 + 1/3*b**3. Find h, given that t(h) = 0.
-2, -1, 1
Let j(n) be the second derivative of 2*n**7/21 + 124*n**6/15 + 236*n**5/5 + 232*n**4/3 - 1326*n + 2. Determine g, given that j(g) = 0.
-58, -2, 0
Suppose -2*j - y + 179 = 0, 49 = 3*y + 34. Suppose 51 = -12*c + j. Factor -3/4*r**2 - 1/2*r + 0 - 1/4*r**c.
-r*(r + 1)*(r + 2)/4
Let z(t) be the third derivative of -1/315*t**7 + 1/504*t**8 + t**2 + 5/36*t**4 + 0*t - 1/45*t**5 - 1/30*t**6 + 1/3*t**3 + 32. Factor z(c).
2*(c - 3)*(c - 1)*(c + 1)**3/3
Let s(c) be the third derivative of c**5/330 - 21*c**4/44 + 236*c**3/33 + 1209*c**2. Factor s(f).
2*(f - 59)*(f - 4)/11
Suppose 3*f = -4*x - 5, -x - 16 = -3*f + 4. Factor -150 + 135*t**2 + 13 - 86*t**3 + 2*t**4 - 43*t**3 - f*t**4 + 129*t + 5.
-3*(t - 1)**2*(t + 1)*(t + 44)
Let x(y) = 10*y**3 + 76*y**2 - 52*y - 10. Let b(t) = -10*t**3 - 76*t**2 + 54*t + 11. Let c(r) = -10*b(r) - 11*x(r). Factor c(q).
-2*q*(q + 8)*(5*q - 2)
Factor 1/3*y**2 + 39*y - 118/3.
(y - 1)*(y + 118)/3
Let n(v) = v**4 - v**2. Let b(i) = 3*i**5 + 56*i + 72*i**3 - 12*i**2 - 30*i**4 - 8*i - 78*i**2. Let f(a) = b(a) + 6*n(a). Factor f(m).
3*m*(m - 2)**4
Let t(v) be the third derivative of -v**8/168 - 13*v**7/420 + 13*v**6/240 + v**5/30 - 352*v**2. Find i such that t(i) = 0.
-4, -1/4, 0, 1
Suppose -5*u + 205 = 5*w, 5*w = 3*u + 4*w - 127. Suppose -10*c + 3*c + u = 0. Factor 131*p**5 + p**2 - 129*p**5 - c*p**3 - 4*p**2 - p**2.
2*p**2*(p - 2)*(p + 1)**2
Factor 1/3*h + 140/3*h**2 - 1/3*h**3 - 140/3.
-(h - 140)*(h - 1)*(h + 1)/3
Let w(o) be the third derivative of -2/3*o**5 + 0*o + 0*o**3 + 5 - 5/8*o**4 - 1/4*o**6 + 0*o**7 - 2*o**2 + 5/336*o**8. Find p such that w(p) = 0.
-1, 0, 3
Let q(u) be the third derivative of -u**8/336 - u**7/15 - u**6/3 + 12*u**5/5 + 18*u**4 - 144*u**3 + 1483*u**2. Factor q(x).
-(x - 2)**2*(x + 6)**3
Let g = -29 - -9. Let l = g - -29. Factor 10*x**2 + 5*x - 8*x**5 - x**4 - l*x**4 + 3*x**5.
-5*x*(x - 1)*(x + 1)**3
Suppose 4*f + 12 = 5*a + 6*f, -3*a + 32 = -5*f. Factor -3*m**a + 3*m**5 - 18*m**3 - 2*m**5 - 3*m**5 - 4*m - 14*m**2 - 7*m**4.
-2*m*(m + 1)**3*(m + 2)
Factor -3507*w**3 - 120*w - 44*w**2 + 3511*w**3 + 16*w**2.
4*w*(w - 10)*(w + 3)
Let n(i) = -2*i + 21*i - 9*i**2 + 8*i - 43. Suppose 73 = 45*f + 163 + 135. Let w(o) = -5*o**2 + 13*o - 21. Let x(a) = f*w(a) + 3*n(a). Let x(y) = 0. What is y?
2, 6
Let y(z) be the second derivative of -z - 3/20*z**5 - 63/2*z**3 - 29 - 17/4*z**4 + 243/2*z**2. Suppose y(a) = 0. Calculate a.
-9, 1
Let -358845 - 4*m**2 + 72991 - 2792*m - 201350 = 0. Calculate m.
-349
Let i(k) be the third derivative of 2/3*k**3 + 31/12*k**4 + 299/60*k**5 + 0 + 0*k + 169/48*k**6 + 132*k**2. What is x in i(x) = 0?
-2/5, -2/13
Let q(p) be the third derivative of -p**5/60 + 719*p**4/6 - 1033922*p**3/3 + p**2 - 2295*p. Factor q(v).
-(v - 1438)**2
Let y(w) be the first derivative of -5*w**3/3 + 125*w**2/2 + 6271. Factor y(a).
-5*a*(a - 25)
Let j(k) be the second derivative of 1/10*k**5 + k**3 + 29*k + k**2 + 1/2*k**4 + 2. Solve j(s) = 0 for s.
-1
Let c = 66455 + -66455. Factor c*l + 4/3*l**2 - 4/3*l**3 - 1/3*l**4 + 0 + 1/3*l**5.
l**2*(l - 2)*(l - 1)*(l + 2)/3
Let s(m) be the third derivative of -165*m**8/112 + 250*m**7/7 - 197*m**6/24 - 104*m**5/3 - 25*m**4/2 + m**2 - 2245*m. Solve s(g) = 0 for g.
-1/3, -2/11, 0, 2/3, 15
Let f be (3 + -1)/(2/(-36)). Let v = -29 - f. Factor -9 - 4*d**3 + 21*d**2 - v - 5*d**3 + 4.
-3*(d - 2)*(d - 1)*(3*d + 2)
Let w be (-1)/((-2)/(-8)*12/(-156)). Factor 24*m**2 - 28*m**2 + 660*m + 21*m**2 + 564*m + m**3 + w*m**2 + 1156.
(m + 1)*(m + 34)**2
Let q(c) be the first derivative of 0*c**3 + 117 - c**5 + 1/12*c**6 + 0*c + 0*c**2 + 25/8*c**4. Solve q(r) = 0.
0, 5
Let m = -401 + 407. Let f(x) = -x**3 - x**2 - 2*x - 1. Let t(r) = 3*r**3 - 139*r**2 + 84*r + 22. Let z(o) = m*f(o) - t(o). Determine h so that z(h) = 0.
-2/9, 1, 14
Suppose 40*p - 43556 + 43476 = 0. Factor -1/7*y**3 - 44/7*y + 4 + 17/7*y**p.
-(y - 14)*(y - 2)*(y - 1)/7
Let d be (2/(-20))/(((-136)/(-85))/(-4)). Let z be (120/(-96))/((-15)/33). Factor d*h**3 - 25/4 + 35/4*h - z*h**2.
(h - 5)**2*(h - 1)/4
Suppose 84*r - 401 = 187 - 84. Let u(l) be the second derivative of -2*l**2 - 47/12*l**4 + 0 + 3/4*l**5 - 49*l + r*l**3. Factor u(m).
(m - 2)*(m - 1)*(15*m - 2)
Let r(p) be the second derivative of 5*p**4/12 + 1315*p**3/3 - 7935*p**2/2 + 2*p + 898. Factor r(m).
5*(m - 3)*(m + 529)
Let r(w) be the second derivative of -w**6/180 - w**5/60 + 5*w**4/24 + 8*w**3/9 + 4*w**2/3 + 1345*w. Suppose r(u) = 0. What is u?
-4, -1, 4
Suppose -1140*d + 218*d**2 - 221*d**2 - 870*d - 336675 = 0. Calculate d.
-335
Factor -8*m**4 + 10*m**4 - 100*m**3 + 136*m**3 + 112*m + 120*m**2.
2*m*(m + 2)**2*(m + 14)
Let t be (34/(-5) + 7)/((-3)/(-285)). Factor 3 - 4*f**2 + 18*f + 4*f**4 + 30*f**3 + 4*f**5 - t + 14*f - 50*f**3.
4*(f - 1)**3*(f + 2)**2
Let s(q) be the first derivative of -1/12*q**5 + 0*q - 7/48*q**6 + 5*q**2 + 0*q**4 + 0*q**3 + 18. Let r(p) be the second derivative of s(p). Factor r(j).
-5*j**2*(7*j + 2)/2
Let j = -298495 - -298499. Find d such that 40*d**2 - 8/3*d + 0 + 98*d**j - 406/3*d**3 = 0.
0, 2/21, 2/7, 1
Let j(c) be the first derivative of -c**3/15 + 7*c**2/10 + 98*c/5 + 647. Let j(v) = 0. What is v?
-7, 14
Let j(p) = -p**3 + 19*p**2 - 46*p - 29. Let u be j(16). Let r(f) = f**3 - 2*f**2 + 4*f. Let o be r(3). Let 14 - 14 + 8 + o*t + 16 - u*t**2 = 0. Calculate t.
-1, 8
Solve -13*h**4 - h**4 - 146*h**4 - 4190*h**2 - 6060 - 27505*h**2 - 36340*h + 74340*h**3 - 85*h**4 = 0 for h.
-2/7, 1, 303
Let p(u) be the second derivative of -u**7/1008 - u**6/72 - u**5/16 - 43*u**4/6 + 45*u. Let h(q) be the third derivative of p(q). Find w, given that h(w) = 0.
-3, -1
Let v = -288447/86 + 3354. Let m = 20/43 - v. Solve 12*h + 72 + m*h**2 = 0 for h.
-12
Let p(k) = -6*k**2 - 3 - 5*k + 11*k**2 + k**3 - 3*k**3 - 4*k**2. Let v(w) = -3*w**3 + w**2 - 8*w - 4. Let h(t) = -8*p(t) + 5*v(t). What is s in h(s) = 0?
-1, 2
Let z(a) be the first derivative of a**7/168 - 7*a**6/72 + 2*a**5/3 - 5*a**4/2 - a**3/3 + 13*a**2 - 6. Let t(i) be the third derivative of z(i). Factor t(k).
5*(k - 3)*(k - 2)**2
Let s be 9 + (-23 + 29)*(-1)/2. Let g(j) = -4*j**2 + 21*j + 20. Let n be g(s). What is a in 1/3*a**3 + 5/3*a**n + 1 + 7/3*a = 0?
-3, -1
Let u = 6883723/1275 - 5399. Let j = 427/1275 + u. Suppose 0*n - j + 1/3*n**2 = 0. Calculate n.
-1, 1
Let l(s) be the first derivative of 3*s**4/2 + 4*s**3 - 79*s**2/2 - 27. Let o(g) = 3*g**3 + 6*g**2 - 39*g. Let w(f) = -6*l(f) + 11*o(f). Factor w(u).
-3*u*(u - 3)*(u + 5)
Solve -54/7*v**2 + 3/7*v**4 - 9/7*v**3 + 120/7*v + 0 = 0 for v.
-4, 0, 2, 5
Let h(z) = 38*z - 93. Let w be h(3). Factor -87*s**2 + 31*s + 18*s**3 - 19*s + 3*s**4 + 33*s + w*s**3.
3*s*(s - 1)**2*(s + 15)
Suppose 4*l - 672 = 4*a, -l = -a + 6*a - 138. What is w in 166*w**4 + 94*w**2 - 75*w**4 - 68*w**4 - l*w**3 - w**5 - 320*w + 100 + 267*w**2 = 0?
1, 10
Let s(y) be the third derivative of y**6/420 + 59*y**5/210 + 34*y**4/3 + 112*y**3 + 2*y**2 + 162. Let s(i) = 0. What is i?
-28, -3
Let l be 12 - (105/15 + -11). Let n(a) be the first derivative of -1/3*a**3 - a + a**2 - l. Solve n(f) = 0.
1
Let o(g) be the first derivative of 4*g**3/3 + 72*g**2 + 1040*g + 7171. Factor o(w).
4*(w + 10)*(w + 26)
Let h(p) = -p**3 - 12*p**2 + 10*p + 21. Let u be h(-13). Let k be 38/u - -15*(-15)/450. Factor 0 + 2/5*g + k*g**2.
2*g*(g + 3)/15
Let g(u) be the first derivative of -5*u**3/7 - 312*u**2/7 - 369*u/7 - 15690. Factor g(o).
-3*(o + 41)*(5*o + 3)/7
Let c be 39065/4329 + 4 + -13. Let q = c + 514/6327. Factor -8/19 - q*o**2 - 10/19*o.
-2*(o + 1)*(o + 4)/19
Let j be (80/(-6))/((-20)/144). Suppose 13 = 2*r + 5*i, 4*r - 21 = j*i - 101*i. Factor -1/9*b**r - 1/3*b**2 + 0*b - 4/9*b**3 + 0.
-b**2*(b + 1)*(b + 3)/9
Suppose 884 - 37*j**2 - 430*j + 17*j**2 - 458*j + 24*j**2 = 0. What is j?
1, 221
Let c(f) be the second deriva