 + 1/60*o**5 + 31*o**2 - g*o**4. Factor v(y).
(y - 3)*(y - 2)
Suppose -25817*a = -25827*a. Let w(g) be the second derivative of a - 1/50*g**5 - 3*g + 1/5*g**2 + 1/15*g**3 - 1/30*g**4. Factor w(q).
-2*(q - 1)*(q + 1)**2/5
Let v(k) be the second derivative of -1/90*k**6 + 4 + 2/3*k**3 + 1/9*k**4 - 2*k - 1/20*k**5 + 0*k**2. Factor v(i).
-i*(i - 2)*(i + 2)*(i + 3)/3
Let h be (-4)/(-5) - 243/330. Let i = h - -79/55. Factor -3/2 + 1/4*t**3 + 11/4*t - i*t**2.
(t - 3)*(t - 2)*(t - 1)/4
Determine k so that 343*k + 4*k**2 - 763 + 86 + 301*k + 29 = 0.
-162, 1
Let m(f) = -6*f**4 + 199*f**3 - 1063*f**2 - 10671*f + 1813. Let q(v) = 6*v**4 - 199*v**3 + 1062*v**2 + 10668*v - 1811. Let o(k) = 3*m(k) + 4*q(k). Factor o(a).
(a - 19)**2*(a + 5)*(6*a - 1)
Let s(y) = -y**3 + 6*y**2 + 21*y + 94. Let g be s(14). Let a be 5/(-4) - 1829/g. Factor 3/10*w**2 - 1/10*w**3 + 1/10 - a*w.
-(w - 1)**3/10
Let n = 510 + -507. Factor -12*v**2 - 33*v - 9*v + 3*v**3 - n*v**2.
3*v*(v - 7)*(v + 2)
Let d(v) be the first derivative of 16*v**3/5 - 36*v**2/5 + 27*v/5 + 2594. Factor d(h).
3*(4*h - 3)**2/5
Let b(r) be the third derivative of 0*r + 0 - 7/16*r**4 - 9/80*r**6 + 0*r**3 - 1/140*r**7 + 51*r**2 - 3/8*r**5. Factor b(l).
-3*l*(l + 1)**2*(l + 7)/2
Let q = -9713 - -9715. Let z(f) be the first derivative of 1/2*f**q + 0*f - 37 + 7/9*f**3 - 1/5*f**5 - 7/12*f**4. Factor z(s).
-s*(s - 1)*(s + 3)*(3*s + 1)/3
Suppose 0 = 12*a + 24 - 60. Let o(k) be the second derivative of -28*k + 160*k**2 + 0 + 40/3*k**a + 5/12*k**4. Solve o(n) = 0 for n.
-8
Solve -137869*k + 363605*k**2 + 731*k**4 - 706*k**4 + 7775*k**3 - 15025*k - 1735*k**3 + 6484*k = 0.
-121, 0, 2/5
Let z(n) be the second derivative of -3/2*n**2 + 5/36*n**4 + 0 + 1/40*n**5 - 17/12*n**3 + 55*n. Factor z(f).
(f - 3)*(f + 6)*(3*f + 1)/6
Let f(o) = -798*o - 17554. Let s be f(-22). Factor -9*n**s - 4 - 14*n + 27/2*n**3 + 27/2*n**4.
(n - 1)*(3*n + 2)**3/2
Suppose -3*f = -h + 34, 0 = -3*f - 3*h - 23 - 7. Let n be (-44)/66 + f/(-3). What is z in 0*z**3 + 4*z - 2*z**5 + 10*z**2 + 2*z**n - 2*z**4 + 4*z**3 = 0?
-1, 0, 2
Suppose 0 = -w + 5*h + 22, -4*w = 22*h - 25*h - 71. Let f(d) be the second derivative of 10*d**2 + w*d + 0 - 5/12*d**4 + 0*d**3. Suppose f(g) = 0. Calculate g.
-2, 2
Find a, given that 9*a**2 + 1/5*a**5 + 108/5*a - 57/5*a**3 + 0 + 7/5*a**4 = 0.
-12, -1, 0, 3
Let f(l) be the second derivative of l**5/130 - 14*l**4/39 - 59*l**3/39 - 30*l**2/13 + 9*l - 4. Let f(k) = 0. What is k?
-1, 30
Let s(y) be the second derivative of y**7/168 + y**6/30 - 13*y**5/80 - 7*y**4/12 + 5*y**3/2 - 17*y + 10. Factor s(g).
g*(g - 2)**2*(g + 3)*(g + 5)/4
Let k(a) = -a + 36. Let w be k(9). Suppose -20*l**2 + 10*l**2 - 2*l**2 + w*l**2 + 6*l**3 + 6*l = 0. What is l?
-2, -1/2, 0
Factor -404/7 - 18/7*k**2 + 1822/7*k.
-2*(k - 101)*(9*k - 2)/7
Let b(x) be the third derivative of -29/330*x**5 + 1/66*x**4 + 2*x**2 + 105 + 0*x + 0*x**3. Factor b(u).
-2*u*(29*u - 2)/11
Let r(a) be the third derivative of -a**5/150 + 368*a**4/5 - 1625088*a**3/5 + 7804*a**2. Let r(k) = 0. What is k?
2208
Let x(c) = -c**3 + 8*c**2 - 5*c - 8. Let t(p) = 5*p**3 - 25*p**2 + 15*p + 25. Let j = 263 - 253. Let h(u) = j*x(u) + 3*t(u). Factor h(n).
5*(n - 1)*(n + 1)**2
Let q(n) be the third derivative of n**5/60 - n**3/3 - 34*n**2. Let z(t) = 30*t**2 + 240*t - 295. Let m(l) = -25*q(l) + z(l). Factor m(d).
5*(d - 1)*(d + 49)
Let i be (-1)/2 + (-8275)/10. Let u = i - -2485/3. Factor 20/3*r + 16/3 + 8/3*r**2 + u*r**3.
(r + 2)**2*(r + 4)/3
Let a(w) = w**2 - w + 1. Let t(m) = -2*m**2 - 7*m + 8. Let c(b) = b**3 + 6*b**2 - 30. Let g be c(-5). Let j(u) = g*t(u) - 5*a(u). Solve j(q) = 0.
-9, 1
Suppose -4*t = -3*t - 2. Let q be -19 + 1 + 504/24. Factor 0*j - 4/3*j**q + 16/3*j**t + 0.
-4*j**2*(j - 4)/3
Factor -1/8*m**3 - 831/2*m + 417/4*m**2 + 415.
-(m - 830)*(m - 2)**2/8
Let n(o) = -32*o - 3131. Let k be n(-98). Let r(q) be the third derivative of -1/40*q**k - 1/8*q**3 + 0 + 0*q - 5/64*q**4 - 1/320*q**6 - 13*q**2. Factor r(d).
-3*(d + 1)**2*(d + 2)/8
Let h = -359 + 3581/10. Let l = 143/70 + h. Suppose -4/7 - 12/7*p + 12/7*p**4 + 8/7*p**3 - l*p**2 + 4/7*p**5 = 0. What is p?
-1, 1
Let z(a) = -312*a + 66. Let h be z(-6). Find c, given that 1662 - 22*c - 7*c + 4*c**2 + 269*c + h = 0.
-30
Let s(m) be the third derivative of m**7/1960 + m**6/420 + m**5/280 + 13*m**3/3 + 24*m**2 - 1. Let q(v) be the first derivative of s(v). Factor q(y).
3*y*(y + 1)**2/7
Let n(i) be the first derivative of -i**3/3 - 41*i**2 + 344*i + 1683. Factor n(a).
-(a - 4)*(a + 86)
Let g be 1/(-3) - 20/(-24). Let r = 52185 + -52181. Factor -3/2*z**3 + 0 - 1/2*z**r - g*z - 3/2*z**2.
-z*(z + 1)**3/2
Suppose -3/7*a**2 - 576/7 + 156/7*a = 0. Calculate a.
4, 48
Suppose 1992*y + 2346*y + 1045*y**2 - 1047*y**2 + 198*y = 0. Calculate y.
0, 2268
Let b(n) be the first derivative of 3*n - 58*n**3 - 18*n**2 - 189/5*n**5 + 66 - 69*n**4 - 8*n**6. Determine v so that b(v) = 0.
-1, 1/16
Let i(f) be the first derivative of f**3/3 - 144*f**2 + 20736*f - 1668. Determine z so that i(z) = 0.
144
Let m(p) be the first derivative of -1/2*p**4 - 4/5*p**2 + 1/25*p**5 + 0*p + 17/15*p**3 + 108. Solve m(f) = 0.
0, 1, 8
Let a(o) be the third derivative of 0 + 1/40*o**5 - 7/8*o**4 - 46*o**2 - 15/4*o**3 - o. Suppose a(s) = 0. Calculate s.
-1, 15
Let a = -861 - -868. Find m such that -57*m**2 + 2*m**4 - a*m**2 + 26*m - 26*m**3 + 62*m**2 = 0.
-1, 0, 1, 13
Factor -144*x + 132*x**3 + 4*x**5 - 413*x**4 - 20*x**2 - 56*x + 4 - 4 + 369*x**4.
4*x*(x - 5)**2*(x - 2)*(x + 1)
Suppose 562 = 350*l - 69*l. Let f(h) be the third derivative of 1/20*h**5 + l*h**3 + 0 + 0*h + 1/2*h**4 - 6*h**2. Suppose f(j) = 0. What is j?
-2
Suppose 2850*y - 2840*y = 0. Let u(k) be the third derivative of 0*k**4 + 1/105*k**6 + 0*k**3 + 0*k**5 - 11*k**2 + 0*k + y + 2/735*k**7. Factor u(j).
4*j**3*(j + 2)/7
Let b(o) be the third derivative of o**7/420 - 3*o**6/160 + o**5/20 - o**4/24 - 40*o**2 - 7. Factor b(d).
d*(d - 2)**2*(2*d - 1)/4
Factor -140 - 2/11*l**2 + 318/11*l.
-2*(l - 154)*(l - 5)/11
Suppose 31*m - 225 = -47*m + 3*m. Let z(q) be the second derivative of 0*q**m + 17*q + 0 + 0*q**2 + 1/35*q**6 + 1/35*q**5 - 1/42*q**4. Factor z(u).
2*u**2*(u + 1)*(3*u - 1)/7
Suppose -20*n**2 - 2540*n + 6*n**2 - 908*n - 1272 + 288 = 0. Calculate n.
-246, -2/7
Let t be 114/15 - (-20)/50. Factor -8*g + 4*g - 6*g**2 + 27*g**3 - t*g**3 + 21*g**3.
2*g*(4*g + 1)*(5*g - 2)
Let o(x) be the first derivative of -68 + 14*x**2 - 4/3*x**3 + 32*x. Let o(v) = 0. What is v?
-1, 8
Suppose c - 4*b - 7 = 0, -3*b = c + b - 31. Factor c*m**3 + 24*m + m**3 + 4*m**3 + 4*m**4 + 44*m**2.
4*m*(m + 1)*(m + 2)*(m + 3)
Let n(d) = -48*d - 90. Let c be n(-6). Factor -9 + 9 + c*g**2 - 202*g**2 + 44 + 40*g.
-4*(g - 11)*(g + 1)
Let l(c) be the first derivative of -c**3/7 - 489*c**2/14 + 492*c/7 + 1369. Determine m, given that l(m) = 0.
-164, 1
Let f = 479 - 464. Let k(s) = 2*s**2 - 29*s - 12. Let l be k(f). Solve 8/13*y**2 + 2/13*y**l + 0 + 6/13*y = 0 for y.
-3, -1, 0
Let d(t) be the second derivative of 25/48*t**4 + 5/8*t**3 - 5/2*t**2 - 1/24*t**6 - 60*t + 0 - 3/16*t**5. Suppose d(v) = 0. What is v?
-4, -1, 1
Let z(y) be the first derivative of -65 - 16/19*y - 364/57*y**3 + 68/19*y**2 + 147/38*y**4. Solve z(o) = 0 for o.
2/7, 2/3
Let c(m) be the third derivative of 0 + m**2 - 361/9*m**3 - 1/90*m**5 + 0*m - 19/18*m**4. Determine n so that c(n) = 0.
-19
Let k(b) = 2*b**3 - 6*b**2 + 2. Let z(a) = -65*a**3 - 980*a**2 - 375*a - 50. Let c(v) = -25*k(v) - z(v). Factor c(y).
5*y*(y + 75)*(3*y + 1)
Let x(p) = -12*p**2 + 1578*p - 1040. Let o(y) = -15*y**2 + 1582*y - 1038. Let i(v) = 2*o(v) - 3*x(v). Factor i(w).
2*(w - 261)*(3*w - 2)
Let p(n) be the third derivative of n**8/336 + n**7/140 - n**6/120 - 5137*n**2. Find h, given that p(h) = 0.
-2, 0, 1/2
Let p be (-28)/8*(-1184)/1036. Let l(d) be the first derivative of d**2 + 42 + 7/4*d**p - 3*d**3 + 0*d. Factor l(m).
m*(m - 1)*(7*m - 2)
Let z(b) = -2*b**3 - 1022*b**2 - 1960*b - 994. Let j(o) = -4*o**2 + 5*o. Let a(g) = -6*j(g) + z(g). Determine f, given that a(f) = 0.
-497, -1
Let i(u) = 7*u**3 - 400*u**2 + 23*u + 394. Let n(p) = 2*p**3 + 3*p - 1. Let d(c) = i(c) - 6*n(c). Solve d(a) = 0.
-80, -1, 1
Factor 3*x**2 - 50 - 75 + 4*x + 224 + 38*x.
3*(x + 3)*(x + 11)
Let v(u) = 6*u + 66. Let z be v(-10). Let 