hird derivative of 2*k**7/105 + 4*k**6/5 - 47*k**5/3 + 109*k**4 - 384*k**3 + 2*k**2 + 42*k + 32. Factor a(h).
4*(h - 3)**2*(h - 2)*(h + 32)
Find g, given that -17/2*g - 42 - 1/4*g**2 = 0.
-28, -6
Let o(v) be the second derivative of -9/20*v**5 - 7/6*v**3 + 5/4*v**4 + 0*v**2 + 0 - 43*v + 1/30*v**6. Factor o(m).
m*(m - 7)*(m - 1)**2
Suppose -1/8*c**5 - 45/2*c + 49/8*c**3 + 23/2 - 21/8*c**4 + 61/8*c**2 = 0. Calculate c.
-23, -2, 1, 2
Let a be ((-36)/240)/((-42)/9 + 2/12). Let s(r) be the second derivative of 0*r**2 - 27*r + 8/3*r**3 - 2/3*r**4 - a*r**6 - 7/20*r**5 + 0. Factor s(k).
-k*(k - 1)*(k + 4)**2
Suppose -196/5 - 192/5*f**2 - 78*f + 2/5*f**3 = 0. Calculate f.
-1, 98
Suppose 6*b - 10*b = 20, 30 = 3*p + 3*b. Suppose 278*u**3 + 65*u**2 - 10*u - p - 155*u**3 - 163*u**3 = 0. Calculate u.
-3/8, 1
Solve -37/2*p**2 - 1/6*p**4 - 2/3*p + 20/3*p**3 + 74/3 = 0 for p.
-1, 2, 37
Let v(n) be the first derivative of 2*n**6/21 + 68*n**5/35 + 75*n**4/7 - 52*n**3/21 - 544*n**2/7 + 768*n/7 + 1376. Let v(a) = 0. Calculate a.
-8, -3, 1
Suppose 0 = 11*p - 74 + 162. Let q be (-1)/(-3) + 7/168*p. Factor 1/5*y**4 + q - 3/5*y - y**3 + 7/5*y**2.
y*(y - 3)*(y - 1)**2/5
Let b(k) = -34*k**2 + 83*k + 37. Let t(y) = 52*y**2 - 124*y - 56. Let o = 51 - 56. Let v(q) = o*t(q) - 8*b(q). Factor v(i).
4*(i - 4)*(3*i + 1)
Let w be ((-5580)/(-217) - (4 + -2)) + (-28)/2. Solve -4/7*s**4 - w*s**3 - 180/7*s**2 - 172/7*s - 8 = 0.
-14, -1
Let n be (-14)/(-12)*32*55/770. Suppose 34/3*v**4 - n + 32/3*v**3 + 8/3*v**5 - 40/3*v - 26/3*v**2 = 0. Calculate v.
-2, -1, -1/4, 1
Suppose 15*b = 4*v + 6, 51 - 65 = 5*b - 4*v. Factor -1/3*r**3 - 25/3*r**b - 9 + 53/3*r.
-(r - 1)**2*(r + 27)/3
Let n(i) be the first derivative of -5*i**6/6 + 4*i**5 + 365*i**4/4 + 280*i**3/3 - 330*i**2 - 3473. Suppose n(o) = 0. What is o?
-6, -2, 0, 1, 11
Let j = -740 - -732. Let o be 0/(-12 - j) + (-36)/(-26). Suppose 0 - o*g**2 - 4/13*g = 0. What is g?
-2/9, 0
Let c(r) = -4*r**3 + 5*r**2 + 291*r + 470. Let a(w) = 20*w**3 - 28*w**2 - 1456*w - 2352. Let k(l) = 5*a(l) + 24*c(l). What is i in k(i) = 0?
-5, -2, 12
Let z = 211089/8 + -26386. Find q such that 0 - 9/8*q**2 + 0*q - 9/8*q**3 + 1/8*q**4 + z*q**5 = 0.
-3, -1, 0, 3
Suppose m + 6 = 4*m. Let q be (m/4)/((-4)/(-224)). Factor -28*x**2 + x + 7*x + 8 - q*x.
-4*(x + 1)*(7*x - 2)
Let w(s) be the third derivative of -3 + 7/108*s**4 + 1/540*s**6 + 1/54*s**5 + 0*s + s**2 + 1/9*s**3. Factor w(b).
2*(b + 1)**2*(b + 3)/9
Let t(x) = -5*x**3 - 13*x**2 - 43*x - 32. Let a(s) = 44*s**3 - 1108 + 735 + 386*s + 661 + 118*s**2. Let g(w) = 6*a(w) + 52*t(w). Let g(o) = 0. What is o?
-4, -2
Let v = 25366 - 25343. Let h(o) be the second derivative of -1/6*o**5 + v*o + 0 + 1/45*o**6 + 1/3*o**4 + 0*o**2 + 0*o**3. Factor h(w).
2*w**2*(w - 3)*(w - 2)/3
Let b(h) = 18*h**2 - 206*h + 4. Let y be b(32). Let v be y/(-1092) - 11/(-1). Factor -10/13*n**2 + v*n - 2/13*n**3 + 10/13.
-2*(n - 1)*(n + 1)*(n + 5)/13
Let q(w) be the first derivative of 3*w**4/28 + 18*w**3/7 - 2592*w/7 + 3696. Determine i, given that q(i) = 0.
-12, 6
Let z(b) = b**4 + b**2 + b - 1. Let a(l) be the first derivative of -2*l**5/5 + 5*l**4/4 - l**3 - 9*l**2/2 + l + 139. Let k(q) = 4*a(q) + 4*z(q). Factor k(w).
-4*w*(w - 4)*(w - 2)*(w + 1)
Let j = 641893 + -641889. Determine r, given that 0 + 64/3*r**3 + 44/3*r**j - 8*r + 8/3*r**5 + 4/3*r**2 = 0.
-3, -2, -1, 0, 1/2
Let n(p) be the first derivative of p**3/8 + 303*p**2/8 + 30603*p/8 + 8936. Factor n(m).
3*(m + 101)**2/8
Let c(d) be the first derivative of -4*d**5/5 - d**4 + 16*d**3 - 836. Factor c(l).
-4*l**2*(l - 3)*(l + 4)
Let r be ((-272)/(-85))/((-9)/(-15)). Let w(z) be the first derivative of 11*z**2 + r*z**3 + 6*z - 2*z**4 - 6. Find x, given that w(x) = 0.
-1/2, 3
Suppose -3*u = -5*k + 22, -5 = 3*k + 3*u + 1. Factor -88*s**3 - 8*s**k - 81*s**3 + 250*s**3 + 12*s - 82*s**3 + s**4.
s*(s - 2)**2*(s + 3)
Let m(z) be the second derivative of -z**6/75 - 2*z**5/25 + 3*z**4/5 - 4*z**3/3 + 7*z**2/5 - 711*z. Find d such that m(d) = 0.
-7, 1
Suppose -h + 4*t + 5 = -3, -4 = -2*h + 2*t. Suppose -o - o + 4 = h. Suppose -879*p**o + 875*p**2 - 4*p**3 + 4*p**4 + 6*p**5 - 2*p**5 = 0. Calculate p.
-1, 0, 1
Let s(t) = -t**2 - 4. Let w(a) = a**2 + 5 + 19 - 22. Let d(g) = -3*s(g) - 5*w(g). Factor d(l).
-2*(l - 1)*(l + 1)
Find h, given that -90*h**3 - 152*h**3 + 84*h + 198*h**3 + 296*h**2 = 0.
-3/11, 0, 7
Factor -228975*i + 43*i**3 + 226845 + 42*i**3 + 2135*i**2 + 46*i**3 - 136*i**3.
-5*(i - 213)**2*(i - 1)
Let s(o) be the second derivative of o**6/240 + o**5/12 - 13*o**4/16 - 30*o**2 - 255*o. Let w(f) be the first derivative of s(f). Suppose w(z) = 0. Calculate z.
-13, 0, 3
Let x(b) be the first derivative of -6750*b**2 - 135000*b - 150*b**3 - 5/4*b**4 + 77. Find g such that x(g) = 0.
-30
Let h(m) be the third derivative of -6/25*m**5 - 66*m**2 - 1/150*m**6 - 8/3*m**3 + 0 + m + 13/10*m**4. Solve h(f) = 0 for f.
-20, 1
Let w(z) = -56*z + 342. Suppose -a + 4*i = 6, -3*a - i = -4*a + 3. Let s be w(a). Solve -s*m - 3/4*m**2 + 0 = 0 for m.
-8, 0
Let c(t) be the first derivative of 3*t**5/5 - 117*t**4/2 + 69*t**3 + 942*t**2 - 2772*t + 4473. Factor c(j).
3*(j - 77)*(j - 2)**2*(j + 3)
Let i be (1 + -1 - 3)*-1. Let g = -2957 + 2959. Factor -3*b**g - 15 + 3*b**2 - i*b**2 - 18*b.
-3*(b + 1)*(b + 5)
Let t(x) be the second derivative of 18/5*x**3 - 27*x + 9/20*x**5 + 0 + 47/20*x**4 + 6/5*x**2. Let t(m) = 0. What is m?
-2, -1, -2/15
Suppose 0 = -1000*i + 997*i. Let h(l) be the second derivative of 1/2*l**3 + i*l**4 + 0*l**2 - 3/20*l**5 - 9*l + 0. Factor h(m).
-3*m*(m - 1)*(m + 1)
Factor 513157*t - 90354 - 137*t**2 - 77*t**2 - 505535*t + 2*t**3.
2*(t - 37)**2*(t - 33)
Let x(b) be the third derivative of 0*b + 31/170*b**5 + 0 + 29791/51*b**3 - 43*b**2 - 961/68*b**4 - 1/1020*b**6. Find z such that x(z) = 0.
31
Suppose 4*k = s + 10, 13*s - 40 = 17*s. Factor 6/7*v**4 - 2/7 + k*v + 12/7*v**2 - 16/7*v**3.
2*(v - 1)**3*(3*v + 1)/7
Factor 306/7*g**2 + 0 + 310/7*g**4 - 614/7*g**3 - 2/7*g**5 + 0*g.
-2*g**2*(g - 153)*(g - 1)**2/7
Suppose 15*r + 95 = 125. Let 432*o**5 - 864*o**5 - 144*o**r - 68*o**3 + 436*o**5 - 80*o = 0. What is o?
-2, -1, 0, 5
Let g(k) = 4*k**3 + 17*k**2 - 3*k - 3. Let o(w) = 13 + 6*w**3 + 13 - 4*w - 41 + 18*w**2 + 11. Let u(z) = -4*g(z) + 3*o(z). Factor u(i).
2*i**2*(i - 7)
Suppose 5*x = -1 + 26, 3*x = 2*h + 11. Suppose 38*i**4 - 4*i**3 - 36*i**4 + 10*i**3 + h*i + 6*i**2 = 0. Calculate i.
-1, 0
Let r(x) be the third derivative of x**6/240 + x**5/80 - 97*x**3/6 - x**2 - 7*x. Let z(o) be the first derivative of r(o). Let z(a) = 0. What is a?
-1, 0
What is z in -2/21*z**2 - 134456/3 + 392/3*z = 0?
686
Let y = -1/2103 - -14725/8412. Find o, given that -3 - y*o - 1/4*o**2 = 0.
-4, -3
Let t = 574/185 - -48/37. Factor 1/5*c**3 + t - 31/5*c + 8/5*c**2.
(c - 2)*(c - 1)*(c + 11)/5
Let o be 200/450*(308/16 - -4). Factor -5/3*f**3 - o*f + 5/3 + 31/3*f**2.
-(f - 5)*(f - 1)*(5*f - 1)/3
Let c(o) = -17*o**2 - 24*o + 13. Let r(z) = 14*z**2 + 22*z - 8. Let y(a) = -4*c(a) - 5*r(a). Factor y(v).
-2*(v + 1)*(v + 6)
Determine t, given that -75*t**3 - 157*t**2 + 81*t**3 + 21 - 53*t + 351*t**2 - t**5 - 160*t**2 - 7*t**4 = 0.
-7, -3, 1
Let d = -338 + 343. Let l(t) = 11*t - 55. Let f be l(d). Factor -2/7*a**2 + 2/7*a**4 + 2/7*a**3 - 2/7*a + f.
2*a*(a - 1)*(a + 1)**2/7
Let d be -2 - ((-18)/4 - (-9 + 7)). Let u(a) = -a**3 - 51*a**2 + 40*a - 624. Let i be u(-52). Factor -1/2*x**5 - d*x**3 + 0 + 0*x - x**4 + i*x**2.
-x**3*(x + 1)**2/2
Let k(b) = 2*b**4 - 28*b**3 + 124*b**2 + 126*b - 550. Let g(p) = -p**3 - p**2 + 1. Let i(o) = -10*g(o) - k(o). Factor i(h).
-2*(h - 15)*(h - 3)**2*(h + 2)
Factor -235*t + 19*t - 102*t**2 - 149*t - 67*t + 2*t**3 - 440.
2*(t - 55)*(t + 2)**2
Let l(j) be the third derivative of -j**4/8 - 5*j**3/3 - 14*j**2. Let c be l(-4). Factor -2 + 1 + 0 + c*b - b**2 - 4*b.
-(b + 1)**2
Let 28*i**2 + 13/2*i**3 + 1/2*i**4 + 46*i + 24 = 0. What is i?
-6, -4, -2, -1
Let n = -28867 - -144963/5. Let g = -1804/15 + n. Factor 2/9*f**5 + 20/9*f**4 + g + 26/3*f**3 + 148/9*f**2 + 136/9*f.
2*(f + 1)*(f + 2)**3*(f + 3)/9
Factor 0 + 4/7*m**2 - 156/7*m.
4*m*(m - 39)/7
Let q(v) = -9*v**2 - 38*v - 83. Let c(a) = -7*a**2 - 40*a - 77. Let r(t) = -3*c(t) + 2*q(t). Factor r(o).
(o + 13)*(3*o + 5)
What is i in -2*i**3 + 6049 - 31137 - 246