rivative of -i**8/672 - i**7/105 + i**2 - 3*i. Factor g(t).
-t**4*(t + 4)/2
Let p be -2 + (1 - (-3 - 3)). Factor -p*b**2 - 413*b**5 - 3*b**2 + 2*b**2 + 2 - b + 410*b**5 + 4*b**4 + 4*b**3.
-(b - 1)**3*(b + 1)*(3*b + 2)
Let c be -3*(-5)/(-9)*(-31 + 1). Let o be 1/5 + (-85)/c - -2. Factor 0*r - r**3 - o*r**4 + 0 - 1/2*r**2.
-r**2*(r + 1)**2/2
Determine c, given that 4*c**2 - 2785 + 1267 + 867 - 2713 - 8*c**2 + 232*c = 0.
29
Let r(n) be the first derivative of -2*n**5/55 + 17*n**4/22 - 42*n**3/11 - 81*n**2/11 - 87. Find i, given that r(i) = 0.
-1, 0, 9
Let o = 268 + -2411/9. Let v(r) be the second derivative of 0*r**2 - 4/45*r**6 + 1/5*r**5 + 1/63*r**7 + o*r**3 + r + 0 - 2/9*r**4. Suppose v(z) = 0. What is z?
0, 1
Find l such that 16*l**2 + 0*l**2 + 14*l**2 + l**4 - 22*l**3 + 4*l + 19 - 62*l + 30*l**2 = 0.
1, 19
Let c(t) = -t**5 + 3*t**4 + 6*t**3 - 5*t**2 - 6*t - 1. Let s(l) = -2*l**4 - l**3 - 1. Let m(r) = -3*c(r) + 3*s(r). Factor m(x).
3*x*(x - 6)*(x - 1)*(x + 1)**2
Let n be 2/((-2)/(-3)) + -341. Let y be 6*(-4)/(-6) + n/91. Factor 2/7*o + 0 - y*o**2.
-2*o*(o - 1)/7
Let -75/4 - 7*q - 1/4*q**2 = 0. Calculate q.
-25, -3
Let l be 5*(-10)/(-125) - 2/5. Let q(p) be the third derivative of 1/60*p**6 + 0 + 3*p**2 + 0*p + 0*p**4 - 1/30*p**5 + l*p**3. Factor q(z).
2*z**2*(z - 1)
Factor -1/2*v**3 + 0 + 0*v**2 + 2*v.
-v*(v - 2)*(v + 2)/2
Let q(w) = w**3 - 8*w**2 + 54*w + 47*w + 4 - 110*w. Let k be q(9). Factor 2/5*p**k - 8/5 - 8/5*p**3 + 6/5*p**2 + 8/5*p.
2*(p - 2)**2*(p - 1)*(p + 1)/5
Let y(c) be the first derivative of 2*c**5/25 + 7*c**4/10 + 12*c**3/5 + 4*c**2 + 16*c/5 + 59. Factor y(s).
2*(s + 1)*(s + 2)**3/5
Factor 8/3*h**2 - 2*h + 4/9*h**3 + 0 - 2/9*h**5 - 8/9*h**4.
-2*h*(h - 1)**2*(h + 3)**2/9
Suppose 2*l - j - 5 = 0, -2*j + 2 = -4. Let i be -3*(l/16 - 1). Suppose 9/4*y + 3/4 + 3/4*y**3 + i*y**2 = 0. Calculate y.
-1
Let g(u) = -2*u**2 - 13*u + 6. Let h be g(-6). Let l(q) be the first derivative of 0*q + 5/6*q**6 + h + 0*q**2 - 5/4*q**4 + q**5 - 5/3*q**3. Factor l(t).
5*t**2*(t - 1)*(t + 1)**2
Let n(a) = -a**3 + 7*a**2 - 172*a + 1000. Let r be n(6). Factor 2/13*m**2 + 18/13*m**r + 0 - 12/13*m**3 + 0*m.
2*m**2*(3*m - 1)**2/13
Let q be (1/3 + 1)*3. Suppose 3*j + 14 = q*s, 5*s = -0*j - 2*j + 6. Determine p so that 0*p**2 - 11*p**3 + p**4 + 7*p**3 + 4*p**s = 0.
0, 2
Let p(g) be the third derivative of g**7/11340 + g**6/1620 - g**5/180 + 3*g**4/8 - 6*g**2. Let a(v) be the second derivative of p(v). Factor a(f).
2*(f - 1)*(f + 3)/9
Suppose 52 + 28 = -4*l. Let n be (1 + 14/l)/(4/90). Factor 21/4*b**3 + 0 - n*b**2 + 3/2*b.
3*b*(b - 1)*(7*b - 2)/4
Let a be (84/(-21))/(4/(-2)). Factor -9*c**2 - 2*c**2 + 8*c + 7*c**a.
-4*c*(c - 2)
Let n(s) be the first derivative of -3*s**5/35 - 3*s**4/14 + s**3 - 6*s**2/7 - 446. Solve n(q) = 0 for q.
-4, 0, 1
Factor 1/5*i**4 + 8/5*i**3 + 6/5*i**2 - 8*i + 5.
(i - 1)**2*(i + 5)**2/5
Let a = 382 + -376. Let v(t) be the third derivative of 1/945*t**7 + 1/540*t**a + 0*t**3 + 0 + 0*t + 5*t**2 + 0*t**4 - 1/135*t**5. Factor v(q).
2*q**2*(q - 1)*(q + 2)/9
Let n(t) = -4*t**4 - 4*t**3 + t - 5. Let m(g) = -3*g**4 - 3*g**3 + g**2 + g - 4. Let y(s) = 6*m(s) - 4*n(s). Suppose y(f) = 0. What is f?
-2, -1, 1
Let k = -118 + 109. Let r(y) = y**3 + 8*y**2 - 10*y - 7. Let s be r(k). What is g in -3/2*g**s - 1/2 + 6*g**4 - 9/4*g + 9/4*g**5 + 4*g**3 = 0?
-1, -1/3, 2/3
Factor 3*p**4 - 36*p + 30*p**2 + 12 + 9*p**2 + 2351*p**3 - 2369*p**3.
3*(p - 2)**2*(p - 1)**2
Let l(n) be the third derivative of -n**8/336 + n**7/210 + 11*n**6/120 - 29*n**5/60 + 13*n**4/12 - 4*n**3/3 + 165*n**2. Factor l(t).
-(t - 2)*(t - 1)**3*(t + 4)
Suppose -10 = -3*p + 5*u, 2*u - 7 - 15 = -4*p. Suppose t + 3 = -x + 2*x, -p*t - 7 = -x. Find k such that 4/5*k**x + 0 + 16/5*k = 0.
-4, 0
Let d(a) be the first derivative of -3/28*a**4 - 3*a + 39/14*a**2 + 2 - 5/7*a**3. Factor d(k).
-3*(k - 1)**2*(k + 7)/7
Let r(s) be the second derivative of 0 - 21*s - 2/5*s**2 + 1/3*s**3 - 1/15*s**4. Let r(w) = 0. What is w?
1/2, 2
Let -23*s**3 + 0*s + 13080*s**2 - 20*s**4 - 2*s**5 - 41*s**3 - 13144*s**2 + 0*s = 0. Calculate s.
-4, -2, 0
Factor 2955 - 1476 + 11*h**2 - 1479 - h**3.
-h**2*(h - 11)
Let t be 1/(-4) - (-9)/4. Let c(r) = 71*r - 706. Let a be c(10). Factor -18*z**2 + 5*z**3 - 7*z + 2*z**3 - 5*z**a + 21*z**2 + t.
-(z - 1)**2*(z + 1)*(5*z - 2)
Let m be 3/1 + -10*(-255)/(-924). Let w = 1/22 + m. Find y such that 4/7*y - 2/7 - w*y**2 = 0.
1
Let h(x) be the third derivative of x**7/168 - x**6/24 + 5*x**4/6 - 8*x**3/3 - 3*x**2. Let p(w) be the first derivative of h(w). Let p(v) = 0. What is v?
-1, 2
Let f(p) be the second derivative of -p**5/20 + 5*p**4/12 - p**3 + 3*p**2/2 - p. Let x be f(3). Factor 0*d**x - 2*d - 3*d**4 + 2*d**3 - 7*d**2 - 10*d**3.
-d*(d + 1)**2*(3*d + 2)
Solve 62*h**3 + 53*h**3 + 8*h + 8*h**2 - 121*h**3 = 0 for h.
-2/3, 0, 2
Suppose -37*p - 27 = -46*p. Let s(v) be the third derivative of 1/24*v**4 - 1/8*v**p + v**2 + 0 + 0*v - 1/240*v**5. Solve s(g) = 0.
1, 3
Suppose 64 = 5*g - 61. Let r = 25 - g. Factor -5*i**3 + 4*i + i**3 + r*i.
-4*i*(i - 1)*(i + 1)
Let t(n) be the second derivative of -n**8/3360 - n**7/280 - n**6/60 - n**5/30 + 5*n**3 + 46*n. Let b(g) be the second derivative of t(g). Factor b(w).
-w*(w + 2)**3/2
Solve -18/13*y**4 - 2/13*y**2 - 24/13 + 112/13*y - 68/13*y**3 = 0 for y.
-3, -2, 2/9, 1
Let x(t) = t**3 + 2 - 5*t**2 - 11*t + 8*t**2 + 2*t + 5. Let q be x(-5). Suppose 0*u + 0 - 3/2*u**4 + u**3 + 1/2*u**5 + 0*u**q = 0. What is u?
0, 1, 2
Factor -18*k + 50*k - 4214 + 4278 - k**4 - 8*k**3 - 12*k**2.
-(k - 2)*(k + 2)*(k + 4)**2
Let z(d) be the third derivative of -d**6/360 - d**5/120 - 2*d**3 - 15*d**2 - 3. Let s(n) be the first derivative of z(n). Factor s(f).
-f*(f + 1)
Let u(z) be the first derivative of -z**3 - 51*z**2/2 - 90*z - 227. Factor u(m).
-3*(m + 2)*(m + 15)
Let o(m) = -m**4 - 4*m**2 + m + 1. Let x(g) = -8*g**4 - 40*g**3 - 148*g**2 - 156*g - 60. Let w(b) = 4*o(b) - x(b). Factor w(q).
4*(q + 1)**2*(q + 4)**2
Let k(h) be the second derivative of -h**7/42 + h**6/15 + 27*h**5/20 + 13*h**4/3 + 14*h**3/3 + 3*h - 24. Factor k(r).
-r*(r - 7)*(r + 1)*(r + 2)**2
Let c = 76 - 60. Factor -5*d + c - d + 3*d**2 - 16.
3*d*(d - 2)
Factor -358*m + 8*m**3 + 216 + 62*m**2 - 10*m**3 + 134*m.
-2*(m - 27)*(m - 2)**2
Let a = -14149/2 + 6889. Let d = 187 + a. Suppose -d*x**2 - 3/2*x**3 + 3/2*x**5 + 3/2*x**4 + 0 + 0*x = 0. What is x?
-1, 0, 1
Solve 2*w**2 + 1/3*w**4 + 4/3*w**3 + 4/3*w + 1/3 = 0 for w.
-1
Solve -272 + 520*t - 133 + 5*t**2 - 120 = 0.
-105, 1
Let h(q) be the third derivative of q**6/90 - q**5/30 - 25*q**3/6 + 2*q**2 + 14. Let y(s) be the first derivative of h(s). Solve y(t) = 0 for t.
0, 1
Let x be ((-3)/6)/(3/(-18)). Suppose p - b = -x*p - 4, -p = -3*b + 12. Find v, given that 7*v - 4*v - 3*v**2 + p*v + 2 + 4 = 0.
-1, 2
Let m = 247/17 + -6491/476. Let d = -3/4 + m. Suppose d*v**2 + 0 + 1/7*v = 0. What is v?
-1, 0
Solve 336*z**2 - 259*z - 419*z - 302*z - 44*z**3 + 2*z**4 + 686 = 0.
1, 7
Suppose x = i - 1, -5*x = i - 2*x - 9. Let t(q) be the third derivative of 1/32*q**4 - 1/4*q**i - 8*q**2 + 0*q + 0 + 1/80*q**5. Factor t(g).
3*(g - 1)*(g + 2)/4
Let p = -1/3164 + 44099/2373. Let c = p - 52/3. Factor 7/4*j - 1/2 - c*j**2.
-(j - 1)*(5*j - 2)/4
Let k(y) = -267*y - 1863. Let s be k(-7). Determine g, given that 6/5 - 8/5*g**3 - s*g**2 - 16/5*g = 0.
-3, -1, 1/4
Let s = -35 + 31. Let w(j) = j**3 + 4*j**2 + 3. Let p be w(s). Factor p*c**2 - 2*c**2 - 5*c**2 + 8*c - 4.
-4*(c - 1)**2
Let w(n) be the first derivative of n**4 + 8*n**3/3 - 30*n**2 + 158. Determine z, given that w(z) = 0.
-5, 0, 3
Suppose 11*a - 1682 + 1660 = 0. Factor 1/3*c**3 + 2/3*c**a + 1/3*c + 0.
c*(c + 1)**2/3
Let k(i) be the first derivative of -i**3 - 21*i**2/2 - 18*i + 322. Factor k(w).
-3*(w + 1)*(w + 6)
Suppose l = -4*u + 3, -2*u + u = 5*l + 23. Factor 71*r + 3*r**2 - 2*r**3 - 165*r + 78*r - 13*r**u - 8.
-2*(r + 1)*(r + 2)**2
Let o(a) be the second derivative of 0 - 1/20*a**5 - a**2 + a**3 - 4*a - 1/8*a**4. Let x(m) be the first derivative of o(m). Determine f, given that x(f) = 0.
-2, 1
Let r(l) be the second derivative of -1/48*l**4 + 0 - 5*l + 1/12*l**3 + 0*l**2. Factor r(m).
-m*(m - 2)/4
Factor 8*q**3 + q + 0*q - 7*q**2 + 1498*q**4 - 1482*q**4.
q*(q + 1)*(4*q - 1)**2
Let n(t) be the first deriv