 - 1/3*j**2.
-(j - 5)*(j + 15)/3
Let y(w) be the first derivative of w**4/10 - w**3 - 88*w**2/5 - 84*w/5 + 781. Factor y(n).
(n - 14)*(n + 6)*(2*n + 1)/5
Let v(m) be the second derivative of -2*m**7/7 + 4*m**6 - 219*m**5/20 - 161*m**4/4 + 77*m**3/2 + 363*m**2/2 - 2055*m. Suppose v(t) = 0. What is t?
-1, 1, 11/2
Let d(r) be the third derivative of r**8/1008 - 2*r**7/315 + r**6/72 - r**5/90 - 4*r**2 - 34*r + 2. Factor d(t).
t**2*(t - 2)*(t - 1)**2/3
Factor -1057 - 47*q**2 + 1732 + q**3 + 290*q - 1075.
(q - 40)*(q - 5)*(q - 2)
Let b(k) be the third derivative of k**5/24 + k**4/12 - k**3/12 - 26*k**2 - 63*k. Factor b(u).
(u + 1)*(5*u - 1)/2
Let y(w) be the first derivative of 5/24*w**3 + 18*w - 1/2*w**2 - 1/48*w**4 + 22. Let x(k) be the first derivative of y(k). What is h in x(h) = 0?
1, 4
Let j(v) be the second derivative of -21*v**5/20 + 57*v**4/2 - 226*v**3 + 180*v**2 + 1431*v. Determine u, given that j(u) = 0.
2/7, 6, 10
Determine k so that -5/2*k**3 + 1260895840 + 5970*k**2 - 4752120*k = 0.
796
Let b(y) be the second derivative of y**7/1050 - y**6/600 - y**5/75 + y**4/30 - 237*y**2/2 + 12*y. Let v(n) be the first derivative of b(n). Factor v(f).
f*(f - 2)*(f - 1)*(f + 2)/5
Let z be 0/((-91 - 19)/(-22)). Factor r**2 + 0 + z*r**3 - 2/3*r - 1/3*r**4.
-r*(r - 1)**2*(r + 2)/3
Let 220/3 - 2/21*a**2 - 134/21*a = 0. Calculate a.
-77, 10
Let l = -104 - -106. Find p, given that -3*p**3 - 215*p + 6*p**l + 208*p - 4*p**4 + 10*p**3 - 2 = 0.
-1, -1/4, 1, 2
Let q(z) = 51*z - 288. Let o be q(6). Let u be -1*5 - (o - 25). Solve 0*a + 0*a**3 - 2/3 - 1/6*a**4 + 5/6*a**u = 0 for a.
-2, -1, 1, 2
Let h be 3 - (8 + (5 - 14)). Let i be 31/h - (-56 - -63). Solve 21/4*o - i*o**2 - 9/2 = 0 for o.
1, 6
Let l(a) be the first derivative of 0*a - 7/18*a**3 + 1/180*a**5 - 12 + 1/12*a**4 + 5/2*a**2. Let d(b) be the second derivative of l(b). Factor d(h).
(h - 1)*(h + 7)/3
Let b(x) be the third derivative of x**8/1008 - x**7/105 - 7*x**6/360 + 23*x**5/45 - 2*x**4 + 32*x**3/9 + 1398*x**2. Let b(i) = 0. What is i?
-4, 1, 4
Find f, given that 585 - 4164*f**3 + 615 + 452*f**4 - 228004*f + 222404*f + 20*f**5 + 8092*f**2 = 0.
-30, 2/5, 1, 5
Let h(r) be the first derivative of 2*r**5/5 - 602*r**4 + 322404*r**3 - 64963604*r**2 + 128962402*r + 3119. Factor h(k).
2*(k - 401)**3*(k - 1)
Let d(f) be the third derivative of 2 + 1/40*f**6 + 0*f**5 + 0*f + 0*f**3 - 1/8*f**4 + 2*f**2. Factor d(o).
3*o*(o - 1)*(o + 1)
Let p = -8545/42 + 4283/21. Factor -5/4*f**2 + 5/4*f**4 + 1/2*f**3 + 0 - p*f.
f*(f - 1)*(f + 1)*(5*f + 2)/4
Let r(d) = 35*d**4 - 112*d**3 + 5*d**2 + 92*d + 4. Let n(f) = -45*f**4 + 115*f**3 - 5*f**2 - 90*f - 5. Let a(t) = 4*n(t) + 5*r(t). Factor a(m).
-5*m*(m - 1)*(m + 1)*(m + 20)
Let k(z) be the first derivative of -1/3*z**3 + 0*z**2 + 19 + 1/8*z**4 + 7*z. Let g(q) be the first derivative of k(q). Find f such that g(f) = 0.
0, 4/3
Suppose 26*p - 43*p + 51 = 0. Solve -2*s**2 + 27*s + 8*s**p - s**2 - s**4 - 15*s**3 - 12*s - 4*s**2 = 0 for s.
-5, -3, 0, 1
Let r(m) be the first derivative of 7*m - 31*m**2 - 16/5*m**5 + 53*m**3 - 22*m**4 + 11. Determine x so that r(x) = 0.
-7, 1/4, 1
Let o = -3534 - -3537. Let m(y) be the second derivative of 0 + 1/15*y**o + 22*y - 1/60*y**4 - 1/10*y**2. Factor m(c).
-(c - 1)**2/5
Factor -1/7*k**2 - 310/7 + 157/7*k.
-(k - 155)*(k - 2)/7
Let u(j) be the first derivative of 1 + 5*j + 0*j**2 + 1/60*j**6 + 1/20*j**5 + 1/24*j**4 + 0*j**3. Let n(c) be the first derivative of u(c). Factor n(z).
z**2*(z + 1)**2/2
Let k = 321/226 - -9/113. Let y(v) be the second derivative of 0 - 2/3*v**3 - k*v**4 + 0*v**2 - 13*v. Factor y(l).
-2*l*(9*l + 2)
Suppose 0 = 5*r + 4*q - 37, 0 = -4*r - q + 13 + 10. Let w(g) be the third derivative of -1/8*g**3 - 7/16*g**4 - 49/80*g**r + 0 + 0*g - 13*g**2. Factor w(o).
-3*(7*o + 1)**2/4
Let z be ((-50)/(-6))/(20/36)*11/110. Factor 1/2*a**4 - 3/2*a**3 - 1 + z*a + 1/2*a**2.
(a - 2)*(a - 1)**2*(a + 1)/2
Suppose 5*q = 3*q + 8. Let i = 182 - 77. Solve -134*y**4 + 22*y**5 - 55*y**2 + i*y**3 + 3*y**5 + 49*y**q + 10*y = 0.
0, 2/5, 1
Let i(d) = -7*d**3 - 21*d**2 - 41*d - 13. Let q(m) = 9*m**3 + 21*m**2 + 45*m + 12. Let j(t) = -3*i(t) - 2*q(t). Factor j(v).
3*(v + 1)**2*(v + 5)
Let k(z) be the second derivative of z**6/195 + z**5/130 - z**4/13 + 356*z. Factor k(d).
2*d**2*(d - 2)*(d + 3)/13
Let l(t) be the third derivative of t - 1/42*t**7 + 0 + 1/12*t**5 - 46*t**2 - 5/12*t**4 + 0*t**3 + 1/12*t**6. Factor l(s).
-5*s*(s - 2)*(s - 1)*(s + 1)
Let x(t) = 322*t + 1936. Let i be x(-6). Find a, given that -49/5 - 20*a**3 + 314/5*a**2 - 112/5*a - 4/5*a**5 - 49/5*a**i = 0.
-7, -1/4, 1
Let h(x) be the third derivative of -79*x**5/20 - 239*x**4/8 - 3*x**3 - 2*x**2 - 63*x + 1. Let h(w) = 0. What is w?
-3, -2/79
Let c(i) be the third derivative of i**7/210 - 11*i**6/30 + 161*i**5/20 + 11*i**4/6 - 242*i**3/3 + 32*i**2 - 6*i. Let c(o) = 0. What is o?
-1, 1, 22
Let b(j) be the second derivative of -56/9*j**3 + 1 - 5*j + 23/3*j**4 + 8/3*j**2 + 10/9*j**6 - 14/3*j**5. Determine n so that b(n) = 0.
2/5, 1
Let w be 10/40 - (5600/128)/(-25). Factor 13/6*k**2 - 1/6*k**3 - w*k + 0.
-k*(k - 12)*(k - 1)/6
Let a(q) be the second derivative of -q**7/84 - 37*q**6/60 - 169*q**5/40 - 295*q**4/24 - 113*q**3/6 - 16*q**2 + 254*q - 3. Let a(n) = 0. What is n?
-32, -2, -1
Suppose -3*i - 4 = -13. Suppose 31 + 94 = i*y - m, 4*m - 20 = -y. Factor -2*z**3 - 28*z**2 + y*z + 6*z**3 - 20 + 4*z.
4*(z - 5)*(z - 1)**2
Let j(s) = 144*s**2 + 220*s + 96. Let f(x) = -13*x**2 - 6*x - 8*x - 9 + x - 7*x. Let g(p) = 32*f(p) + 3*j(p). Let g(v) = 0. Calculate v.
-5/4, 0
Let l = 448147 + -448144. Factor 7/2*v + l - 1/2*v**3 + 0*v**2.
-(v - 3)*(v + 1)*(v + 2)/2
Let v(f) = -13*f**2 + 1201*f + 84500. Let k(a) = -80*a**2 + 7195*a + 507000. Let b(g) = 9*k(g) - 55*v(g). Factor b(r).
-5*(r + 130)**2
Suppose -19*u + 120 - 44 = 0. Let r(n) be the second derivative of 3/50*n**5 + 1/15*n**3 + 0*n**2 + 1/10*n**u + 4*n + 1/75*n**6 + 0. Solve r(j) = 0 for j.
-1, 0
Factor 6*q**4 + 40*q**3 - 3*q**4 + 31*q**2 - 43*q**2 - q**3 - 156*q.
3*q*(q - 2)*(q + 2)*(q + 13)
Determine w so that 0 + 261/4*w**3 - 9/2*w + 15/4*w**2 - 33*w**4 = 0.
-3/11, 0, 1/4, 2
Suppose 32/5*r + 24 + 2/5*r**2 = 0. What is r?
-10, -6
Let f be (-4 - -15) + -6 + -10 - -193. Let v = 755/4 - f. Factor 0*h - 9/4*h**3 + 0 + 3/2*h**2 + 0*h**4 + v*h**5.
3*h**2*(h - 1)**2*(h + 2)/4
Let n(i) = 2*i**5 - 2*i - 4. Let c(p) = 6*p**5 - p**4 - p**3 + p**2 - 5*p - 10. Let f(u) = 4*c(u) - 10*n(u). Factor f(m).
4*m**2*(m - 1)**2*(m + 1)
Let s(k) = k**2 + 0*k + 12*k**2 + k**2 - 15*k**2 + 10*k - 9. Let d(c) = c**2 - 6*c + 5. Let y(q) = -7*d(q) - 3*s(q). Factor y(h).
-4*(h - 2)*(h - 1)
Let k(r) be the third derivative of -r**7/2520 + r**6/144 - 11*r**4 - r**2 - 31. Let d(o) be the second derivative of k(o). What is c in d(c) = 0?
0, 5
Let 0 + 0*a**4 + 0*a + 8/5*a**3 - 2/5*a**5 + 0*a**2 = 0. What is a?
-2, 0, 2
Let o(k) = -89*k**2 - 977*k + 4748. Let u(i) = -1560*i**2 - 16610*i + 80715. Let x(v) = 35*o(v) - 2*u(v). Factor x(q).
5*(q - 190)*(q - 5)
Let k(i) be the third derivative of i**7/840 + 7*i**6/120 - i**4/12 + 3*i**3/2 - 115*i**2. Let p(w) be the second derivative of k(w). Let p(l) = 0. What is l?
-14, 0
Let v be 18/(-15)*(-5)/9. Let x(j) be the third derivative of -10*j**2 - 3/20*j**5 + 0 + 0*j - v*j**3 - 5/6*j**4. Factor x(g).
-(g + 2)*(9*g + 2)
Let h be 26 + (-2 - (-2 + 4)). Let w be 6 + 4*h/(-33). Let -2*o**3 + w*o**2 - 2/3*o**4 - 8/3 + 2*o = 0. What is o?
-4, -1, 1
Let q(y) be the third derivative of y**6/90 + 53*y**5/180 + 13*y**4/9 + 55*y**3/18 - 2*y**2 + 522*y. Factor q(i).
(i + 1)*(i + 11)*(4*i + 5)/3
Find d, given that 290/3*d**2 - 1160/9 + 296/9*d**3 + 2/9*d**4 - 8/9*d = 0.
-145, -2, 1
Let w(f) be the third derivative of -f**6/420 + 11*f**5/105 + 43*f**4/28 + 54*f**3/7 - 2*f**2 + 10*f + 41. Let w(d) = 0. Calculate d.
-3, -2, 27
Let d(i) be the third derivative of -2*i**7/105 - 37*i**6/15 + 77*i**5/15 + 25*i**4 - 402*i**2 + 5*i. Factor d(m).
-4*m*(m - 2)*(m + 1)*(m + 75)
Suppose 14 = -p + 4*f - 0*f, -5*f + 14 = -3*p. Suppose 152 - 10*o - 312 + 245*o**p + 160 = 0. What is o?
0, 2/49
Find y such that -51/4 + 3/2*y**2 + 27/8*y = 0.
-17/4, 2
Let q(k) = k**3 - 49*k**2 + 204*k - 255. Let s(c) = -4*c**3 + 148*c**2 - 612*c + 764. Let y(o) = 8*q(o) + 3*s(o