3.
u**2*(u + 1)/4
Let a(b) be the second derivative of -b**4/24 - 9*b**3/4 + 76*b. What is z in a(z) = 0?
-27, 0
Let z(b) = -7*b**4 - 19*b**3 - 101*b**2 - 167*b + 288. Let g(y) = -6*y**4 - 19*y**3 - 103*y**2 - 166*y + 289. Let f(p) = 6*g(p) - 5*z(p). Factor f(u).
-(u - 1)*(u + 6)*(u + 7)**2
Let o(l) be the first derivative of -7 - 25/3*l**3 - 10*l - 5/3*l**6 + 7*l**5 + 35/2*l**2 - 25/4*l**4. Let o(i) = 0. Calculate i.
-1, 1/2, 1, 2
Let r(h) = 6*h - 62. Let f be r(11). Factor 120*u**2 + 13*u**4 + 160*u + 19*u**3 + 80 - 8*u**f + 21*u**3.
5*(u + 2)**4
Let u(r) be the third derivative of -28*r**2 + 1/60*r**6 + 0*r + 2/15*r**5 + 2/3*r**3 + 5/12*r**4 + 0. Suppose u(w) = 0. What is w?
-2, -1
Let s = 667 - 667. Let r(o) be the first derivative of 0*o**2 - 4 + s*o**4 + 4/21*o**3 - 2/35*o**5 - 2/7*o. Find d, given that r(d) = 0.
-1, 1
Let c(k) be the second derivative of k**7/105 - k**5/30 + 11*k**2/2 - 6*k. Let o(f) be the first derivative of c(f). What is b in o(b) = 0?
-1, 0, 1
Let s(k) be the first derivative of -2*k**3/33 - 19*k**2/11 - 16*k + 309. Find h, given that s(h) = 0.
-11, -8
Suppose -2*o - 12 - 18 = 0. Let y be 6 + ((-9)/o - 3). Determine h so that y*h**2 + 3/5*h**4 - 12/5*h - 12/5*h**3 + 3/5 = 0.
1
Let h be (-9)/(-63) - 334/(-14). Suppose 3*d - 5*r - h = d, -22 = -d + 5*r. Factor -6/5 - 33/5*a**d + 39/5*a.
-3*(a - 1)*(11*a - 2)/5
Suppose -6/7 - 12*d**2 - 39/7*d**3 - 51/7*d = 0. Calculate d.
-1, -2/13
Factor 21/2*l**3 + 105 - 375*l**2 + 519/2*l.
3*(l - 35)*(l - 1)*(7*l + 2)/2
What is j in 3*j - 4*j**2 - 103 + 111 + j = 0?
-1, 2
Let a(p) be the second derivative of p**7/1260 - p**6/135 + p**5/45 + 2*p**3/3 - 13*p. Let n(o) be the second derivative of a(o). Factor n(i).
2*i*(i - 2)**2/3
Suppose 10 = b - i, 0*i + 20 = 2*b + 2*i. Suppose -13*w + b*w = 0. Find o such that -3/5*o**3 - 3/5*o**2 + 3/5*o**5 + 3/5*o**4 + w*o + 0 = 0.
-1, 0, 1
Let z = 130 - 131. Let i be (1 + z)*(-2 - (-15)/6). Determine x so that -2/3*x**4 + 2/3*x - 2/3*x**3 + i + 2/3*x**2 = 0.
-1, 0, 1
Let f(k) be the third derivative of 11/24*k**4 - 3/5*k**5 + 0*k - 1/6*k**3 + 2/15*k**6 + 0 + 32/105*k**7 - 5*k**2. Factor f(l).
(l + 1)*(4*l - 1)**3
Let v(l) be the third derivative of -l**6/1440 + l**5/240 - 11*l**3/2 - 39*l**2. Let s(c) be the first derivative of v(c). Factor s(g).
-g*(g - 2)/4
Suppose 505 = 2*y + 503. Let n be y/(-2) - (-231)/126. Suppose -n*m - 2/3*m**2 + 0 = 0. What is m?
-2, 0
Suppose -2*j - 34 + 42 = 0. Determine c so that -5*c**5 - 4*c + 44*c**4 - 8*c**2 + 41*c**4 - 81*c**4 + j + c**5 + 8*c**3 = 0.
-1, 1
Let x = -2939 - -8818/3. Suppose 4*r = 8*r. Suppose 0*y + 1/3*y**4 + 2/3*y**3 + r + x*y**2 = 0. Calculate y.
-1, 0
Let z(y) = -5*y - 90. Let x be z(-19). Suppose x*m - 10 = 5. Factor 76/9*f**2 + 16/9 + 88/9*f + 2*f**m.
2*(f + 2)**2*(9*f + 2)/9
Let c(t) = -35*t**3 - 95*t**2 - 100*t - 45. Let w(o) = -o**4 + o**2 + 1. Let m = -145 + 146. Let l(h) = m*c(h) + 5*w(h). Factor l(y).
-5*(y + 1)*(y + 2)**3
Let k(f) be the second derivative of -f**7/42 + 7*f**6/45 - 4*f**5/15 + f**4/18 + f**3/6 - 173*f. Let k(m) = 0. What is m?
-1/3, 0, 1, 3
Let k(l) be the first derivative of l**5/360 - l**3/36 - 4*l**2 + 12. Let i(s) be the second derivative of k(s). Factor i(r).
(r - 1)*(r + 1)/6
Let t(y) = -2*y**3 + 8*y**2 + 6*y + 20. Let q be t(5). Suppose -3*i + 10 = 2*b, 5*b - i + 0*i = 8. Factor -2/9*o**b + q - 2/9*o**3 + 4/9*o.
-2*o*(o - 1)*(o + 2)/9
Determine r so that -7*r**4 + 4*r**5 + 11*r - r**4 - 11*r = 0.
0, 2
Let y(b) be the second derivative of -3*b**5/20 + 13*b**4/12 - 4*b**3/3 - 6*b**2 + 157*b. Factor y(t).
-(t - 3)*(t - 2)*(3*t + 2)
Determine l so that -24*l**3 - 2/5*l**4 - 220*l**2 - 12250 + 4200*l = 0.
-35, 5
Let v(c) be the first derivative of -c**6/8 - 9*c**5/10 - 3*c**4/8 + 5*c**3 + 81*c**2/8 + 15*c/2 - 329. Find y, given that v(y) = 0.
-5, -1, 2
Let w(r) be the third derivative of r**7/840 - r**5/10 + r**4 + 8*r**2. Let b(h) be the second derivative of w(h). Suppose b(a) = 0. What is a?
-2, 2
Let d = -581 + 592. Let r(b) be the second derivative of -d*b + 0 - 5/6*b**3 + 0*b**2 + 5/12*b**4. Factor r(s).
5*s*(s - 1)
Let h(r) be the second derivative of -r**6/780 + r**4/52 - 2*r**3/39 - 7*r**2/2 + 7*r. Let z(a) be the first derivative of h(a). Factor z(f).
-2*(f - 1)**2*(f + 2)/13
Let x(n) be the second derivative of -n**5/170 - 2*n**4/51 + 5*n**3/51 - 26*n. Factor x(d).
-2*d*(d - 1)*(d + 5)/17
Let c = 6773 - 6771. Determine j, given that -4/7*j - 4/7*j**c + 0 = 0.
-1, 0
Let z(m) = 36*m**3 + 172*m**2 - 8*m - 172. Let p(a) = -4*a**3 - 19*a**2 + a + 19. Let f(u) = -28*p(u) - 3*z(u). Factor f(y).
4*(y - 1)*(y + 1)*(y + 4)
Let x(t) be the second derivative of -2/9*t**3 - 7/18*t**4 - 1/63*t**7 - 3/10*t**5 + 0*t**2 - 18*t + 0 - 1/9*t**6. Determine r so that x(r) = 0.
-2, -1, 0
Let a(t) be the first derivative of 8/75*t**3 + 1/25*t**2 - 8/25*t + 23 - 1/50*t**4. Let a(i) = 0. What is i?
-1, 1, 4
What is o in -357/4*o**3 + 4 - 29*o + 76*o**2 + 45*o**4 - 27/4*o**5 = 0?
1/3, 2/3, 1, 4
Suppose 15 = -t - 2*t, -2*t - 19 = 3*o. Let v be (-2)/o*9 + -4. Factor 0*n**v - 3*n**4 - 4*n**3 + 5*n**4 + 2*n**2.
2*n**2*(n - 1)**2
Suppose -w + 2*r = 3*r, -5*w + 5*r + 20 = 0. Let m(p) be the first derivative of -1/10*p**4 - 2/15*p**3 - 1 + 2/5*p + 1/5*p**w. Let m(l) = 0. What is l?
-1, 1
Let u be (-27)/(-15) - (-21)/(-70). Factor 3/2 + u*t**2 - 3*t.
3*(t - 1)**2/2
Let o be (-1)/(7/((-308)/(-180)) + -4). Let y(m) = -2*m**2 - 12*m - 12. Let t(u) = -6*u**2 - 36*u - 37. Let k(w) = o*y(w) + 4*t(w). Factor k(x).
-2*(x + 2)*(x + 4)
Let 112/5*c - 136/15*c**2 - 128/15 - 44/5*c**3 + 6/5*c**4 = 0. Calculate c.
-2, 2/3, 8
Let r(w) be the third derivative of -1/8*w**4 - 3/20*w**6 - 1/5*w**5 + 0*w**3 + w**2 - 2/35*w**7 - 1/112*w**8 + 0*w - 1. Find m such that r(m) = 0.
-1, 0
Factor -1936/5*g**2 - 64/5*g**4 + 2/5*g**5 + 0 + 132*g**3 - 2662/5*g.
2*g*(g - 11)**3*(g + 1)/5
Let r(v) = v**2 - 2*v - 5. Let t be r(4). Suppose 8 = 2*p - 2*b + b, -4*b - 17 = -t*p. Factor p*a + 3/5 + 9/5*a**3 + 21/5*a**2.
3*(a + 1)**2*(3*a + 1)/5
Let v be (36/30)/((-12)/(-1040)). Let r = 109 - v. Solve -2/13*l**2 + 0 - 2/13*l**r + 2/13*l**4 + 2/13*l**3 + 0*l = 0 for l.
-1, 0, 1
Suppose 2*p - 2 = 2. Determine x so that 14*x + 8*x**2 + 8*x + 7*x**p - 5*x**4 - 12*x = 0.
-1, 0, 2
Let k(g) be the first derivative of -g**8/336 - g**7/210 + g**6/60 - 2*g**2 + 19. Let t(m) be the second derivative of k(m). Determine r so that t(r) = 0.
-2, 0, 1
Let p(l) = -2*l**4 + 6*l**3 - 4*l**2 - 6*l + 4. Let t(v) = -4*v**4 + 11*v**3 - 8*v**2 - 11*v + 7. Let n(h) = 5*p(h) - 2*t(h). Factor n(x).
-2*(x - 3)*(x - 1)**2*(x + 1)
Suppose 4*n - 27 = 5*n. Let w = -21 - n. Factor 6*p**2 - w*p + 5*p - 7*p**2.
-p*(p + 1)
Let w(c) be the first derivative of 10 + 23/2*c**2 - 5/3*c**3 + 10*c. Suppose w(j) = 0. Calculate j.
-2/5, 5
Let n(d) be the third derivative of d**6/1260 - d**5/105 + 5*d**4/252 + 49*d**2. Factor n(f).
2*f*(f - 5)*(f - 1)/21
Let v be (4/3)/((-2)/6). Let d(k) = 13*k**3 + 19*k**2 - 13*k - 19. Let p(h) = -4*h**3 - 6*h**2 + 4*h + 6. Let s(a) = v*d(a) - 14*p(a). Solve s(c) = 0.
-2, -1, 1
Let h(y) be the third derivative of -y**6/80 - 3*y**5/20 + 91*y**2. Factor h(p).
-3*p**2*(p + 6)/2
Let n(i) = i**2 + 58*i + 7. Let a(s) = s**2 - s - 1. Let p(q) = -6*a(q) + n(q). Factor p(d).
-(d - 13)*(5*d + 1)
Let m(b) be the first derivative of -b**4/2 + 150*b**3 - 16875*b**2 + 843750*b + 245. What is g in m(g) = 0?
75
Suppose -4*d - 3*f = 9, 218*f = 215*f - 9. Factor d*n**2 - 2/5*n**4 - 4/5*n**3 + 0 + 0*n.
-2*n**3*(n + 2)/5
Let 11*a**4 - 11*a**2 + 6*a**3 + 0 + 5/2*a - 17/2*a**5 = 0. What is a?
-1, 0, 5/17, 1
Let z = 11 + -3. Suppose -2*n - z = 3*r - 4*n, -3*n = 2*r - 12. Factor 2*b**4 - 2*b**2 + 5*b**5 + r*b**2 - 3*b**5 - 2*b**3.
2*b**2*(b - 1)*(b + 1)**2
Suppose 18*p - 33*p = -30. Solve -8/3*v**p - 16/3 - 12*v = 0 for v.
-4, -1/2
Let a(n) be the third derivative of -n**7/3360 - n**6/96 - 5*n**5/32 + 3*n**4/8 - 4*n**2. Let p(m) be the second derivative of a(m). Factor p(b).
-3*(b + 5)**2/4
Let z(a) be the third derivative of a**5/300 - 19*a**4/120 + 3*a**3/5 + 2*a**2 + 27. Factor z(q).
(q - 18)*(q - 1)/5
Let x(n) be the first derivative of n**8/2352 - 2*n**7/735 + n**6/168 - n**5/210 + 19*n**2/2 - 24. Let k(u) be the second derivative of x(u). Factor k(r).
r