- 3*t + 3. Let i be m(-3). Factor 2*a + 2*a**i + 0*a**3 - 4*a**2 + w*a**2.
2*a*(a - 1)**2
Let z(a) be the second derivative of 0 - 3*a + 0*a**2 + 1/9*a**4 - 1/18*a**3. Determine d, given that z(d) = 0.
0, 1/4
Solve -1/3*b**5 - 8/3*b + 8/3*b**4 + 22/3*b**2 - 7*b**3 + 0 = 0 for b.
0, 1, 2, 4
Suppose 0 = d + 2*d - 3*j - 12, 4 = -5*d - j. Let q(i) be the third derivative of d*i - 1/180*i**5 + 0 + i**2 + 0*i**3 - 1/36*i**4. Find y, given that q(y) = 0.
-2, 0
Let a be (22/4 + -5)/1. Factor -a - 3*m - 9/2*m**2.
-(3*m + 1)**2/2
Let p(x) be the second derivative of -x**7/42 - x**6/5 - 7*x**5/10 - 4*x**4/3 - 3*x**3/2 - x**2 - 14*x. Let p(y) = 0. Calculate y.
-2, -1
Factor -5*o + 17*o**2 - 4*o + 19*o**2 + 14 - 35*o**2.
(o - 7)*(o - 2)
Let a = 445 - 442. Let r = 8/19 - 13/76. Factor -r*f**a - 1/4*f + 0 + 1/2*f**2.
-f*(f - 1)**2/4
Let d(n) be the third derivative of -n**6/360 + n**5/180 - 7*n**2. Factor d(b).
-b**2*(b - 1)/3
Let h(s) be the third derivative of s**7/35 - s**6/30 - s**5/10 + s**4/6 + 11*s**2. Determine k, given that h(k) = 0.
-1, 0, 2/3, 1
What is q in -9*q**4 - q**5 + 27*q + 66*q**3 + 4*q**5 - 15*q**4 - 72*q**2 = 0?
0, 1, 3
Let a be (0 - 2/(-6))*(29 - 23). Let f(u) be the first derivative of 3 + 1/5*u**a - 2/15*u**3 + 4/5*u. Factor f(y).
-2*(y - 2)*(y + 1)/5
Factor 4 + 4*k**3 - 4*k - k**4 - 5*k**4 + 5*k**4 - 3*k**2.
-(k - 2)**2*(k - 1)*(k + 1)
Let m = -11 - -5. Let v = m - -6. Suppose -2/3*o**3 + 2/3*o + 0 + v*o**2 = 0. What is o?
-1, 0, 1
Let m(z) = z**3 + 11*z**2 + 14*z + 22. Let a be m(-10). Let q be (2/6)/((-4)/a). Let 3/2*y - 3/2*y**3 + q*y**2 - 3/2 = 0. What is y?
-1, 1
Suppose 0*s = -s. Suppose 6 = -s*l + 2*l. Factor -1/4*i**4 - 1/4*i**2 + 1/2*i**l + 0 + 0*i.
-i**2*(i - 1)**2/4
Solve 0 - 2/3*u + 2/9*u**2 = 0 for u.
0, 3
Suppose -13*m + 31 + 8 = 0. Determine l so that 0*l**2 + 8/7*l**m + 0 + 0*l + 2/7*l**5 - 8/7*l**4 = 0.
0, 2
Let i = 4 + -13. Let l(h) = h**3 + 8*h**2 - 8*h + 11. Let w be l(i). Factor -4/7*j**2 + 2*j**3 + 4/7 - w*j.
2*(j - 1)*(j + 1)*(7*j - 2)/7
Let r(o) be the third derivative of -o**6/120 + o**5/15 - o**4/6 + o**3/3 + o**2. Let a(d) be the first derivative of r(d). Determine j so that a(j) = 0.
2/3, 2
Suppose 0 = -g + 3*v - 15, -13*g + 2*v - 10 = -11*g. Factor g - 2/13*z**3 + 0*z - 4/13*z**2 + 2/13*z**4.
2*z**2*(z - 2)*(z + 1)/13
Let n be (-19)/57 - (-110)/6. Let r = n + -16. Factor 0*f + 4/3*f**r - 2/3 + 0*f**3 - 2/3*f**4.
-2*(f - 1)**2*(f + 1)**2/3
Let k(y) = y**2 + 16*y + 60. Let d be k(-11). Determine s so that 0*s**2 + 2*s**d - 8/3*s**4 + 0 + 2/3*s**3 + 0*s = 0.
0, 1/3, 1
Let z(a) be the second derivative of 25*a**7/21 + 2*a**6 - 18*a**5/5 + 4*a**4/3 - 2*a + 10. Factor z(g).
2*g**2*(g + 2)*(5*g - 2)**2
Let n be 14/35*(15/36 - 0). Let b(c) be the second derivative of -1/6*c**4 - 3*c + 0*c**5 + 0*c**2 + 0 + 1/15*c**6 - 1/42*c**7 + n*c**3. Factor b(s).
-s*(s - 1)**3*(s + 1)
Find p such that -4*p**2 + 3*p**3 - 2*p**2 - 3*p - 7*p**2 + 10*p**2 + 3 = 0.
-1, 1
Let c(q) = -q**2 - 3*q - 1. Let i be c(-3). Let h = 7 + i. Factor 3 + h*y**2 + 3*y**3 - 3.
3*y**2*(y + 2)
What is r in 5*r - 5/3*r**2 + 0 = 0?
0, 3
Let x(z) be the third derivative of z**6/40 - 3*z**5/20 + z**4/4 - 4*z**2. Factor x(r).
3*r*(r - 2)*(r - 1)
Let h(y) be the third derivative of y**5/15 - y**4/3 + 2*y**3/3 + 3*y**2. Factor h(d).
4*(d - 1)**2
Factor 6/7*f**2 - 6/7*f**5 - 2*f**4 + 4/7*f - 6/7*f**3 + 0.
-2*f*(f + 1)**3*(3*f - 2)/7
Let w be (-10)/(-12) - (2/6 + 0). Let y(s) be the first derivative of w*s**4 + 3 - 2/3*s**3 + 0*s + 2/5*s**5 - s**2. Factor y(o).
2*o*(o - 1)*(o + 1)**2
Let k(l) be the first derivative of -2*l**5/45 - l**4/9 - 2*l**3/27 - 4. Factor k(j).
-2*j**2*(j + 1)**2/9
Let t = 3/622 - -9913/8086. Solve -68/13*k**2 - 50/13*k**5 - 98/13*k**3 + 40/13*k + t + 160/13*k**4 = 0.
-2/5, 1, 2
Let j = 160/93 + -12/31. Let g(a) be the first derivative of -j*a**3 - 2 + 1/2*a**4 + 0*a + a**2. Suppose g(l) = 0. What is l?
0, 1
Suppose 3*u + 9 = u - 3*l, 3*u - 3*l = 9. Let -4*f**4 + u*f**3 - 2*f + 0*f**3 + 0*f**3 + 6*f**3 = 0. Calculate f.
-1/2, 0, 1
Let g(m) be the first derivative of m**3/15 + 3*m**2/10 - 21. Factor g(t).
t*(t + 3)/5
Let b be (0 - -3)/(-3) - -9. Suppose 1 = 3*n - b. Factor -1/2*u**4 + 0 - 3/2*u**n - 1/2*u - 3/2*u**2.
-u*(u + 1)**3/2
Let 4*t**5 - t**5 + 2*t**3 - t**4 - 4*t**4 = 0. What is t?
0, 2/3, 1
Let u(z) be the first derivative of 0*z + 1/6*z**2 - 1/9*z**3 - 6. Factor u(r).
-r*(r - 1)/3
Let z(u) be the third derivative of u**7/350 - u**6/40 + 2*u**5/25 - u**4/10 - 8*u**2. Factor z(h).
3*h*(h - 2)**2*(h - 1)/5
Let c be (25/(-10))/(((-15)/6)/5). Let m(y) be the third derivative of 0*y**6 + 0*y**c - 2*y**2 + 0*y**3 + 0*y**4 + 1/105*y**7 + 0*y + 0. Solve m(l) = 0.
0
Let z(p) be the third derivative of -p**8/3360 - p**7/420 + p**5/15 - p**4/12 - 3*p**2. Let h(k) be the second derivative of z(k). Solve h(l) = 0 for l.
-2, 1
Let c(d) be the second derivative of -d**4/4 + 2*d**3 + 15*d**2/2 - 2*d. Solve c(m) = 0.
-1, 5
Suppose 4/9*z - 2/9*z**2 + 0 - 2/9*z**3 = 0. Calculate z.
-2, 0, 1
Find h, given that -2/3*h + 0 + 2/3*h**2 = 0.
0, 1
Let w(g) be the third derivative of -g**5/540 + g**4/72 - g**3/27 + 11*g**2. Determine c so that w(c) = 0.
1, 2
Find d, given that 5*d - 33/4*d**2 + 5*d**3 - 1 - d**4 = 0.
1/2, 2
Let m(x) = 4*x**4 + 10*x**3 + 8*x**2 + 2. Let d(k) = k**4 + k**3 + 1. Let y = 13 + -9. Suppose -6 = y*q - q. Let j(v) = q*d(v) + m(v). What is t in j(t) = 0?
-2, 0
Let a(b) be the third derivative of -b**7/273 - 9*b**6/260 - 3*b**5/26 - 29*b**4/156 - 2*b**3/13 - 2*b**2. Suppose a(n) = 0. Calculate n.
-3, -1, -2/5
Solve 0*j - 31*j**3 - 2*j + 35*j**3 - 2*j**5 = 0.
-1, 0, 1
Let y(b) be the first derivative of b**3 - 9*b**2/2 + 6. Factor y(m).
3*m*(m - 3)
Suppose -5*x - 4*i - 20 = -132, -4*x - 2*i + 86 = 0. Suppose u - x = -u. Suppose 5 + 6*a**2 - u*a + 4*a - 2*a**3 - 3 = 0. What is a?
1
Let c be 343/315 + (-3)/15. Let -16/9*v + 46/9*v**2 + 6*v**3 - c - 6*v**4 - 6*v**5 = 0. Calculate v.
-1, -1/3, 2/3
Let j(u) be the first derivative of -6 - 2/45*u**5 + 0*u + 2/27*u**3 - 1/18*u**4 + 1/9*u**2. Suppose j(x) = 0. What is x?
-1, 0, 1
Suppose 0 = 8*k - 16. Suppose -4/7*l**k + 2/7 - 2/7*l + 2/7*l**4 + 4/7*l**3 - 2/7*l**5 = 0. What is l?
-1, 1
Let u(v) be the third derivative of v**7/105 - v**6/60 - v**5/10 + 5*v**4/12 - 2*v**3/3 - 8*v**2. Factor u(y).
2*(y - 1)**3*(y + 2)
Solve 52/3*a**2 - 4*a - 52/3*a**3 + 0 + 4*a**4 = 0 for a.
0, 1/3, 1, 3
Let d(o) be the first derivative of -5*o**3 + 9*o**2 + 5 + 7/8*o**4 - 4*o. Suppose d(f) = 0. What is f?
2/7, 2
Let b be -3*2/6*8. Let z(c) = -11*c**2 - 8*c + 3. Let v(f) = 7*f**2 + 5*f - 2. Let y(l) = b*v(l) - 5*z(l). Factor y(k).
-(k - 1)*(k + 1)
Suppose -50 = 4*p + p. Let a be (12/(-5))/(3/p). Factor -2*o**2 - a*o**4 - 12*o**3 - o - o - 6*o**2 - 2*o**5.
-2*o*(o + 1)**4
Let d(x) = -36*x + 6 + 4*x - 38*x**2 - 26 - 2*x. Let y(m) = -13*m**2 - 11*m - 7. Let t(k) = 3*d(k) - 8*y(k). Factor t(h).
-2*(h + 1)*(5*h + 2)
Let c be 6/(-33) + 171/33. Suppose c*b + 4 = -4*d, -2*b - 2*b - 32 = -4*d. Factor -8*g**3 - 2*g**3 + 4*g**d - 4*g**2 + 10*g**4.
2*g**2*(g - 1)*(7*g + 2)
Let b(l) = l**3 - 5*l**2 + 4*l + 1. Let a be b(3). Let g = -3 - a. Determine c, given that -3 - g*c**2 + c**2 - 2 + c + 7 = 0.
-1, 2
Let y = -8 + 8. Suppose 0 = -y*f + f - 2. Find x such that 0*x**4 + 2*x**4 - 3*x**5 - 6*x**4 - 4*x + 4*x**f + 7*x**3 = 0.
-2, -1, 0, 2/3, 1
Suppose d = -2*d. Solve -9*b**3 + 6*b**2 + d*b - 3*b + 18*b**3 = 0 for b.
-1, 0, 1/3
Solve -4*k**3 - 2*k**4 - 1/4 - 15/4*k**2 - 3/8*k**5 - 13/8*k = 0 for k.
-2, -1, -1/3
Let i(q) be the first derivative of -2*q**3/15 + q**2/5 + 10. Factor i(p).
-2*p*(p - 1)/5
Suppose -15*o**2 - 236*o - 3*o**3 - 14 + 275*o + 12 - 19 = 0. What is o?
-7, 1
Let d(f) be the second derivative of 0*f**4 + 0*f**5 + 1/45*f**6 + f - 4/63*f**7 + 0 + 0*f**2 + 0*f**3. Factor d(l).
-2*l**4*(4*l - 1)/3
Let u(t) = 3*t**2 - 8*t + 5. Let g(i) = -i**2 - i - 22. Let a be g(0). Let d(q) = q**2 - 2*q + 1. Let m(l) = a*d(l) + 6*u(l). Let m(w) = 0. Calculate w.
-2, 1
Suppose -3*g - 105 = -2*g. Let x be 2/(-6) + (-125)/g. Factor -2/7*u**3 + x*u**2 - 2/7*u**4 + 4/7 + 10/7*u.
-2*(u - 2)*(u + 1)**3/7
Let v(p) be the second derivative of -p**6/360 + p**5/60 + p**3/2 - p. Let y(d) be the second derivative of v(d). Determi