- 78*c**2 - 71*c - 45. Let m(i) = i - 4. Let y(a) = -15*m(a) + 3*s(a). Suppose y(o) = 0. Calculate o.
-25, -1
Let l = 24 + -26. Let n = 0 - l. Factor -1/2*s**n - s + 0.
-s*(s + 2)/2
Let i(f) = -f**2 + 7*f - 6. Let z be i(2). Let b(p) be the second derivative of 2*p + 2/27*p**3 + 1/54*p**z + 0 - 1/3*p**2. Suppose b(d) = 0. Calculate d.
-3, 1
Let d = 36 - 4. Factor -5*w**3 - d*w**2 - 34*w - 8*w**2 - 66*w - 80.
-5*(w + 2)**2*(w + 4)
Let r(w) be the second derivative of w**7/42 - w**6/5 - 3*w**5/20 + 14*w**4/3 - 8*w**3 + 50*w - 2. Factor r(j).
j*(j - 4)**2*(j - 1)*(j + 3)
Let -27/4 + 15/2*f - 3/4*f**2 = 0. Calculate f.
1, 9
Let b be ((-1620)/(-132) - 2) + -10 - 20/154. Solve -b*w**4 + 3/7*w + 2/7 - 3/7*w**3 - 1/7*w**2 = 0.
-2, -1, 1
Let h(n) be the second derivative of -n**8/1176 + n**7/245 - n**6/210 - 27*n**2/2 + 28*n. Let x(a) be the first derivative of h(a). Let x(y) = 0. Calculate y.
0, 1, 2
Suppose -3*p + 28*p = 0. Let b(c) be the second derivative of -8*c - 1/55*c**5 - 1/66*c**4 + 0*c**3 - 1/165*c**6 + 0*c**2 + p. Factor b(q).
-2*q**2*(q + 1)**2/11
Suppose 3*h - h - 4 = 0. Factor 0 + 12*v**h - 7*v**2 - 10*v**2 + 5.
-5*(v - 1)*(v + 1)
Let z(c) be the second derivative of c**7/294 + c**6/70 - c**5/140 - c**4/28 - 246*c. Solve z(f) = 0 for f.
-3, -1, 0, 1
Let u(a) = 7*a**2 + 13*a - 1. Let b(o) = 3*o**2 + 6*o. Let m(h) = -5*b(h) + 2*u(h). Let v be m(-2). Suppose 1/4*t**3 - 3/4*t**v - 1/4 + 3/4*t = 0. What is t?
1
Let p(h) be the second derivative of -h**6/90 - 2*h**5/15 + 19*h**4/36 - 5*h**3/9 + 3*h + 4. Find x such that p(x) = 0.
-10, 0, 1
Suppose y - 4*q = 24, 4*y - 13 = 5*q + 28. Let l(o) be the second derivative of -1/120*o**6 - 1/48*o**y + 12*o + 0*o**2 + 0 + 1/40*o**5 + 0*o**3. Factor l(x).
-x**2*(x - 1)**2/4
Suppose 2*x + 3*b - 43 = -2*x, 0 = -2*b + 2. Suppose x = 4*v - 10. Factor 0*u**5 + 7*u**4 - 6*u**4 + 0*u**5 + u**v.
u**4*(u + 1)
Factor -15488/21 - 2/21*c**2 + 352/21*c.
-2*(c - 88)**2/21
Let q = -29992/7 + 4285. Factor -24/7*c**2 + 0 - q*c**4 - 15/7*c**3 - 12/7*c.
-3*c*(c + 1)*(c + 2)**2/7
Suppose 5*i + 27 = r, -3*r = 3*i - 25 + 34. Suppose -2/11*q**3 - 2/11*q**r + 0 + 4/11*q = 0. What is q?
-2, 0, 1
Let i be (-5 + 54/14)*(-1)/6. Let c(f) be the second derivative of 3/10*f**5 + 4/7*f**4 + 0 - 7/15*f**6 + 0*f**2 - 3*f + i*f**3. Find h, given that c(h) = 0.
-2/7, 0, 1
Suppose -11*c + c = -50. Factor 2*u**5 + 12*u**3 - 1 + 3 + 4 + 18*u**2 - 21*u - 24*u**4 + 7*u**c.
3*(u - 1)**3*(u + 1)*(3*u - 2)
Let h be 192/39 + 1428/(-1547). Find v such that 0*v + 1/6*v**h + 0 + 5/6*v**3 + 2/3*v**2 = 0.
-4, -1, 0
Let z be -2 + 4 - (-45)/(-21). Let u = z - -11/28. Let 1/4 - 1/4*v**2 + 1/4*v - u*v**3 = 0. Calculate v.
-1, 1
Suppose i**2 - 1/2*i**3 + 3/2*i + 0 = 0. Calculate i.
-1, 0, 3
Let b = -7 - -11. Find f such that -1056*f**2 - 21*f + b*f**3 + 1056*f**2 - f**3 - 18 = 0.
-2, -1, 3
Let y(h) be the first derivative of -h**5/5 + h**4/4 + 16*h**3/3 + 10*h**2 + 322. Factor y(i).
-i*(i - 5)*(i + 2)**2
Let p(k) = -25*k**2 + 17*k + 34. Let w(a) = 3*a**2 - 2*a - 4. Let d(y) = -6*p(y) - 51*w(y). Factor d(x).
-3*x**2
Suppose -3*h - 3*h = -30. Let b(n) = -8*n**2 - 4*n - 2. Let u(k) = -7*k**2 - 5*k - 3. Let d(v) = h*b(v) - 6*u(v). Let d(r) = 0. Calculate r.
-4, -1
Determine z, given that 2/13*z**2 - 4/13 - 2/13*z = 0.
-1, 2
Let q(x) be the third derivative of x**6/180 + 7*x**5/90 + 5*x**4/18 + 203*x**2. Factor q(f).
2*f*(f + 2)*(f + 5)/3
Let s(w) be the second derivative of 0 + 0*w**2 + 37*w + 1/15*w**4 + 1/50*w**5 - 1/5*w**3. Factor s(y).
2*y*(y - 1)*(y + 3)/5
Let p be -1 - (-6)/4 - 49/(-14). Factor 6 + p + 0*j**4 + 9*j**2 + 5*j**3 - 8 + 7*j + j**4.
(j + 1)**3*(j + 2)
What is u in -76/9*u + 56/3 - 4/9*u**2 = 0?
-21, 2
Let v(l) be the first derivative of 3*l**5/20 + 5*l**4/4 + 4*l**3 + 6*l**2 + 22*l - 13. Let f(t) be the first derivative of v(t). Factor f(g).
3*(g + 1)*(g + 2)**2
Let t(r) be the first derivative of 2*r**3 + 5/2*r**2 - 9 + 1/4*r**4 + 0*r. Solve t(k) = 0.
-5, -1, 0
Let m(n) be the second derivative of -n**7/14 + n**6/2 + 27*n**5/20 - 17*n**4/4 - 4*n**3 + 18*n**2 + 2*n - 11. Determine f, given that m(f) = 0.
-2, -1, 1, 6
Factor -1/7*t**2 - 3/7 + 5/7*t - 1/7*t**3.
-(t - 1)**2*(t + 3)/7
Find z, given that -z**2 + 163*z - 184*z + z**2 + 3*z**2 = 0.
0, 7
Let 28*c**4 - 148*c**2 + 24*c - 98*c**3 - 24*c**2 - 64*c - 6*c**3 = 0. What is c?
-1, -2/7, 0, 5
Let v be (12/54)/((-56)/(-21)). Let q(g) be the second derivative of -1/2*g**2 + 0 + 5*g + 0*g**3 + v*g**4. Suppose q(t) = 0. What is t?
-1, 1
Factor 0 - 34/25*w - 2/25*w**2.
-2*w*(w + 17)/25
Let x(g) = -g**3 + 6*g**2 - 5. Let q be x(4). Factor 43*b - 5*b**2 - 21*b - q*b.
-5*b*(b + 1)
Let f(u) = -2*u**2 - 9*u + 8. Let a be f(-5). Suppose -a*n - l + 15 = -3*l, 4*n + 2*l = 6. Determine c so that 1/5 - 1/5*c**n - 3/5*c + 3/5*c**2 = 0.
1
Let i = 59 + -707/12. Let m(l) be the first derivative of 4*l + i*l**3 + 9 - l**2. Factor m(d).
(d - 4)**2/4
Let v be 8/20 - 3432/(-495). Suppose 4*o - 9 = o. Factor 8/3 - v*x**2 + 32/3*x - 6*x**o.
-2*(x - 1)*(x + 2)*(9*x + 2)/3
Let q(z) = z**3 + 12*z**2 + 2*z + 29. Let m be q(-12). Suppose -a + m = -0, -4*v + 41 = 5*a. Find i, given that 1/2*i**3 - 5/6*i**2 + 3/2*i**v + 0 + 1/6*i = 0.
-1, 0, 1/3
Let m(z) be the first derivative of -8*z**2 - 68 + 35 + 28 + z**4 - 4*z**3. Let m(k) = 0. What is k?
-1, 0, 4
Let z(d) be the second derivative of -d**4/54 + 7*d**3/27 - 4*d**2/3 - 17*d - 11. What is f in z(f) = 0?
3, 4
Let a(f) = -f**2 + 1. Let i(h) = 3*h**2 + 176*h + 1. Let o(d) = a(d) - i(d). Let o(c) = 0. What is c?
-44, 0
Factor -4*m**4 - 505*m**2 - 498*m**2 - 4*m + 10*m**3 + 1001*m**2.
-2*m*(m - 2)*(m - 1)*(2*m + 1)
Let d = 71/8 + -69/8. Let g(c) be the first derivative of -6 - d*c**3 + 1/2*c + 1/8*c**2. Determine m, given that g(m) = 0.
-2/3, 1
Find b, given that 26*b - 9*b**2 - 18398 - 3*b**2 + 18394 = 0.
1/6, 2
Let m(d) be the second derivative of -d**5/200 + 7*d**4/120 + 17*d**3/60 + 9*d**2/20 - 8*d - 4. Factor m(j).
-(j - 9)*(j + 1)**2/10
Suppose 3*i = -7*l + 34, -10*i + 13*i - 22 = -4*l. Factor -24/5*f**i + 6/5 - 66/5*f**3 - 3*f**5 + 9/5*f - 54/5*f**4.
-3*(f + 1)**4*(5*f - 2)/5
Suppose -48*t + 141 = 45. Suppose -3 + 3/2*k + 3/2*k**t = 0. Calculate k.
-2, 1
Let y(h) be the first derivative of 10 - 1/8*h**4 + 0*h + 1/30*h**5 + 0*h**2 + 1/9*h**3. Factor y(m).
m**2*(m - 2)*(m - 1)/6
Let o be (-2)/(-7) + (-6)/((-15120)/925). Let w = 1/72 + o. What is z in z + w - 1/3*z**3 + 0*z**2 = 0?
-1, 2
Let h = -2419 - -16937/7. Let -1/7*q + 1/7*q**3 + 4/7*q**2 - h = 0. What is q?
-4, -1, 1
Factor 40 - s**2 + 130 + 31 - 2*s**2 - 198*s.
-3*(s - 1)*(s + 67)
Let u(z) = 2*z - 21. Let d be u(15). Let s be 44/45 - (-2)/d. Factor 8/5*l - 2/5*l**2 - s.
-2*(l - 3)*(l - 1)/5
Let c(o) be the second derivative of 4/15*o**6 + 0*o**2 - 7/5*o**5 - 20/3*o**4 + 38*o + 2/21*o**7 - 8*o**3 + 0. Find k, given that c(k) = 0.
-2, -1, 0, 3
Determine l so that 31*l**3 + 15 + 14*l**3 - l**2 - 15*l**2 - 3*l**4 - 59*l**3 + 14*l + 4*l**4 = 0.
-1, 1, 15
Let m be (-12)/(-20) + -15 + 896/60. Let a(x) = x**3 + 3*x**2 - x. Let f be a(-2). Factor -54/5*s**4 + 0 - m*s + 64/15*s**2 - f*s**3.
-2*s*(s + 1)*(9*s - 2)**2/15
Factor 16*r + 9*r + 91*r**2 - 86*r**2 + 30.
5*(r + 2)*(r + 3)
Let s(p) be the second derivative of p**6/285 - p**5/38 + 2*p**4/57 + p**3/19 - 17*p**2/2 - 6*p. Let f(n) be the first derivative of s(n). Factor f(m).
2*(m - 3)*(m - 1)*(4*m + 1)/19
Let h = 11 - 8. Suppose 0 = w - h - 0. Let 4*m**5 + w*m**4 - 8*m**3 + 4 + 0*m**4 - 8*m**2 + 2*m**4 + 4*m - m**4 = 0. Calculate m.
-1, 1
Let t(k) be the third derivative of 5*k**2 + 0*k**3 - 1/160*k**6 - 1/280*k**7 + 0*k**4 + 0 + 1/448*k**8 + 1/80*k**5 + 0*k. What is a in t(a) = 0?
-1, 0, 1
Let m(g) be the first derivative of 5/2*g**2 - 7/60*g**5 + 0*g - 1/3*g**3 + 3/8*g**4 - 1. Let l(z) be the second derivative of m(z). Factor l(q).
-(q - 1)*(7*q - 2)
Let g be (-4)/8 + (-140)/(-120). Let o be (6/(-4))/((-6)/8). Factor 0 + 2/3*d**5 + 0*d + 2*d**3 + g*d**o + 2*d**4.
2*d**2*(d + 1)**3/3
Solve 3*o**5 + 75/4*o**3 + 81/4*o**4 - 54*o**2 + 0 + 12*o = 0.
-4, 0, 1/4, 1
Suppose -6*g = -20*g + 28. Let k(s) be the first derivative of 2/25*s**5 + 0*s + g + 1/5*s**2 + 3/10*s**4 + 2/5*s**3. Solve k(a) = 0 for a.
-1, 0
Solve -56/3*j**3 + 8*j - 4/3 + 12*j**2 = 0 for j.
-1/2, 1/7, 1
