3*t**4 - 10*t**2 - 8*t - 8*t**3 - 5*t**4 - 2*t**2.
-2*(t + 1)**4
Let f be (12/(-10))/(5/25). Let v(p) = p**2 + 6*p + 3. Let r be v(f). Factor -3*z**4 - 2*z**4 + 4*z**4 + 2*z**r - z**3.
-z**3*(z - 1)
Let i be ((-2)/(-18)*2)/((-2)/(-21)). Let t(c) be the first derivative of -i*c**3 + 3/2*c**4 + c**2 + 1 + 0*c. Find k such that t(k) = 0.
0, 1/2, 2/3
Let n be (-9)/2*(-4)/3. Suppose -2*p - n = -4*p. Factor -2 + l**3 - 4*l + 3*l**p + 0 + 2*l**4.
2*(l - 1)*(l + 1)**3
Let f(y) be the third derivative of -y**8/2240 + y**6/80 + y**5/20 + 7*y**4/24 + 8*y**2. Let n(l) be the second derivative of f(l). Solve n(w) = 0.
-1, 2
Let g(v) be the first derivative of -3/8*v**4 + 6 + 0*v + 0*v**2 + 0*v**3 - 1/4*v**6 - 3/5*v**5. Suppose g(j) = 0. What is j?
-1, 0
Let m(u) be the first derivative of -4*u**5/5 - 8*u**4 - 32*u**3 - 64*u**2 - 64*u - 13. Factor m(l).
-4*(l + 2)**4
Let q(s) be the second derivative of s**7/210 + s**6/75 + s**5/100 - 23*s. Determine o so that q(o) = 0.
-1, 0
Let p(u) be the second derivative of -u**6/15 - u**5/10 + u**4/6 + u**3/3 + 3*u. Factor p(s).
-2*s*(s - 1)*(s + 1)**2
Let a(h) be the third derivative of -3*h**2 + 0*h**4 + 1/360*h**5 + 0 + 0*h**3 - 1/360*h**6 + 1/1260*h**7 + 0*h. Factor a(i).
i**2*(i - 1)**2/6
Let c = 305 - 305. Factor c + 2/9*r**2 - 2/3*r.
2*r*(r - 3)/9
Let a(t) be the first derivative of t**6/10 + 3*t**5/5 + 3*t**4/4 + 6*t - 6. Let z(f) be the first derivative of a(f). Solve z(i) = 0.
-3, -1, 0
Determine d, given that -40*d**3 - 6*d**4 - 7*d - 55*d**2 - 23*d**2 - 29*d = 0.
-3, -2/3, 0
Suppose -454*h = -478*h. Suppose h*s + 0 + 2/11*s**4 + 8/11*s**2 - 8/11*s**3 = 0. What is s?
0, 2
Let r(q) be the first derivative of -2/35*q**5 + 0*q**2 + 0*q + 2/21*q**3 + 0*q**4 - 3. Factor r(l).
-2*l**2*(l - 1)*(l + 1)/7
Let c = -8 - -10. Determine i, given that 3*i + c*i - 5*i - i + i**2 = 0.
0, 1
Let k(s) = -6*s**2 - 4*s + 7. Let d(m) = -11*m**2 - 8*m + 13. Let i = -15 + 12. Let z(t) = i*d(t) + 5*k(t). What is a in z(a) = 0?
-2, 2/3
Let q be (0 - -2)/((-1)/(-2)). Let m(y) = 4*y + 11 + 0*y + 11*y**2 + y. Let b(d) = -5*d**2 - 2*d - 5. Let v(l) = q*m(l) + 9*b(l). Factor v(h).
-(h - 1)**2
Let q be 30/105 + (-12)/(-7). Determine m so that 1 + 4 - 12*m**q - 1 + 8*m**3 = 0.
-1/2, 1
Let b(c) be the second derivative of 7*c**5/60 + 4*c**4/9 + 11*c**3/18 + c**2/3 + 7*c. Solve b(d) = 0 for d.
-1, -2/7
Suppose 0 - 1/4*c**2 - 5/4*c**3 + 0*c - c**4 = 0. What is c?
-1, -1/4, 0
Let -31 + k**3 + 31 - k**2 - 2*k = 0. What is k?
-1, 0, 2
Let f = 68 + -68. Factor -2/9*p**3 - 4/9*p + f - 2/3*p**2.
-2*p*(p + 1)*(p + 2)/9
Let t be (-88)/(-5) - 8/(-20). Let h be 2 - (-2 - -5) - -11. Factor -12*j**2 - h*j**3 + 4 + 14*j**2 - t*j + 22*j**2.
-2*(j - 1)**2*(5*j - 2)
Let p(u) = -4*u - 31. Let s be p(-8). Factor -11/2*t - s - 9/2*t**2.
-(t + 1)*(9*t + 2)/2
Let g(j) be the second derivative of j**6/225 - j**5/50 + 4*j**3/45 - 23*j. Factor g(p).
2*p*(p - 2)**2*(p + 1)/15
Let z(c) be the second derivative of c**7/5040 + c**6/2160 - c**5/720 - c**4/144 - c**3/6 + 2*c. Let b(o) be the second derivative of z(o). Factor b(u).
(u - 1)*(u + 1)**2/6
Let 12*v + 5*v**2 + 7*v**2 - 17*v**3 - 2*v**2 + v**3 - 6*v**4 = 0. Calculate v.
-3, -2/3, 0, 1
Let b(o) = 7*o - 26. Let z be b(4). Solve -2*s**z + 0 - 4/3*s = 0 for s.
-2/3, 0
Let i(b) = -14*b**2 + 14*b - 8. Let w(y) = -5*y**2 + 5*y - 3. Let t(x) = -3*i(x) + 8*w(x). Factor t(v).
2*v*(v - 1)
Let d(f) be the second derivative of -f**5/80 + f**4/24 + f**3/24 - f**2/4 - 2*f. Factor d(c).
-(c - 2)*(c - 1)*(c + 1)/4
Let g(r) be the first derivative of 5*r**6/6 - r**5 - 5*r**4/4 + 5*r**3/3 - 3. Find h, given that g(h) = 0.
-1, 0, 1
Let x be -11 + -1 - (-3 - -6). Let b = -10 - x. Determine p so that -1/2 + p**3 - 1/2*p**4 - 1/2*p - 1/2*p**b + p**2 = 0.
-1, 1
Suppose 0 = -5*r + 9 + 11. What is p in -r*p + p + p**3 - p**2 + 3*p = 0?
0, 1
Let p(k) be the first derivative of -2 - 4/5*k + 1/5*k**2 - 1/10*k**4 + 4/15*k**3. What is j in p(j) = 0?
-1, 1, 2
Factor -4*g**3 + 3*g + 3*g**3 - g**3 + 4*g**2 - 5*g.
-2*g*(g - 1)**2
Let w(i) = -60*i**4 + 136*i**3 - 116*i**2 + 24*i. Let r(c) = -20*c**4 + 45*c**3 - 39*c**2 + 8*c. Let t(o) = 8*r(o) - 3*w(o). Suppose t(v) = 0. What is v?
0, 2/5, 1
Let d(i) be the first derivative of -i**6/2 + 18*i**5/5 - 6*i**4 - 2*i**3 + 27*i**2/2 - 12*i + 6. Determine r so that d(r) = 0.
-1, 1, 4
Let b be -6 - 2/(-6) - -6. Find m, given that -1/3*m**4 - b*m**2 + 0 + 0*m - 2/3*m**3 = 0.
-1, 0
Let x = 19 + -13. Factor 5*o**2 + 4 + 5*o**2 - 8 + x*o.
2*(o + 1)*(5*o - 2)
Let g be 8/(-6)*9/(-6). Suppose -5*h - 4*r + 4 + 8 = 0, -2*h - g*r = -4. Suppose 0*f**2 + 0*f**3 + 0 + 0*f + 0*f**h - 2/9*f**5 = 0. Calculate f.
0
Let o(m) be the third derivative of 0*m**3 - 81/112*m**8 - 9/14*m**7 + 0*m + 4/5*m**6 + 0 + 0*m**4 - 1/5*m**5 - 5*m**2. Factor o(f).
-3*f**2*(f + 1)*(9*f - 2)**2
Let l(c) = -c**3 + 7*c**2 - 6*c - 2. Let u be l(6). Let p be (-3*u/3)/1. Factor 2*r - r**4 + 4*r**p - 2*r**5 - 4*r**4 + r**4 + 0*r.
-2*r*(r - 1)*(r + 1)**3
Let p(c) = 13*c - 1. Let y be p(1). Suppose -5*d - y + 32 = 0. Let -5*a**2 + 2*a + 5*a**d - a**5 + a**3 + a**5 - 3*a**5 = 0. What is a?
-1, 0, 2/3, 1
Let h be (-6)/(-27) - 3/(54/(-32)). Let m(g) be the second derivative of 8/5*g**h + 2*g - 4/5*g**3 - 1/50*g**5 + 0 + 1/5*g**4. Factor m(d).
-2*(d - 2)**3/5
Let d = -7 - -10. Factor -4/9*m**d - 2/9*m**4 + 2/9*m**5 + 2/9*m - 2/9 + 4/9*m**2.
2*(m - 1)**3*(m + 1)**2/9
Suppose -q = 2*q - 42. Let d = q + -12. Factor 0 - 1/4*w**4 - 1/4*w**3 + 1/4*w + 1/4*w**d.
-w*(w - 1)*(w + 1)**2/4
Suppose 5*v = u + 2*u + 25, 0 = -v + 5*u + 27. Suppose 8 = -v*m + 4*m. Factor 2/5*h + 12/5*h**3 + 0 - 8/5*h**2 - 8/5*h**m + 2/5*h**5.
2*h*(h - 1)**4/5
Let k(i) = -i**3 + i + 1. Let y(z) = -2*z**3 + 3*z**2 + 2*z + 2. Let u = -5 - 0. Let x(n) = u*k(n) + y(n). Suppose x(r) = 0. Calculate r.
-1, 1
Let v(c) be the first derivative of 1/6*c**4 + 1/20*c**5 + 0*c**2 - 2*c - 2 + 1/6*c**3. Let p(q) be the first derivative of v(q). Factor p(g).
g*(g + 1)**2
Let l = -9 + 13. Suppose -9 = -l*z + z. What is t in -1/3*t**5 + t + 1/3 + 2/3*t**2 - 2/3*t**z - t**4 = 0?
-1, 1
Let x(i) = -3*i**5 - 2*i**4 + 2*i**3 - 3*i - 2. Let a(h) = -h**5 - h**4 - h - 1. Suppose 1 - 19 = -3*d. Let v(r) = d*a(r) - 3*x(r). Factor v(b).
3*b*(b - 1)**2*(b + 1)**2
Let r(i) = -1. Let x(o) = o**3 + o**2 - 1. Let c(l) = 3*r(l) - 3*x(l). Factor c(y).
-3*y**2*(y + 1)
Let y be (4/(-10))/(1/4) + 2. Determine w so that y*w**2 - 2/5*w + 0 = 0.
0, 1
Let a(u) be the first derivative of u**7/600 - u**6/900 - 7*u**5/600 + u**4/60 + u**3/3 + 5. Let q(v) be the third derivative of a(v). Factor q(b).
(b - 1)*(b + 1)*(7*b - 2)/5
Let f(t) be the first derivative of 4/5*t**3 + 3/2*t**2 + 3/20*t**4 + 6/5*t + 1. Factor f(r).
3*(r + 1)**2*(r + 2)/5
Suppose x + x = 4. Factor 7*q - 12*q**x + 14 - 15*q - 14.
-4*q*(3*q + 2)
Let x(w) = -8*w**4 - 6*w**3 + 17*w - 3. Suppose -11 = 3*k - 4*k. Let a(p) = -3*p**4 - 2*p**3 + 6*p - 1. Let g(l) = k*a(l) - 4*x(l). Solve g(h) = 0 for h.
-1, 1
Let l = -79 - -82. Find q, given that 3/5*q**2 + 3/5*q**l + 0*q + 0 = 0.
-1, 0
Let a = -21 + 26. Let q(n) be the third derivative of 0 - 2/3*n**a + 5/8*n**4 + 0*n + 1/48*n**8 - 2*n**2 + 5/12*n**6 - 1/3*n**3 - 1/7*n**7. Factor q(g).
(g - 1)**4*(7*g - 2)
Let n(x) be the first derivative of 19*x**4/18 - 80*x**3/27 + 23*x**2/9 - 4*x/9 + 25. What is u in n(u) = 0?
2/19, 1
Let w(h) be the first derivative of -h**7/420 + h**6/180 + h**5/30 + 2*h**3/3 - 5. Let i(j) be the third derivative of w(j). Factor i(q).
-2*q*(q - 2)*(q + 1)
Factor -25*o**2 + 59*o**3 + 30*o - 31*o**3 - 23*o**3.
5*o*(o - 3)*(o - 2)
Let b(m) = -3*m**3 + 3*m**2 + m. Let x be b(3). Let o = x - -461/9. Solve 2/9 - o*t**2 + 2/9*t**3 - 2/9*t = 0 for t.
-1, 1
Let s(i) be the third derivative of i**8/840 + i**7/504 - i**6/180 - 3*i**5/20 - 8*i**2. Let w(h) be the third derivative of s(h). Factor w(g).
2*(3*g + 2)*(4*g - 1)
Solve 0 - 3/5*p**3 - 6/5*p - 21/5*p**2 + 21/5*p**4 + 9/5*p**5 = 0 for p.
-2, -1, -1/3, 0, 1
Factor 8/5*j + 0*j**2 + 0 + 2/5*j**4 - 6/5*j**3.
2*j*(j - 2)**2*(j + 1)/5
Let j(o) = 5*o**4 + 4*o**3 + 2*o**2 + 3*o - 3. Let m = 2 + 2. Let d(g) = -6*g**4 - 4*g**3 - 2*g**2 - 4*g + 4. Let n(c) = m*j(c) + 3*d(c). Factor n(l).
2*l**2*(l + 1)**2
Let w be (-2)/6*-2*3. Let j be w + 0 + 2 + -2. Factor -7*