4 - 2 - 1 - 6*q**2.
3*(q - 1)**2*(q + 1)**2
Solve 0 - 4/7*l**4 + 2/7*l**5 + 0*l**2 + 2/7*l**3 + 0*l = 0.
0, 1
Factor 4*m + 4*m - m**2 - 15*m.
-m*(m + 7)
Let x be (5 - 6) + 10/9. Let v(c) be the second derivative of -1/18*c**4 + 0 + 0*c**2 + 2*c - x*c**3. Factor v(o).
-2*o*(o + 1)/3
Let i(g) be the first derivative of -g**5/20 + 3*g**4/16 - 7. Factor i(k).
-k**3*(k - 3)/4
Let a(f) be the second derivative of 1/6*f**4 + 1/15*f**6 + 0*f**2 + f - 1/5*f**5 + 0*f**3 + 0. Find w, given that a(w) = 0.
0, 1
Let r be -1 - 3 - (-178)/8. Let w = -18 + r. Factor 0*i**3 + 0*i**2 + 0*i + 1/4*i**5 + w*i**4 + 0.
i**4*(i + 1)/4
Suppose -5 = 7*o - 19. Let b(i) be the first derivative of 1/8*i**o + 1/12*i**3 - 1/16*i**4 - 1/4*i + 1. Let b(y) = 0. Calculate y.
-1, 1
Let w(j) = j - 6. Let o be w(6). Factor 1 - s**3 + 1 - 3*s - 1 + 3*s**2 + o*s**2.
-(s - 1)**3
Let b(j) be the first derivative of 0*j**2 - 21/8*j**4 + 0*j - j**3 - 1. Factor b(m).
-3*m**2*(7*m + 2)/2
Solve -3*s**4 - 4*s**3 - 31*s**2 - 11*s**3 - 21*s + 4*s**2 - 6 = 0 for s.
-2, -1
Let w(a) be the second derivative of 35/6*a**4 + 2*a - 26/3*a**3 + 4*a**2 + 0 + 49/20*a**5. Factor w(b).
(b + 2)*(7*b - 2)**2
Let v(s) be the first derivative of s**7/630 - s**5/180 + s**2 + 2. Let u(w) be the second derivative of v(w). Factor u(k).
k**2*(k - 1)*(k + 1)/3
Let j(a) = -4*a**2 - 13*a - 4. Let o(v) = v**2 + 4*v + 1. Let i = -21 + 12. Let u = i + 5. Let q(x) = u*j(x) - 14*o(x). Factor q(r).
2*(r - 1)**2
Let k(z) be the second derivative of -2/3*z**3 - 4*z**2 - z + 1/3*z**4 + 0. Factor k(y).
4*(y - 2)*(y + 1)
Let p = 4 - 0. Suppose -3*t = 3*x - 0*t + 12, 5*x + p = -t. Determine d so that 9/5*d**3 + 6/5*d**2 - 6/5*d**4 + x - 9/5*d**5 + 0*d = 0.
-1, -2/3, 0, 1
Let c(j) be the second derivative of -j**4/114 - 6*j. Factor c(y).
-2*y**2/19
Let u(w) = w**3 - 3*w - 2*w**2 - 1 + 2*w + w - 2*w. Let v be u(3). Find k such that -9/2*k**v + 1 - 3/2*k + 5*k**3 = 0.
-1/2, 2/5, 1
Let p = 77899/748 - -20/187. Let g = 105 - p. What is l in -1/4*l**2 - 1/4*l**4 + 1/2 - 3/4*l + g*l**3 = 0?
-1, 1, 2
Let r(s) be the third derivative of s**6/600 + s**5/100 + s**4/40 + s**3/30 + 13*s**2. Factor r(z).
(z + 1)**3/5
Let k(u) be the second derivative of -u**5/60 + u**3/18 + 2*u. Factor k(a).
-a*(a - 1)*(a + 1)/3
Let p(i) be the third derivative of 2*i**2 + 0*i**3 + 0 + 2/15*i**5 + 0*i + 1/12*i**4. Let p(v) = 0. Calculate v.
-1/4, 0
Let x be (2/(-8))/((-3)/16). Suppose -16*z - 6 = -70. Find u such that -2*u + 2*u**3 - 14/3*u**2 + x + 10/3*u**z = 0.
-1, 2/5, 1
Determine i so that -13*i**2 + 2*i**4 + 6*i**2 - i**2 = 0.
-2, 0, 2
Factor 99*x**2 - 2*x**4 - 21*x + 12 - 93*x**2 - x + 6*x**3.
-2*(x - 3)*(x - 1)**2*(x + 2)
Let m be -1 + 1 - 1376/(-14). Let x = m + -98. Factor -2/7*r**2 + 2/7*r - 2/7*r**3 + x.
-2*(r - 1)*(r + 1)**2/7
Let 0 - 8/7*m**2 + 6/7*m + 8/7*m**4 - 4/7*m**3 - 2/7*m**5 = 0. What is m?
-1, 0, 1, 3
Let g(o) be the third derivative of 0*o + 2*o**2 + 1/100*o**5 + 0 + 0*o**3 + 1/60*o**4 - 1/30*o**6 - 1/50*o**7. Suppose g(c) = 0. What is c?
-1, -2/7, 0, 1/3
Let v(b) = b**2 - 4*b + 3. Let s be v(4). Solve -7*t + 2 - 3*t + 7*t**4 + 5*t**s + 5*t - 9*t**2 = 0 for t.
-1, 2/7, 1
Let l be (1 - 7/(-6)) + 2/(-1). Let f(r) be the first derivative of 3 + 1/3*r**2 + 2/9*r**3 - 2/3*r - l*r**4. Determine c, given that f(c) = 0.
-1, 1
Let j(p) = -p**2 + p + 1. Let q(t) = -3*t**2 + 5*t - 1. Let a be (-3 + 2)*(-4 + 3). Let v(r) = a*j(r) - q(r). Determine k so that v(k) = 0.
1
Let a(g) be the first derivative of g**3/2 + 35*g**2/4 + 11*g + 13. Factor a(d).
(d + 11)*(3*d + 2)/2
Let o(z) be the second derivative of -7/45*z**5 + 2/27*z**3 + 1/9*z**6 + 4*z + 0*z**2 + 0 - 1/18*z**4. Find a such that o(a) = 0.
-2/5, 0, 1/3, 1
Suppose -2 = -2*u - 14. Let l be 3/u + 22/28. Factor 0 + 8/7*s**4 + 2/7*s + l*s**5 + 12/7*s**3 + 8/7*s**2.
2*s*(s + 1)**4/7
Suppose f = 5*v + 1, 2*v = f + 3*v + 17. Let k be 6/f + (-165)/(-140). Let 1/4*u**3 - 1/4 + k*u - 3/4*u**2 = 0. Calculate u.
1
Let z(g) be the first derivative of -g**5 + 5*g**4/2 - 5*g**3/3 - 9. Solve z(n) = 0 for n.
0, 1
Let z = -24/5 + 92/15. Determine m so that -z*m + 0 - 44/3*m**3 + 38/3*m**4 + 22/3*m**2 - 4*m**5 = 0.
0, 1/2, 2/3, 1
Let p(m) = m**2 + m - 1. Let y(i) = -15*i**3 + 21*i**2 + 15*i - 15. Suppose -4*d + 0*a - a - 60 = 0, -45 = 3*d + 2*a. Let w(f) = d*p(f) + y(f). Factor w(k).
-3*k**2*(5*k - 2)
Let n be 68/12 - 3/(-9). Let v(z) = z. Let i(o) = 9*o**3 + 11*o**2. Let m(g) = n*v(g) + 3*i(g). Factor m(u).
3*u*(u + 1)*(9*u + 2)
Let j = -121/4 + 147/4. Let d = j - 6. Factor -1/2*z + 0 - 1/4*z**4 + d*z**3 + 1/4*z**2.
-z*(z - 2)*(z - 1)*(z + 1)/4
Let t(n) be the third derivative of n**5/120 + n**4/24 - n**3/4 + n**2. Factor t(k).
(k - 1)*(k + 3)/2
Suppose 0*w + 4*w = 0. Suppose 0 = g - w*p - 2*p - 10, 0 = 4*g + 2*p. Factor -3*k**g + 6*k**3 + 4*k**4 + 2*k**2 + 2*k**2 + k**5 + k + 3*k**2.
k*(k + 1)**4
Let h(t) be the third derivative of t**6/80 + 3*t**5/40 + 3*t**4/16 + t**3/4 + t**2. Suppose h(v) = 0. Calculate v.
-1
Let w(h) be the first derivative of -2*h**5/25 - h**4/5 + 2*h**2/5 + 2*h/5 - 6. Let w(f) = 0. What is f?
-1, 1
Let n(w) be the third derivative of w**8/840 - 4*w**7/525 + w**6/50 - 2*w**5/75 + w**4/60 - 4*w**2. Let n(c) = 0. Calculate c.
0, 1
Suppose 0*m = -3*m + 12. Let n be (m/(-10))/(3/15). Let o(l) = l**3 + l**2 + 1. Let u(a) = a**3 - 2*a**2 - a - 1. Let b(d) = n*u(d) - 2*o(d). Factor b(q).
-2*q*(q - 1)*(2*q + 1)
Let g(f) be the first derivative of 3 - 2/21*f**3 - 1/7*f**2 + 0*f. Determine z so that g(z) = 0.
-1, 0
Solve -14*w + 3*w**2 + 35*w - 3*w + 27 = 0 for w.
-3
Suppose 8*s - 6 = 5*s. Suppose -4/7*r + 2/7 + 2/7*r**s = 0. Calculate r.
1
Let d(c) = 2*c - 7. Let z be d(15). Factor -19*r**4 + 4*r**5 + 75*r**3 + r + 48*r**2 + 15*r + 43*r**4 - z*r**3.
4*r*(r + 1)**2*(r + 2)**2
Let r(i) be the first derivative of -3*i**5 + 25*i**4/4 - 5*i**3/3 - 5*i**2/2 + 14. Factor r(h).
-5*h*(h - 1)**2*(3*h + 1)
Let c(z) = 4*z**2 + z. Let p be c(1). Suppose 3 - k**2 + 5*k + p - 13*k + 3*k**2 = 0. Calculate k.
2
Factor -4/3*s**3 + 2*s + 4/3*s**2 - 2*s**4 - 2/3*s**5 + 2/3.
-2*(s - 1)*(s + 1)**4/3
Let n = 1 + 2. Let r be 0 - (3 + -2 + -4). Factor 1 - 2*s**4 - n*s**5 - s**3 - 5*s**4 - s**r + 6*s**2 + 5*s.
-(s - 1)*(s + 1)**3*(3*s + 1)
Let d(w) be the third derivative of w**6/24 - w**5/6 + 5*w**4/24 + 25*w**2. Suppose d(b) = 0. What is b?
0, 1
Let u(r) = -2*r**3 + 4*r**2 - 2*r + 2. Let o(w) = w - 1. Let j(q) = -4*o(q) - 2*u(q). Solve j(z) = 0 for z.
0, 2
Let p(s) be the third derivative of 0 - 2*s**2 + 0*s**4 + 1/5*s**6 + 0*s - 2/15*s**5 - 1/35*s**7 + 0*s**3 - 5/168*s**8. Solve p(b) = 0 for b.
-2, 0, 2/5, 1
Suppose 0*l - 5 = -l + d, 3*l + 3*d = -3. What is f in 4*f**3 + 3*f**2 + f**l - 6*f**3 = 0?
0, 2
Factor 6 - 6*c**2 + 11 + 21*c - 43 + 11.
-3*(c - 1)*(2*c - 5)
Let a(p) be the third derivative of 1/12*p**5 - 1/210*p**7 + 0 - 1/40*p**6 - 1/12*p**4 + 1/336*p**8 + 0*p**3 + p**2 + 0*p. Solve a(t) = 0 for t.
-2, 0, 1
Let a(c) be the second derivative of -c**5/70 - c**4/21 - c**3/21 - 7*c. Factor a(o).
-2*o*(o + 1)**2/7
Let f = 30 + -33. Let t be 2/f + 8 + -7. Factor -t*m**2 + 2/3 + 1/3*m.
-(m - 2)*(m + 1)/3
Let t(q) be the first derivative of 1/14*q**6 - 3/14*q**4 - 2/7*q**3 + 3/35*q**5 + 5 + 3/7*q + 3/14*q**2. Factor t(i).
3*(i - 1)**2*(i + 1)**3/7
Let s(a) be the first derivative of 3*a**4/4 - 5*a**3 + 21*a**2/2 - 9*a - 2. Suppose s(m) = 0. What is m?
1, 3
Let i(j) = -j**3 - 16*j**2 - 16*j - 13. Let n be i(-15). Let 0*h - 1/3*h**3 - h**5 + 0 - 1/3*h**n + 5/3*h**4 = 0. What is h?
-1/3, 0, 1
Let h(a) be the second derivative of -a**5/4 - 5*a**4/12 + 5*a**3/6 + 5*a**2/2 + 2*a - 15. Factor h(n).
-5*(n - 1)*(n + 1)**2
Let f(l) be the first derivative of -l**6/3 + 32*l**5/35 + 3*l**4/14 - 32*l**3/21 + 4*l**2/7 - 19. What is u in f(u) = 0?
-1, 0, 2/7, 1, 2
Let u be 2/20*(-3)/(-6). Let t(z) be the first derivative of 1/8*z**4 - u*z**5 + 1/4*z - 1 - 1/4*z**2 + 0*z**3. Suppose t(q) = 0. Calculate q.
-1, 1
Let s(f) be the third derivative of f**7/7560 + f**6/1080 + f**5/360 - f**4/12 + 4*f**2. Let m(g) be the second derivative of s(g). Let m(v) = 0. What is v?
-1
Solve -12/5 - 16/5*d**2 + 38/5*d - 2*d**3 = 0.
-3, 2/5, 1
Let y(v) be the first derivative of v**4/12 - v**3/18 - 3. Find l, given that y(l) = 0.
0, 1/2
Factor 4/