- 4*n(s). Factor r(u).
3*u*(u - 1)*(u + 1)
Let a(c) be the first derivative of c**3 - 4 + 0*c - 3/2*c**2. Factor a(v).
3*v*(v - 1)
Let l(c) be the third derivative of -c**8/420 - 16*c**7/105 - 64*c**6/15 - 1024*c**5/15 - 2048*c**4/3 - 65536*c**3/15 - 71*c**2 - 2. Solve l(f) = 0 for f.
-8
Let r(v) = 24*v**3 - 73*v**2 - 85*v - 16. Let p(u) = u**2 - u. Let s(m) = p(m) - r(m). Find b, given that s(b) = 0.
-2/3, -1/4, 4
Factor 17*n**2 + 23*n**2 - 36*n**2 - 36*n.
4*n*(n - 9)
Let o(w) be the first derivative of w**6/4 + 6*w**5/5 + 9*w**4/4 + 2*w**3 + 3*w**2/4 - 1. What is j in o(j) = 0?
-1, 0
Factor 6/7*b**3 - 24/7 + 0*b + 18/7*b**2.
6*(b - 1)*(b + 2)**2/7
Suppose 15 = 4*h - 17. Let a = -6 + h. Factor 1 - w + 3*w**2 - w**3 - 2*w**a + 2*w - 2.
-(w - 1)**2*(w + 1)
Let q(o) be the third derivative of -o**6/280 + o**4/14 - 9*o**2. Let q(x) = 0. Calculate x.
-2, 0, 2
Suppose 11/4*t**3 + 0*t**2 - t + 1/2*t**5 + 0 - 9/4*t**4 = 0. What is t?
-1/2, 0, 1, 2
Suppose i + 0 = -3*u - 5, 0 = -4*i - 2*u. Let k be 324/14 + -1 + i. Factor -8/7 - 72/7*g - k*g**2.
-2*(9*g + 2)**2/7
Let b = -1/30 - -47/60. Let o = -7/29 + 173/116. Suppose -o*c - 1/4*c**2 + 5/4*c**3 - 1/2 + b*c**4 = 0. What is c?
-1, -2/3, 1
Let z(t) be the second derivative of -t**6/10 - 3*t**5/10 - t**4/4 - 8*t. Determine x, given that z(x) = 0.
-1, 0
Let y be 153/34*2/3. Let u(j) be the second derivative of 1/15*j**y - 3*j - 1/30*j**4 + 0*j**2 + 0. Solve u(n) = 0.
0, 1
Solve -1/6*n**5 + 0 + 1/6*n**3 + 1/6*n**4 + 0*n - 1/6*n**2 = 0 for n.
-1, 0, 1
What is i in -1/5*i**2 + 0 + 0*i = 0?
0
Let b = 111 - 111. Solve 2/3*a + 0 + b*a**3 - a**2 + 1/3*a**4 = 0 for a.
-2, 0, 1
Let a(k) = k + 2. Let p be a(-2). Factor 2*x**2 + 0*x**2 + p*x + 3*x - x.
2*x*(x + 1)
Let q(y) = -4*y**3 + 36*y**2 - 16*y + 16. Let f(r) = 0 - 5*r + 14*r**2 - 2*r**2 + 5 - r**3. Let i(d) = 16*f(d) - 5*q(d). Let i(s) = 0. What is s?
-3, 0
Let c(v) = -3*v**5 + 4*v**4 - 2*v**3 - 2*v**2 - v + 2. Let p(g) = 4*g**5 - 5*g**4 + 3*g**3 + 2*g**2 + 2*g - 3. Let i(l) = -6*c(l) - 4*p(l). Factor i(o).
2*o*(o - 1)**3*(o + 1)
Let f(q) be the third derivative of -q**7/525 - q**6/75 - q**5/75 + q**4/15 + q**3/5 - 11*q**2. Determine y, given that f(y) = 0.
-3, -1, 1
Let n(p) be the first derivative of 0*p**2 - 4 + 0*p - 1/5*p**3. Let n(j) = 0. What is j?
0
Suppose 2 - 14 = 4*g, -3*b - 3*g = 39. Let a be 1*1*(-28)/b. Determine w so that -a*w**3 - 6/5*w**2 - 4/5 + 2*w**4 + 14/5*w = 0.
-1, 2/5, 1
Let s(h) = h**3 + h**2 + 1. Let w(g) = 12*g**5 + 20*g**4 - 40*g**3 - 96*g**2 - 64*g - 28. Let x(q) = -12*s(q) - w(q). Determine v so that x(v) = 0.
-1, -2/3, 2
Let o(j) be the third derivative of 1/84*j**8 - 2/15*j**5 + 4/105*j**7 + 0*j + 0*j**3 - 7*j**2 - 1/6*j**4 + 0*j**6 + 0. Factor o(v).
4*v*(v - 1)*(v + 1)**3
Factor -3*f**2 + 247*f**4 - 8*f + 4*f**2 + 11*f**2 - 251*f**4.
-4*f*(f - 1)**2*(f + 2)
Let f(i) be the first derivative of 2*i**3/9 - 8*i/3 + 26. Determine h so that f(h) = 0.
-2, 2
Suppose -2/5 + 22/5*v**2 + 7/5*v = 0. What is v?
-1/2, 2/11
Let n(s) be the first derivative of s**5/35 - s**4/14 - s**3/7 + 4*s**2/7 - 4*s/7 + 5. Factor n(i).
(i - 2)*(i - 1)**2*(i + 2)/7
Factor -56/3*r + 8/3*r**3 + 20/3 + 28/3*r**2.
4*(r - 1)*(r + 5)*(2*r - 1)/3
Let d(r) be the second derivative of -r**6/15 + r**4/2 - 2*r**3/3 - 22*r. Factor d(m).
-2*m*(m - 1)**2*(m + 2)
Let a(o) be the third derivative of o**8/16800 + o**7/2100 + o**6/600 + o**5/300 - o**4/6 - 2*o**2. Let j(l) be the second derivative of a(l). Factor j(n).
2*(n + 1)**3/5
Let s = 127 + -507/4. What is d in 1/4*d**2 + 0 - s*d = 0?
0, 1
Let b be 2 + 43/(-22) - (-6)/12. Factor -b + 2/11*i**2 + 4/11*i.
2*(i - 1)*(i + 3)/11
Let k(w) = 4*w**2 - 3*w - 12. Let m(q) = -2*q**2 - 3*q + 2. Let r(x) = 4*x**2 + 5*x - 5. Let z(h) = 7*m(h) + 4*r(h). Let d(i) = 3*k(i) - 5*z(i). Factor d(j).
2*(j - 3)*(j + 1)
Suppose 0 = 5*n - 2*q - 29, 2*n = 4*q - 3*q + 12. Suppose 4*b + 4 = -v, 0*v + 12 = n*b - 3*v. Suppose 0 - 2/3*h**4 + 4/3*h**3 + b*h - 2/3*h**2 = 0. Calculate h.
0, 1
Let v = -1/184 + -2941/552. Let n = v - -6. Factor 2/3*a**2 + n - 5/3*a.
(a - 2)*(2*a - 1)/3
Let f(p) = 9*p + 2. Let b(r) = -4*r - 1. Let i(k) = 7*b(k) + 3*f(k). Let u be i(-3). Factor 0*j**u + 1/2*j**4 - 2*j + 0 + 3/2*j**3.
j*(j - 1)*(j + 2)**2/2
Let v(k) = 23*k - 274. Let r be v(12). Factor -r*j + 2 + 1/2*j**2.
(j - 2)**2/2
Let f(l) be the second derivative of -4*l - 1/27*l**4 - 4/45*l**6 + 0 - 1/10*l**5 + 0*l**3 - 5/189*l**7 + 0*l**2. Find p, given that f(p) = 0.
-1, -2/5, 0
Suppose 71 - 57 = 7*w. Find a such that 0 - 4/3*a**w - 4/3*a = 0.
-1, 0
Let v = -1429/10 - -143. Let o(c) be the second derivative of 2*c - 1/3*c**4 + 0 - v*c**5 - 1/3*c**3 + 0*c**2. Determine u, given that o(u) = 0.
-1, 0
Let y be ((-8)/(-7))/(1*(-6)/(-3)). Find f such that y*f**2 + 0*f + 2*f**3 + 0 = 0.
-2/7, 0
Let s(n) be the first derivative of 1/3*n**3 - 1 + 0*n**2 - 1/5*n**5 + 1/21*n**7 + n + 0*n**4 + 0*n**6. Let c(y) be the first derivative of s(y). Factor c(k).
2*k*(k - 1)**2*(k + 1)**2
Let a = 40 + -358/9. Let i = 13/18 - a. Factor i - 9/4*r**2 - 5/2*r**3 + 3/4*r.
-(r + 1)*(2*r - 1)*(5*r + 2)/4
Let c be (-150)/(-270) - 2/12*2. Factor 4/9 + c*a**2 + 2/3*a.
2*(a + 1)*(a + 2)/9
Factor -16/3*j**3 + 56/3*j**2 - 25/3*j + 1.
-(j - 3)*(4*j - 1)**2/3
Suppose v - 12 = -3*v. Let 4 + 0*z + 2*z - 6 - 4*z**2 - 2*z**v + 6*z**2 = 0. Calculate z.
-1, 1
Let -2/3*j**4 + 2/3*j - 2/3*j**3 - 4/3 + 2*j**2 = 0. What is j?
-2, -1, 1
Let d(h) be the first derivative of h**3/4 - 3*h**2 + 12*h + 14. Factor d(w).
3*(w - 4)**2/4
Let a(y) be the first derivative of -4/9*y**2 + 2/27*y**3 + 3 + 8/9*y. Factor a(z).
2*(z - 2)**2/9
Let g(h) be the third derivative of 3*h**8/112 - h**7/10 - h**6/4 + 7*h**5/5 - h**4 - 6*h**2. Determine x, given that g(x) = 0.
-2, 0, 1/3, 2
Suppose 4*s - s - 5*i = 14, 0 = 3*i + 3. Suppose q - 4*u - 2 = 0, 8 = s*q + q - 2*u. Suppose 2*g**3 - g + g - 1 + g**4 - q*g = 0. What is g?
-1, 1
Let o be 3 + (-4)/(-12)*(-8)/1. Determine s so that 1/3*s**2 + 0*s - o = 0.
-1, 1
Let v be (-3)/(-12)*(0 + 8). Let u = 4 - v. Factor 2*o**5 + 0 - 3/2*o**4 + 0*o**u + 0*o + 1/4*o**3.
o**3*(2*o - 1)*(4*o - 1)/4
Let h(i) = i**2 + 2*i + 1. Let l be h(-1). Let n(m) = m**3 - m**2 - m + 8. Let a be n(l). Factor a*j**2 - j - 3 + 0 + 1 - 5*j.
2*(j - 1)*(4*j + 1)
Let j = 2 + 4. Let b(z) = -2*z**5 - 12*z**4 - 4*z**3 + 10*z**2 - 4. Let x(c) = -c**4 + c**2 - c - 1. Let o(f) = j*x(f) - b(f). Suppose o(v) = 0. Calculate v.
-1, 1
Let f(q) be the first derivative of q**7/315 - q**6/90 + q**4/18 - q**3/9 - q**2/2 + 4. Let v(z) be the second derivative of f(z). Factor v(g).
2*(g - 1)**3*(g + 1)/3
Let f(j) be the third derivative of 1/9*j**3 - 1/90*j**6 + 1/504*j**8 + 1/315*j**7 - 4*j**2 + 0*j + 0 + 1/36*j**4 - 1/45*j**5. Factor f(x).
2*(x - 1)**2*(x + 1)**3/3
Let a(p) be the second derivative of -1/20*p**5 + 0*p**4 + 0 + 1/6*p**3 - 2*p + 0*p**2. Factor a(m).
-m*(m - 1)*(m + 1)
What is n in 2*n**3 + 24*n**4 - 1 - 14*n - 2*n**3 + 16*n**5 - 7*n**3 - 23*n**2 + 5*n = 0?
-1, -1/4, 1
Let u(j) be the third derivative of -j**5/105 - j**4/21 - 17*j**2. Find y, given that u(y) = 0.
-2, 0
Let o = 4 + -1. Let o*d - d + 4*d**2 - 2*d**2 = 0. What is d?
-1, 0
Let h = 96 + -191/2. Find y, given that 2*y - 3/2*y**2 - h = 0.
1/3, 1
Let i = 182 - 180. Factor -3/5*m**3 + 3/5*m - 6/5 + 6/5*m**i.
-3*(m - 2)*(m - 1)*(m + 1)/5
Let -7*l**3 + 6*l**2 - 4/7*l**4 + 4/7*l + 15/7*l**5 - 8/7 = 0. What is l?
-2, -2/5, 2/3, 1
Let i(o) be the first derivative of 2*o**6/135 + o**5/90 + o**3/3 + 7. Let c(u) be the third derivative of i(u). What is r in c(r) = 0?
-1/4, 0
Let k(o) = 20*o**5 - 14*o**4 - 34*o**3 + 8*o**2 - 24*o. Let d(l) = l**5 - l**4 - l**3 - l. Let h(j) = -44*d(j) + 2*k(j). Factor h(u).
-4*u*(u - 1)**4
Let i(w) be the third derivative of -5*w**8/336 + w**7/14 + 5*w**6/24 - w**5/4 - 5*w**4/6 + 2*w**2. Solve i(v) = 0 for v.
-1, 0, 1, 4
Let h(s) be the second derivative of -1/55*s**5 + 5/66*s**4 - 1/33*s**6 + 7*s + 2/33*s**3 + 0*s**2 + 0. Determine x so that h(x) = 0.
-1, -2/5, 0, 1
Let j(s) = s**3 - s**2 - s - 1. Let d(f) = 12*f**3 - 34*f**2 + 86*f - 138. Let o(y) = -d(y) + 10*j(y). Factor o(m).
-2*(m - 4)**3
Let r(m) be the second derivative of m**7/189 + m**6/27 + 7*m**5/90 - m**4/54 - 8*m**3/27 - 4*m**2/9 - 13*m. Solve r(u) = 0 for u.
-2, -