*c - 5439.
-5*(c - 39)**2
Suppose 16*p = 9*p + 14. Let q(f) be the first derivative of 1 - 2*f + 1/3*f**3 - 1/2*f**p. Factor q(v).
(v - 2)*(v + 1)
Let q(w) be the second derivative of 12*w + 0 + 7*w**2 + 1/6*w**4 - 8/3*w**3. Factor q(h).
2*(h - 7)*(h - 1)
Let v(o) be the second derivative of -o**7/252 + o**6/18 - 7*o**5/30 - o**4/9 + 32*o**3/9 - 32*o**2/3 + 8*o + 7. What is s in v(s) = 0?
-2, 2, 4
Let i(j) = -13*j**3 + 757*j**2 - 17672*j - 5. Let t(z) = -72*z**3 + 4164*z**2 - 97196*z - 28. Let k(q) = 28*i(q) - 5*t(q). Let k(n) = 0. Calculate n.
0, 47
Factor -6*x**2 + 9*x**2 + 36*x**2 - 7*x**3 - 90*x + 4*x**3.
-3*x*(x - 10)*(x - 3)
Factor 74/3*j - 50/3 - 1/6*j**3 - 47/6*j**2.
-(j - 2)*(j - 1)*(j + 50)/6
What is p in -2/7*p**4 - 20/7*p**3 - 120/7*p - 74/7*p**2 - 72/7 = 0?
-3, -2
Let s(y) be the first derivative of -59*y**4/14 + 76*y**3/7 - 51*y**2/7 - 8*y/7 - 125. Find w, given that s(w) = 0.
-4/59, 1
Let h(z) be the first derivative of -1/30*z**6 + 0*z**2 - 10*z - 1/12*z**4 - 1/10*z**5 - 1 + 0*z**3. Let v(s) be the first derivative of h(s). Factor v(c).
-c**2*(c + 1)**2
Let s = -12 - -14. Factor 12*i**4 + 22*i**3 - s*i**4 + 5*i**5 - 17*i**3.
5*i**3*(i + 1)**2
Let x(n) = -n**3 + 14*n**2 + 53*n + 6. Let m be x(-3). Let r(p) be the first derivative of 2/45*p**5 + 2/9*p**3 + 4 + m*p + 1/9*p**2 + 1/6*p**4. Factor r(b).
2*b*(b + 1)**3/9
Suppose 0 = -h - 2*h - 2*c - 6, 4*h - 5*c - 15 = 0. Suppose -20 = -57*o + 47*o. Suppose -2/3*g**o + h + 2/3*g**3 - 4/3*g = 0. What is g?
-1, 0, 2
Suppose 710 - 203 = -5*q - 3*y, 5*y - 311 = 3*q. Let k = q + 105. Factor 0*v**k + 1/3*v + 2/3*v**2 + 0 - 1/3*v**5 - 2/3*v**4.
-v*(v - 1)*(v + 1)**3/3
Let t be (-1)/4*2/((-330)/335). Let o = t + 8/33. Factor -3/4*a**2 + 3/4*a**3 - o*a + 3/4.
3*(a - 1)**2*(a + 1)/4
Let w = 1/85 - -248/595. Find n such that w*n**2 + 9/7 + 12/7*n = 0.
-3, -1
Let a(f) = -8*f**2 + 5*f - 8. Let r = -2140 - -2136. Let w(j) = 2*j - j**2 - 3 - j**2 - j**2. Let l(s) = r*a(s) + 11*w(s). Determine b so that l(b) = 0.
1
Let z(l) = 4*l**2 - 23*l + 16. Suppose -5*p - 9 + 49 = 0. Let f(c) = 2*c**2 - 17*c**2 + 3*c**2 - 48 + 68*c. Let b(v) = p*z(v) + 3*f(v). Factor b(j).
-4*(j - 4)*(j - 1)
Suppose 5*s = 2 + 23. Let q(t) be the first derivative of -4/15*t**s + 0*t**3 + 0*t + 0*t**4 - 2/9*t**6 + 0*t**2 + 8. Determine j, given that q(j) = 0.
-1, 0
Let d = 10489/6 + -1743. Let g = d - 343/78. Factor 4/13 + 18/13*z**2 - 14/13*z - g*z**3 + 2/13*z**4.
2*(z - 2)*(z - 1)**3/13
Let i(l) = -16 + 16*l + 26*l**3 - 7*l**2 - 14*l**2 - 5*l**2 + 0*l**2. Let w(a) = 5*a**3 - 5*a**2 + 3*a - 3. Let c(r) = 3*i(r) - 16*w(r). Factor c(g).
-2*g**2*(g - 1)
Let g be -3 - (2 - 3 - (-2483)/(-143))/2. Factor -16/11 + 18/11*c**2 + g*c.
2*(c + 4)*(9*c - 2)/11
Let a(m) be the first derivative of 0*m**4 - 8/3*m**3 + 0*m**2 + 4*m + 9 + 4/5*m**5. Let a(v) = 0. What is v?
-1, 1
Factor -1/8*c**2 - 1/8*c + 1/4.
-(c - 1)*(c + 2)/8
Let b = 1/131 + 259/393. Let a be 3 - (1 - (-4)/3). Let 0*z + b*z**3 + 2/3*z**2 + 0 - 2/3*z**5 - a*z**4 = 0. What is z?
-1, 0, 1
Let y(g) be the first derivative of -g**3/7 + 69*g**2/14 + 731. Factor y(v).
-3*v*(v - 23)/7
Let x(l) = 2 - 1 - 9 + 4*l - 2*l. Let o be x(6). Factor -o*q**2 - 4*q**3 + 3*q**4 + 7*q**3 + q**2 - 3*q**5.
-3*q**2*(q - 1)**2*(q + 1)
Let i be -5*(-5)/((-500)/(-8)). Let z = 12/25 + -2/25. Factor -i*n**4 - z*n**3 + 2/5*n + 2/5*n**2 + 0.
-2*n*(n - 1)*(n + 1)**2/5
Suppose 10*m = -10*m + 1260. Let v = m + -181/3. Determine u so that 10/9*u**2 + 0 - 2/9*u - 34/9*u**4 + 2/9*u**3 - v*u**5 = 0.
-1, 0, 1/4, 1/3
Let f be 4 + ((-533)/164 - (-10)/8). Determine s so that -4/3*s**5 - 2*s**2 + f*s**4 + 0 + 2/3*s + 2/3*s**3 = 0.
-1, 0, 1/2, 1
Let r = 1020/83 - 243301/1245. Let q = -183 - r. Determine h, given that -4/15*h - 2/15 - q*h**2 = 0.
-1
Suppose -26 = -4*j + q + q, -j = -3*q - 14. Suppose j*w + w = 5*w. Let 1/2*r**5 + 0*r**4 + 0*r**2 + w - r**3 + 1/2*r = 0. Calculate r.
-1, 0, 1
Let w(t) = 4*t. Let p be w(1). Let 2*a**4 + a**4 - 2*a + a**p - 4*a**2 + 0*a**5 + 2*a**5 = 0. Calculate a.
-1, 0, 1
Let y(n) be the first derivative of n**6/33 - 3*n**4/22 - 4*n**3/33 + 69. Factor y(c).
2*c**2*(c - 2)*(c + 1)**2/11
Let y be 8*(26 + (-1442)/56). Factor -2/5*d + 4/15 + 2/15*d**y.
2*(d - 2)*(d - 1)/15
Suppose -20/3*x - 2/3*x**2 - 50/3 = 0. What is x?
-5
Let v(g) be the second derivative of g**7/21 + 2*g**6/15 - g**5/5 - 2*g**4/3 + g**3/3 + 2*g**2 + 333*g. Determine d, given that v(d) = 0.
-2, -1, 1
Let j(f) be the first derivative of -5/6*f**6 - 1125/2*f**2 - 405*f - 34 - 75/2*f**4 + 15*f**5 - 950/3*f**3. Let j(x) = 0. Calculate x.
-1, 9
Let g(u) be the third derivative of -1/60*u**6 + 1/420*u**7 + 0*u**3 + 1/24*u**5 - 16*u**2 - 1/24*u**4 + 0*u + 0. Determine b, given that g(b) = 0.
0, 1, 2
Let f(j) be the third derivative of 12*j**2 + 0*j + 0 + 0*j**4 - 1/21*j**7 + 1/15*j**6 - 2/75*j**5 + 0*j**3. Determine m, given that f(m) = 0.
0, 2/5
Let l(y) be the third derivative of -1/9*y**3 + 1/90*y**5 + 0 - 19*y**2 - 1/60*y**6 + 1/12*y**4 + 0*y. Let l(w) = 0. What is w?
-1, 1/3, 1
Let s(o) be the second derivative of -8/15*o**3 + 0 - o - 1/15*o**4 - 6/5*o**2. Factor s(f).
-4*(f + 1)*(f + 3)/5
Let x = 508/3 + -168. Let s be 4/(-10) - (1 - (-78)/(-45)). Let -x - 4/3*k - s*k**2 = 0. Calculate k.
-2
Suppose 2*x + 8 = 0, -4*x - 64 = -4*t - 6*x. What is c in -28*c**2 - 25*c**3 + 4*c**3 - t*c - 41*c**2 = 0?
-3, -2/7, 0
Let h(r) = -r**2 - 6*r - 6. Let m be h(-4). Let k = -33 - -33. Factor m*s - 2*s**2 + 0*s**2 + k*s**2.
-2*s*(s - 1)
Let t(p) be the second derivative of 20*p**4/3 - 22*p**3 + 20*p**2 + 70*p. Find b such that t(b) = 0.
2/5, 5/4
Find v, given that 15129 - 4*v**2 + 246*v + 4*v**2 - 5*v**2 - 6*v**2 + 12*v**2 = 0.
-123
Let f(y) be the third derivative of -5*y**8/336 - y**7/7 - 5*y**6/24 + 5*y**5/3 + 15*y**4/2 + 40*y**3/3 + 161*y**2. Find c, given that f(c) = 0.
-4, -2, -1, 2
Solve 0 + 5*a - 1/3*a**3 + 14/3*a**2 = 0 for a.
-1, 0, 15
Let q(t) be the second derivative of -1/54*t**4 - 1/27*t**3 + 0 + 0*t**2 + 8*t. What is w in q(w) = 0?
-1, 0
Let y(q) be the first derivative of -q**6/21 + 2*q**4/7 - 254. Suppose y(k) = 0. Calculate k.
-2, 0, 2
Let n(q) be the third derivative of q**6/30 + 47*q**5/105 + 5*q**4/3 - 16*q**3/7 - 14*q**2 + 2*q. Find l, given that n(l) = 0.
-4, -3, 2/7
Let u(g) be the third derivative of g**6/80 + 9*g**5/40 + 15*g**4/16 - 25*g**3/4 - 31*g**2 + 1. Solve u(y) = 0.
-5, 1
Factor -26*p**3 + 0 - 1/3*p**4 - 676*p**2 - 17576/3*p.
-p*(p + 26)**3/3
Let h(x) = 17*x**3 + 43*x**2 - x - 1. Let b(n) be the second derivative of -2*n**5/5 - 7*n**4/4 + n**2/2 - 16*n. Let m(k) = 5*b(k) + 2*h(k). Factor m(f).
-(f + 3)*(2*f + 1)*(3*f - 1)
Let q = 368 + -368. Let h(p) be the second derivative of -1/50*p**5 + 1/30*p**3 + 1/210*p**7 + 0*p**2 + 0*p**4 + 0*p**6 + 4*p + q. Factor h(k).
k*(k - 1)**2*(k + 1)**2/5
Let z(s) be the second derivative of s**9/30240 - s**8/4480 + s**7/2520 + 19*s**4/12 + 11*s. Let h(d) be the third derivative of z(d). Factor h(w).
w**2*(w - 2)*(w - 1)/2
Suppose -140*c = -137*c - 2*n - 1, 3*c + 4*n - 43 = 0. Factor -2/9*f**c + 2/9*f**4 + 0*f + 0*f**2 + 4/9*f**3 + 0.
-2*f**3*(f - 2)*(f + 1)/9
Let j(h) be the first derivative of -4*h**5/5 - 32*h**4 - 81. Find u such that j(u) = 0.
-32, 0
Let z be 13 - (17 + 148)/15. Suppose d**4 + 6*d - 5*d**z + 0 + 1/3*d**5 - 7/3*d**3 = 0. Calculate d.
-3, 0, 1, 2
Let w(q) = 11*q**5 - 8*q**4 - 10*q**3 + 7*q**2 + 2*q - 2. Let d(h) = -9*h**5 + 7*h**4 + 10*h**3 - 8*h**2 - 3*h + 3. Let o(s) = -3*d(s) - 2*w(s). Factor o(r).
5*(r - 1)**3*(r + 1)**2
Let p(q) = -q**3 - 9*q**2 - 12*q - 31. Let m be p(-8). Let k(j) = -1. Let x(z) = 33*z**3 - 27*z**2 - 72*z - 15. Let w(b) = m*x(b) - 3*k(b). Factor w(y).
3*(y - 2)*(y + 1)*(11*y + 2)
Find y, given that -9*y**2 - 5*y**3 + 24*y**2 + 91*y - 101*y = 0.
0, 1, 2
Let q = -1/29 - -65/203. Let v = 11362/7 + -1623. Suppose 1/7 + q*n + v*n**2 = 0. What is n?
-1
Suppose 26 + 10 = 9*k. Let m(t) = 3*t**3 - 35*t**2 - 503*t - 2201. Let u(r) = r**3 + r**2 + r - 1. Let h(i) = k*u(i) - m(i). Factor h(l).
(l + 13)**3
Let 6/17*z - 12/17*z**2 + 2/17*z**3 + 20/17 = 0. What is z?
-1, 2, 5
What is l in 561/4*l - 93/4*l**2 + 2601/4 + 3/4*l**3 = 0?
-3, 17
Solve -9*o + 240*o**2 + 26 - 266*o**2 + 11*o - 2*o**3 = 0 for o.
-13, -1, 1
Let k = 2027/4046 + -2/2023.