*2/11
Suppose 1 + 3 = 4*x. Suppose -5*i = -u - 32, -u + x = 4*i - 21. Let c(n) = -4*n**2 - 5. Let k(q) = -7*q**2 - q - 9. Let g(y) = i*k(y) - 10*c(y). Solve g(j) = 0.
-2, -1
Let h(c) = -27*c**3 + 291*c**2 + 21*c. Let s(f) = 5*f**3 - 58*f**2 - 4*f. Let k(b) = -4*h(b) - 21*s(b). Determine t, given that k(t) = 0.
-18, 0
Let b(s) = s**3 + 7*s**2 + 3*s + 1. Let g(h) = h**3 + h**2 - 3*h - 1. Let o(u) = -b(u) - g(u). Let o(c) = 0. Calculate c.
-4, 0
Let z(j) be the third derivative of j**8/2520 - j**6/90 + 2*j**5/45 - j**4/12 - j**3/6 + 16*j**2. Let p(i) be the first derivative of z(i). Factor p(k).
2*(k - 1)**3*(k + 3)/3
Let a(l) be the second derivative of -l**4/54 + 2*l**3/9 - 8*l**2/9 + l - 13. Factor a(u).
-2*(u - 4)*(u - 2)/9
Find t, given that 19368*t**2 + 22188*t**3 + 837*t**5 - 43 - 341 + 4608*t + 2147*t**4 + 5611*t**4 = 0.
-4, -2/3, 2/31
Let g = -328 + 326. Let c be g/2*11/((-891)/72). Solve 5/9*d**2 + 4/9*d**4 + c*d**3 + 1/9*d + 0 = 0.
-1, -1/2, 0
Let y(u) be the second derivative of u**7/210 - u**6/60 + u**2 + 16*u. Let z(q) be the first derivative of y(q). Factor z(n).
n**3*(n - 2)
Let 1/3*n**2 - 14*n + 0 = 0. Calculate n.
0, 42
Suppose -11*g + 14*g + 4*b = -24, 3*b = -18. Factor 0*w + g - 4/5*w**2.
-4*w**2/5
Let z be -8*(2 + 3/(-2)). Let y = z + 6. Factor -4*l + 2*l**2 - l**3 + 3*l**2 - 7*l**y + 3*l**3.
2*l*(l - 2)*(l + 1)
Suppose 3*j = 2*g + 9, 0*j = -3*g + 3*j - 6. Determine h, given that -h**4 + 2*h - h**4 + 2*h**g + 6*h**2 + 2*h**3 + 8 - 18*h = 0.
-2, 1, 2
Let j(y) be the third derivative of -11*y**8/3360 - y**7/80 + y**6/240 - 5*y**5/12 - 6*y**2 + 3*y. Let k(a) be the third derivative of j(a). Factor k(v).
-3*(v + 1)*(22*v - 1)
Let o(c) be the third derivative of -1/210*c**7 + 0*c**3 + 0*c + 0 + 16*c**2 + 1/60*c**6 - 1/60*c**5 + 0*c**4. Factor o(n).
-n**2*(n - 1)**2
Let v(s) be the first derivative of -s**4/20 + s**3/3 + 14*s**2/5 - 32*s/5 + 473. Solve v(x) = 0.
-4, 1, 8
Let u be 188/(-28) + 7 + (-2)/(-42). Let a(v) be the second derivative of u*v**3 + 1/12*v**4 + 0 + 1/2*v**2 - 5*v. Factor a(k).
(k + 1)**2
Suppose -k + 16 = k. Factor 6 + 12*g**2 - 3*g**4 - 4 + 2*g**4 - k*g**3 + 3*g**4 - 8*g.
2*(g - 1)**4
Suppose 0 = -4*f + 13 + 15. Suppose 7*i = 2*i - 2*n + 4, -5*n - f = 4*i. Solve h**i + 2*h + 4*h**2 - 6*h**2 - 1 = 0.
1
Let o be ((-7)/((-98)/12))/(4/8). Factor -o*d**2 + 24/7*d**3 + 0 - 20/7*d**4 + 2/7*d + 6/7*d**5.
2*d*(d - 1)**3*(3*d - 1)/7
Let c(b) be the first derivative of -13 - 1/10*b**4 - 2/5*b**3 + 6/5*b + 1/5*b**2. Find k, given that c(k) = 0.
-3, -1, 1
Let m(n) = 2*n + 23. Let r(q) = q**3 + 8*q**2 - 8*q - 1. Let z be r(-9). Let b be m(z). Factor 0*g**b + 5*g**3 + 30*g**2 + 18*g**2 + 6 - 26*g**3 - 33*g.
-3*(g - 1)**2*(7*g - 2)
Let j(h) be the first derivative of -h**6/60 + h**5/40 + h**4/8 - h**3/12 - h**2/2 - 7*h + 12. Let g(o) be the first derivative of j(o). Solve g(c) = 0.
-1, 1, 2
Let t(v) = -4*v + 70. Let q be t(17). Let n = -11/7 + q. Determine s so that 18/7*s**2 + 13/7*s**4 + s + n*s**5 + 1/7 + 22/7*s**3 = 0.
-1, -1/3
Let y(t) = 13*t**3 - 29*t**2 - 72*t + 216. Let p(o) = 20*o**3 - 44*o**2 - 108*o + 324. Let n(g) = -5*p(g) + 8*y(g). Determine k so that n(k) = 0.
-3, 3
Let i(n) be the second derivative of -n**5/90 + 59*n**4/54 - 58*n**3/27 + 3*n - 1. Factor i(d).
-2*d*(d - 58)*(d - 1)/9
Factor 4/13*l**3 + 20/13*l + 2/13*l**4 - 2*l**2 + 0.
2*l*(l - 2)*(l - 1)*(l + 5)/13
Let o(a) be the first derivative of a**6/24 - a**5/8 - 5*a**4/48 + 5*a**3/12 - 10*a + 3. Let y(r) be the first derivative of o(r). Factor y(c).
5*c*(c - 2)*(c - 1)*(c + 1)/4
Let t(a) = 4*a**2 - 2*a - 2. Let n be t(1). Find i such that 0*i + n*i**2 + 0 + 0*i**3 + 3/4*i**4 - 1/4*i**5 = 0.
0, 3
Suppose w + 2*r - 3 = -6, w - 3*r = 12. Factor -2*c**2 + 0*c**2 - 2*c**3 + 4*c**w.
2*c**2*(c - 1)
Let n(c) = -c**3 + 16*c**2 - c + 18. Let i be -3 - -7 - -11 - -1. Let j be n(i). Factor -1/4*p**j + 1/4*p**3 - 1/2*p + 0.
p*(p - 2)*(p + 1)/4
Let r(g) be the first derivative of -48*g - 4*g**3 + 4 + 87*g**2 + 3*g**3 - 75*g**2. Factor r(y).
-3*(y - 4)**2
Suppose 2*o = -2*r - o + 8, 4*o = -3*r + 12. Factor 6*z**2 - 3*z**r + 1 - 5*z**3 - 8*z**2 - 1.
-z**2*(z + 1)*(3*z + 2)
Factor -52*v**4 + 2355*v**3 + 2*v**4 + 5*v**5 - 2310*v**3.
5*v**3*(v - 9)*(v - 1)
Let z(m) = -m**2 - m - 1. Let i(c) = 7*c**2 - 4*c + 31. Let j = 30 + -31. Let d(v) = j*i(v) - 6*z(v). Factor d(a).
-(a - 5)**2
Let k(l) be the second derivative of l**7/21 + l**6/45 - l**5/3 - 4*l**4/9 - 46*l. Suppose k(h) = 0. Calculate h.
-4/3, -1, 0, 2
Let u(z) = 9*z**4 - 140*z**3 + 830*z**2 + 2100*z + 1125. Let d(v) = 35*v**4 - 560*v**3 + 3320*v**2 + 8400*v + 4500. Let l(j) = 4*d(j) - 15*u(j). Factor l(q).
5*(q - 15)**2*(q + 1)**2
Let d(t) = t**2 - t. Let w(k) = 11*k**2 + 19*k + 6. Let h(c) = -12*d(c) + 3*w(c). Factor h(y).
3*(y + 3)*(7*y + 2)
Let h(j) be the third derivative of -j**9/5040 + j**7/840 - j**4/8 + 10*j**2. Let s(w) be the second derivative of h(w). Suppose s(a) = 0. Calculate a.
-1, 0, 1
Let q(w) = w**2 + 3*w. Let n be q(-3). Suppose n = -5*h + k + 11, 2*k - k = -5*h + 9. Solve 0*z - 1/4 + 1/4*z**h = 0.
-1, 1
Let i(q) = 28*q**2 + 13*q - 7. Let o(m) = -10*m - 19*m**2 - 281 + m + 286. Let n(v) = 5*i(v) + 7*o(v). What is w in n(w) = 0?
-2/7, 0
Let q(v) = v**5 - 3*v**4 + 6*v**2 - 2. Let b(m) = -m**2 + 1. Let s = -14 + 11. Let k be -9 + (-1 - -3) - -1. Let w(c) = k*b(c) + s*q(c). Factor w(h).
-3*h**2*(h - 2)**2*(h + 1)
Let g(t) be the third derivative of 12*t**2 + 0*t + 0 - 1/210*t**6 + 2/21*t**3 + 1/35*t**5 - 1/14*t**4. Determine r so that g(r) = 0.
1
Let d be 2/(-8)*((-152)/30 - -5). Let j(m) be the third derivative of 0*m + 1/150*m**5 + 0 + d*m**4 - 2*m**2 - 2/15*m**3. Factor j(b).
2*(b - 1)*(b + 2)/5
Suppose -11 = -5*k - 4*b - 35, -4*b - 24 = -4*k. Factor 5/7*a**3 - 1/7*a**4 - 4/7*a**2 + k*a + 0.
-a**2*(a - 4)*(a - 1)/7
What is y in y**5 - 42*y**2 + 13*y**2 - 46*y**2 + 6*y**4 + 36*y + 8*y**5 - 75*y**3 - 9*y**2 = 0?
-2, 0, 1/3, 3
Suppose 0 = -5*t + 60 - 0. Let w = -9 + t. Determine m, given that -5 + w*m**2 + 4 + 1 = 0.
0
Let m(o) = -33*o**3 - 160*o**2 - 96*o. Let t(c) = 8*c**3 + 40*c**2 + 24*c. Let u(b) = -2*m(b) - 9*t(b). Suppose u(z) = 0. Calculate z.
-6, -2/3, 0
Suppose 0 = 5*o - 2*n - 19, 0 = -5*o - 0*n + 3*n + 21. Let v(j) be the first derivative of -4 + 1/4*j**2 + 0*j - 1/6*j**o. Factor v(x).
-x*(x - 1)/2
Suppose -6*x = x - 1792. Factor -3*j**2 - x - 107 + 0*j**2 - 66*j.
-3*(j + 11)**2
Let c(r) = -r**3 + r - 4. Let j be (-2 - 1)*8/(-3). Suppose -5*b = -j - 2. Let f(o) = -o - 1. Let u(x) = b*f(x) - c(x). Factor u(h).
(h - 1)**2*(h + 2)
Let r = -312 - -633/2. Suppose -3/2*q**2 + 3/2*q**4 + 3*q - r*q**3 + 0 + 3/2*q**5 = 0. What is q?
-2, -1, 0, 1
Let s(m) = -14*m**2 - 252*m + 15129. Let c(p) = 9*p**2 + 250*p - 15129. Let w(g) = 3*c(g) + 2*s(g). Factor w(t).
-(t - 123)**2
Let v be 6/(-4 + 1) - -4. Suppose -2*i + 18 = v*h, -i - i - 2 = -2*h. Factor 2*u**5 - 9*u**4 + 9*u**4 + i*u**4.
2*u**4*(u + 2)
Suppose 0*i**2 + 6/7*i**4 + 0*i + 3/7*i**5 + 3/7*i**3 + 0 = 0. What is i?
-1, 0
Let r(o) be the third derivative of o**8/588 - o**6/21 + 3*o**4/14 - 149*o**2. Determine m, given that r(m) = 0.
-3, -1, 0, 1, 3
Let q = 142898/11 - 12990. Suppose 0 - 6/11*f**3 + q*f**5 - 10/11*f**4 - 2/11*f + 10/11*f**2 = 0. What is f?
-1, 0, 1/4, 1
Suppose -4*l - 124 - 94 = -c, 5*l + 277 = -c. Let r = l + 57. Solve -2/3 + 2/9*y**3 - 10/9*y**r + 14/9*y = 0 for y.
1, 3
Let a(j) = -7*j**4 + 5*j**3 - 32*j**2 + 4. Let r(s) = 2*s**4 - s**3 + 3*s**2 - 1. Let g(c) = 5*a(c) + 20*r(c). Let g(o) = 0. Calculate o.
-5, 0, 4
Suppose 6/5*t**4 - 26*t - 10*t**2 - 36/5 + 10*t**3 = 0. Calculate t.
-9, -1, -1/3, 2
Let a be 17/(2380/42) - 27/(-10). Let l(k) be the first derivative of -1/5*k**3 - 12/5*k - 6/5*k**2 + a. Determine y so that l(y) = 0.
-2
Let m = -47 - -70. Suppose 15*s + 3*l + m = 19*s, 2*s - 14 = 2*l. Factor 2/9*w**3 + 4/9*w**s + 0 - 2/3*w.
2*w*(w - 1)*(w + 3)/9
Let h(g) = 5*g**4 + 3*g**3 + g**2 - 3*g - 6. Let m = -104 - -105. Let i(x) = x**4 - 1. Let f(j) = m*h(j) - 4*i(j). Determine w so that f(w) = 0.
-2, -1, 1
Let j(y) be the first derivative of 33/32*y**4 + 9/8*y**3 - 3/8*y**2 + 9 + 0*y. Factor j(b).
3*b*(b + 1)*(11*b - 2)/8
Let q(b) be the second derivative of b**7/273 - 7*b**6/195 + 3*b**5/26 - 3*b**4/26 - 4*b. Solve q(x) =