 2
What is h in -32*h - 23*h**3 - 23*h**4 + 7 - 54*h**4 + 73*h**2 + 49*h**5 - 3 + 6*h**3 = 0?
-1, 2/7, 1
Determine c, given that 0 + 0*c - 2/9*c**4 + 2/9*c**2 - 2/9*c**3 + 2/9*c**5 = 0.
-1, 0, 1
Suppose 12 = -3*b + 6. Let k(l) = 33*l**2 + 69*l + 15. Let q(j) = -8*j**2 - 17*j - 4. Let n(u) = b*k(u) - 9*q(u). Factor n(w).
3*(w + 2)*(2*w + 1)
Let i(o) = -6*o**2 + 26*o**2 + 1 - 23*o - 4 - 11. Let y(v) = -7*v**2 + 8*v + 5. Let k(j) = -6*i(j) - 17*y(j). Suppose k(c) = 0. Calculate c.
1
Let a(w) be the second derivative of w**4/54 + w**3/9 + 2*w**2/9 + 3*w. Solve a(z) = 0.
-2, -1
Let v(p) = p**4 + p**3 - p + 1. Let s(h) = 4*h**4 + 16*h**3 - 16*h + 12. Let o(g) = -s(g) + 8*v(g). What is z in o(z) = 0?
-1, 1
Suppose -635 = -2*s - 3*s. Let z = 891/7 - s. Determine k so that z*k - 2/7*k**3 + 4/7 + 2/7*k**4 - 6/7*k**2 = 0.
-1, 1, 2
Let r be 2/3*(-18)/(-12). Let c = r - -3. Find z such that 0 + 5/6*z**2 - 1/6*z**c + 1/6*z**5 - 1/3*z - 1/2*z**3 = 0.
-2, 0, 1
Let a = -8 - -8. Let r(o) be the third derivative of -1/72*o**4 + 1/90*o**5 + 0*o - o**2 - 1/360*o**6 + 0*o**3 + a. Find g, given that r(g) = 0.
0, 1
Factor 10*b**2 - 2*b**2 - b + 0*b - 3*b.
4*b*(2*b - 1)
Let n(f) be the second derivative of -f**4/84 + f**3/21 - f**2/14 - 5*f. Factor n(x).
-(x - 1)**2/7
Suppose -25*l = -34*l + 27. Suppose -3/4*s + 0 - 3/4*s**l + 3/2*s**2 = 0. Calculate s.
0, 1
Let t(c) be the third derivative of c**7/210 - c**6/90 + c**3/2 + c**2. Let m(w) be the first derivative of t(w). Let m(f) = 0. Calculate f.
0, 1
Let s(u) be the third derivative of -u**7/630 - u**6/180 + u**5/15 - 7*u**4/36 + 5*u**3/18 + 39*u**2. Suppose s(l) = 0. What is l?
-5, 1
Suppose -1 + 4 = w - 3*c, -4*w = -c - 34. Let o = w - 5. Find t such that 9*t - 9*t**o + t**4 - 4*t**3 - 2*t - t**5 - 2*t**5 + 2 + 6*t**2 = 0.
-1, -2/3, 1
Factor 3/5*u - 6/5*u**2 - 3/5*u**3 + 6/5.
-3*(u - 1)*(u + 1)*(u + 2)/5
Let n(i) be the second derivative of i**7/840 - i**6/240 - i**5/20 + 7*i**4/12 + 4*i. Let s(t) be the third derivative of n(t). Solve s(q) = 0.
-1, 2
Suppose 0 = 4*l - 5*l - j - 2, j = -2*l + 1. Factor -9*w**4 + 7*w**l - 3*w**3 + 7*w**4.
-2*w**3*(w - 2)
Let t = -3689/30 - -123. Let y(b) be the third derivative of -t*b**5 + 1/6*b**4 - 1/3*b**3 + 0*b + b**2 + 0. Factor y(u).
-2*(u - 1)**2
Let i(t) = t**2. Let f(b) = 5*b**2 - 12*b + 18. Let r(y) = f(y) - 3*i(y). Determine l, given that r(l) = 0.
3
Let g(n) = -3*n**2 + n. Let v(m) = 5*m**2 - 3*m. Let b(l) = 7*g(l) + 3*v(l). Factor b(p).
-2*p*(3*p + 1)
Suppose -5*q + 2 + 26 = n, 2*n - 6 = 0. Suppose -g = q*w - 10, -3*g = -w + 1 + 1. Factor 2*d + d**3 + d**3 + w*d**2 - 6*d**2.
2*d*(d - 1)**2
Let g = 3 - 3. Suppose 4*p = -g*p + 12. Factor -2*c**2 - c**p + 0*c**2 + 0*c - c + 4*c**2.
-c*(c - 1)**2
Factor 10*k + 4 - 2*k**2 - 6*k**3 - 2*k - 2*k**4 - 2*k.
-2*(k - 1)*(k + 1)**2*(k + 2)
Let n(p) = -p + 11. Let w be n(9). Factor -23*k**w + k**5 + 23*k**2 + k - 2*k**3.
k*(k - 1)**2*(k + 1)**2
Determine m, given that -m**4 + 8*m**3 - 110*m - m**4 + 118*m - 12*m**2 - 2 = 0.
1
Let w(s) be the first derivative of -3*s**5/10 + 39*s**4/32 - 15*s**3/8 + 21*s**2/16 - 3*s/8 - 12. Determine x so that w(x) = 0.
1/4, 1
Let a be (4/(-112))/(-1) - 1/(-4). Factor -a*h**3 + 0*h**2 + 0 + 2/7*h.
-2*h*(h - 1)*(h + 1)/7
Let b(s) be the first derivative of -s**5 - 15*s**4/4 - 5*s**3 - 5*s**2/2 - 2. Factor b(y).
-5*y*(y + 1)**3
Determine x, given that -10*x**3 + 0*x**2 - 2*x**3 + 2*x**5 + 8*x**2 + 2*x**5 = 0.
-2, 0, 1
Let b(t) be the third derivative of 0*t - t**2 + 1/840*t**8 + 0*t**5 + 0 + 0*t**4 + 1/300*t**6 + 0*t**3 - 2/525*t**7. What is u in b(u) = 0?
0, 1
Let a(x) be the first derivative of -x - 1/7*x**2 - 4 - 1/42*x**4 + 2/21*x**3. Let n(j) be the first derivative of a(j). Find u such that n(u) = 0.
1
Let t(h) = 3*h**5 + 13*h**4 + 3*h**3. Let w(v) = -v**5 - 4*v**4 - v**3. Suppose 44 = -5*z + 2*z + p, 80 = -5*z + 5*p. Let i(o) = z*w(o) - 4*t(o). Factor i(q).
2*q**3*(q + 1)**2
Let p(s) be the second derivative of 3*s**5/130 - s**4/39 - s**3/13 + 2*s**2/13 - 3*s. Determine t, given that p(t) = 0.
-1, 2/3, 1
Let b(g) be the third derivative of -g**7/2016 - 7*g**6/2880 - g**5/240 - g**4/4 + 6*g**2. Let i(t) be the second derivative of b(t). Factor i(p).
-(p + 1)*(5*p + 2)/4
Let l = -176 - -176. Factor -2/3*p**5 - 14/9*p**4 + 0*p - 2/9*p**2 + l - 10/9*p**3.
-2*p**2*(p + 1)**2*(3*p + 1)/9
Let p(a) be the first derivative of 1 + 7/9*a**3 + 1/3*a + 5/6*a**2 + 1/4*a**4. Factor p(y).
(y + 1)**2*(3*y + 1)/3
Factor -4*x**4 + 4*x**2 - 8*x**2 + 2*x**3 + 6*x**4.
2*x**2*(x - 1)*(x + 2)
Let n(l) be the second derivative of 2*l**7/63 + 4*l**6/45 + l**5/15 + 32*l. Factor n(c).
4*c**3*(c + 1)**2/3
Suppose -3*a = -4*r + 7*r - 12, -5*a - 2*r = -17. Let m(q) be the first derivative of -2*q**a - 2/5*q**5 + 1 + 3/2*q**4 + 0*q + q**2. Factor m(d).
-2*d*(d - 1)**3
Let k(o) be the first derivative of 0*o**2 - 3 + 1/12*o**4 - 1/18*o**6 + 0*o - 1/15*o**5 + 1/9*o**3. Factor k(j).
-j**2*(j - 1)*(j + 1)**2/3
Suppose -2/7*n**4 + 0*n**3 + 0*n + 0 + 2/7*n**2 = 0. Calculate n.
-1, 0, 1
Let c(a) = -a**2 - 4*a + 4. Let l(z) = -3 + z**2 + z + 4 - 2 + 0. Let i(w) = c(w) + 4*l(w). Factor i(b).
3*b**2
Let w(p) be the third derivative of -p**8/168 + p**7/70 + p**6/60 + 5*p**2. Factor w(z).
-z**3*(z - 2)*(2*z + 1)
Let y(q) be the third derivative of -q**5/180 + 11*q**4/72 + 2*q**3/3 + 36*q**2. Factor y(m).
-(m - 12)*(m + 1)/3
Let d(a) be the first derivative of a**6/1800 + a**5/300 + a**4/120 - 2*a**3/3 - 2. Let o(y) be the third derivative of d(y). Factor o(c).
(c + 1)**2/5
Let x be 16/4 - (-1148)/(-330). Let l = x - 4/33. Solve 0 + 2/5*u + l*u**2 = 0.
-1, 0
Factor 6*w**4 + 10*w + 11*w**3 - w**4 + 8*w**3 + w**3 + 25*w**2.
5*w*(w + 1)**2*(w + 2)
Solve 15 - 10 - 2*f**3 + 10*f - 2*f**2 - 8 - 3 = 0 for f.
-3, 1
Let k be (-1)/8 + (-5)/((-6600)/205). Let x(l) be the first derivative of 0*l - 8/55*l**5 - 3/11*l**4 - 8/33*l**3 - k*l**6 + 1 - 1/11*l**2. Factor x(u).
-2*u*(u + 1)**4/11
Suppose -4 = -5*q + 6. Factor -1/3*p**q - 10/3*p**3 - 25/3*p**4 + 0 + 0*p.
-p**2*(5*p + 1)**2/3
Suppose 1 = -2*d + 7. Let b = 830/2709 + -8/387. What is m in 0 + 0*m - b*m**4 - 4/7*m**d - 2/7*m**2 = 0?
-1, 0
Suppose -4*m - 28 = 4. Let j(x) = -5*x**3 + 2*x**3 - 9*x + 5 + 2*x. Let u(h) = 5*h**3 + 11*h - 8. Let s(g) = m*j(g) - 5*u(g). Factor s(c).
-c*(c - 1)*(c + 1)
Let u(i) = -i**3 + i**2 - 1. Suppose 0 = -6*z + 10*z + 40. Let a(f) = 206*f**3 - 514*f**2 + 240*f - 22. Let s(o) = z*u(o) - a(o). Determine v so that s(v) = 0.
2/7, 2
Let s(o) = 4*o**2 - 27*o + 39. Let v(l) = -4*l**2 + 28*l - 40. Let a(z) = 4*s(z) + 3*v(z). Suppose a(c) = 0. What is c?
3
Let u = 333 + -7991/24. Let t(q) be the second derivative of 1/40*q**6 + u*q**3 + 0 + 5/48*q**4 - 2*q + 7/80*q**5 + 0*q**2. Solve t(k) = 0 for k.
-1, -1/3, 0
Suppose 2*d - 4*v + 9*v = -12, -5*d - v + 16 = 0. Let z(k) = -1 - k - 3 + d. Let l(h) = 2*h**2 + 5*h. Let g(w) = -l(w) - 5*z(w). Factor g(x).
-2*x**2
Let l = -1 - -3. Suppose -8*y**2 + 10*y**3 - 8*y**4 + 2*y**3 + 5*y + l*y**5 - 3*y = 0. Calculate y.
0, 1
Factor 10*s + 5/3*s**2 + 25/3.
5*(s + 1)*(s + 5)/3
Suppose -5*f - c = -0*c + 3, 3 = 5*f - c. Factor f*q + 0 + 0*q**2 - 1/3*q**5 - 2/3*q**4 - 1/3*q**3.
-q**3*(q + 1)**2/3
Suppose 0 = 2*b + 3*m + 10 + 5, 4*m = -2*b - 20. Let f(j) be the second derivative of j + 1/60*j**5 + b - 1/36*j**4 - 1/18*j**3 + 1/6*j**2. Factor f(q).
(q - 1)**2*(q + 1)/3
Let d be (1 - -3) + -1 - -2. Let z = 8 - d. Factor -3*x**3 + 18*x**5 + z*x**4 + 3*x**4 - 7*x**3 + 2*x**2 + 0*x**3.
2*x**2*(x + 1)*(3*x - 1)**2
Let m(u) be the third derivative of u**8/336 + u**7/105 - u**5/30 - u**4/24 - 8*u**2. Factor m(i).
i*(i - 1)*(i + 1)**3
Let t(b) = b**3 - 9*b**2 + 9*b - 4. Let j be t(8). Suppose 3*w**2 - 3/2*w**j + 0*w**3 - 3/2 + 0*w = 0. Calculate w.
-1, 1
Let s(h) be the third derivative of 0*h - 1/210*h**7 - 1/60*h**5 + 0 + 5*h**2 - 1/60*h**6 + 0*h**3 + 0*h**4. Suppose s(b) = 0. Calculate b.
-1, 0
Let l(s) be the third derivative of s**8/10080 + s**7/2268 + s**6/1620 + s**4/6 - 7*s**2. Let u(r) be the second derivative of l(r). Solve u(f) = 0.
-1, -2/3, 0
Let t(d) be the third derivative of -1/180*d**5 + 0*d**4 - 2*d**2 + 0 + 1/180*d**6 + 0*d**3 - 1/630*d**7 + 0*d. Factor t(z).
-z**2*(z - 1)**2/3
Let x(z) be the second derivative of -z**4/12 + 11*z**3