 y**6/20 - 22*y**2. What is c in k(c) = 0?
-2/3, 0, 1
Let g(r) be the first derivative of r**7/7 + 2*r**6/15 - 3*r**5/10 - r**4/3 + 6*r + 6. Let b(h) be the first derivative of g(h). Suppose b(d) = 0. Calculate d.
-1, -2/3, 0, 1
Let y = -3/26 - -47/182. Let k(v) be the first derivative of -2/7*v**3 + 2 + 4/7*v + y*v**2. Suppose k(q) = 0. What is q?
-2/3, 1
Let v(d) be the second derivative of -3/7*d**2 + 0 - 3/28*d**4 - 4*d - 5/14*d**3 + 3/140*d**5 + 1/70*d**6. Solve v(j) = 0.
-1, 2
Let p(q) be the third derivative of q**7/280 + q**6/160 - q**5/80 - q**4/32 + 15*q**2. Solve p(c) = 0 for c.
-1, 0, 1
Let s be 0*9/135 - (-4)/18. Factor -s + 2/3*v + 2/9*v**3 - 2/3*v**2.
2*(v - 1)**3/9
Let l = 331 + -1653/5. Factor -l*b**4 + 0*b**3 + 1/5*b + 2/5*b**2 - 1/5*b**5 + 0.
-b*(b - 1)*(b + 1)**3/5
Factor 10/3*f + 4/3 + 8/3*f**2 + 2/3*f**3.
2*(f + 1)**2*(f + 2)/3
Let n = 9/5 - 7/5. Find g, given that 1/5*g**2 + 1/5 - n*g = 0.
1
Let d(z) be the third derivative of -z**6/24 - z**5/6 + 5*z**4/8 - 4*z**2 - 9. Factor d(u).
-5*u*(u - 1)*(u + 3)
Let q(b) be the third derivative of b**7/70 + 3*b**6/40 + b**5/20 - 3*b**4/8 - b**3 - 4*b**2 + 3. Factor q(z).
3*(z - 1)*(z + 1)**2*(z + 2)
Let b(t) be the third derivative of -t**7/315 + t**5/90 + 5*t**2. Factor b(f).
-2*f**2*(f - 1)*(f + 1)/3
Factor 2/9*n**3 - 2/9*n + 0 + 0*n**2.
2*n*(n - 1)*(n + 1)/9
Let i(g) be the first derivative of g**4/12 + g**3/9 - 9. Find x such that i(x) = 0.
-1, 0
Suppose -2 = -2*g - l, 3 + 1 = 4*g + 5*l. Let n be ((-2 - g) + 3)/2. Factor -2/3*b**3 + n + 2/3*b**2 + 0*b.
-2*b**2*(b - 1)/3
Let v(l) be the first derivative of 2*l**5/5 - l**4 + 2*l**2 + l - 6. Let n(y) be the first derivative of v(y). Find m, given that n(m) = 0.
-1/2, 1
Let x(w) = -21*w**5 + 21*w**4 - 36*w**3 + 66*w**2 - 39*w + 9. Let i(k) = -k**5 + k**3. Let l(j) = -18*i(j) + x(j). Factor l(o).
-3*(o - 3)*(o - 1)**4
Let i = 19 - 17. Suppose -3*n = -l + 5, 4*n - 5*n = l - 5. Factor -p**3 + 0 + 0*p**4 + n*p**i + 1/2*p**5 + 1/2*p.
p*(p - 1)**2*(p + 1)**2/2
Let o(c) be the third derivative of c**6/600 + c**5/300 + 5*c**2. Factor o(p).
p**2*(p + 1)/5
Let c(l) be the third derivative of -l**8/3024 - 2*l**7/945 + l**6/540 + l**5/45 - l**4/24 - 37*l**2. Let c(y) = 0. Calculate y.
-3, 0, 1
Let y be (-583)/(-77) - 3/(-3). Factor -24/7 - 54/7*m**2 - 3/7*m**4 + 3*m**3 + y*m.
-3*(m - 2)**3*(m - 1)/7
Let c(t) be the first derivative of 2*t**5/55 - t**4/22 - 2*t**3/33 + t**2/11 + 14. Let c(j) = 0. What is j?
-1, 0, 1
Let y(r) = -15*r - 90. Let p be y(-6). Factor -2/7*d**2 + p*d + 2/7.
-2*(d - 1)*(d + 1)/7
Let i(v) be the second derivative of v**4/36 - 2*v**3/9 + 2*v**2/3 + 6*v. Factor i(z).
(z - 2)**2/3
Let o(b) = -10*b**3 - 2*b - 4. Let p(y) = -y**3 - y**2 + y - 1. Let l(w) = -o(w) + 8*p(w). Determine g so that l(g) = 0.
1, 2
Let k(x) be the first derivative of 2*x**5/75 + x**4/15 - 2*x**3/15 - 4*x**2/15 + 8*x/15 - 6. What is a in k(a) = 0?
-2, 1
What is f in -108/5*f**2 + 0 + 36/5*f**3 + 108/5*f - 4/5*f**4 = 0?
0, 3
Let x = -10 + 13. Suppose 1 = 2*i - x. Determine b so that 0 - 66/5*b**3 - 4*b**i - 16*b**4 - 2/5*b - 32/5*b**5 = 0.
-1, -1/4, 0
Let h = -5/8 + 37/40. Let j(c) be the first derivative of h*c**2 + 0*c**3 - 3/20*c**4 + 0*c + 2. Determine a so that j(a) = 0.
-1, 0, 1
Let 0*n**3 + 8/3 + 0*n - 10/3*n**2 + 2/3*n**4 = 0. Calculate n.
-2, -1, 1, 2
Suppose -2*l = 4*m - l - 16, -3*m = 5*l - 12. Let o(t) be the second derivative of 0*t**2 + 1/54*t**m - 2/27*t**3 + 3*t + 0. Factor o(d).
2*d*(d - 2)/9
Suppose 2*i + 472 = 4*i. Suppose f + f - i = 0. Determine l so that 8*l + f*l**3 + 55*l**4 + 33*l**2 + 23*l**2 + 15*l**4 = 0.
-1, -2/5, -2/7, 0
Suppose 2 = 5*p - 4*p. Let d(j) = -6*j - 3. Let a(t) = -t**2 - 7*t - 4. Let x(g) = p*d(g) - 3*a(g). Factor x(k).
3*(k + 1)*(k + 2)
Let w = -1 - -2. Determine z so that 18*z**3 - 3*z**2 + 1 - 27*z**4 + 12*z**5 - w = 0.
0, 1/4, 1
Suppose -2/3*b**5 + 0 + 0*b - 2/3*b**2 - 2*b**4 - 2*b**3 = 0. Calculate b.
-1, 0
Find j such that -21/4*j**5 + 4*j**2 + 0 + j - 1/4*j**3 - 17/2*j**4 = 0.
-1, -2/7, 0, 2/3
Let n be (-272)/51*(-18)/4. Let h = 24 - n. Factor h - 2/3*s + 1/3*s**2.
s*(s - 2)/3
Let f(g) = -g**2 - 7*g + 21. Let w be f(-9). Let b(s) be the first derivative of -1/2*s**4 + 0*s**w + 0*s + s**2 + 2. Factor b(y).
-2*y*(y - 1)*(y + 1)
Suppose 21 = 5*c - 4*k, 0 = 3*c - 2*c + k - 6. Factor -28/5*p**3 - 12/5*p**2 - 6/5*p**c + 2/5 - 22/5*p**4 + 2/5*p.
-2*(p + 1)**4*(3*p - 1)/5
Suppose -4/3*p**5 + 4*p + 4*p**4 - 8/3*p**2 - 4/3 - 8/3*p**3 = 0. What is p?
-1, 1
Let z(t) be the first derivative of 1 - t + 3/2*t**2 + 1/4*t**4 - t**3. Determine u so that z(u) = 0.
1
Suppose 60 = d + 11*d. Determine c so that 10/9*c**4 + 2*c**3 + 2/9*c**d + 0 + 14/9*c**2 + 4/9*c = 0.
-2, -1, 0
Let g be 27/5 - 3/(-5). Factor -g*o**2 - 2*o**2 - 11*o**4 + 10*o**3 - 1 - 2*o**2 + 6*o**4 + 5*o + o**5.
(o - 1)**5
Let m(t) be the second derivative of t**5/5 - t**4 + 8*t**2 - 10*t. Let m(a) = 0. What is a?
-1, 2
Let q(y) be the third derivative of 0 + 0*y**4 - 2*y**2 - 1/60*y**6 - 1/20*y**5 + 1/6*y**3 + 0*y. Factor q(v).
-(v + 1)**2*(2*v - 1)
Let p = -13 - -14. Let x(c) be the first derivative of -p - 9/10*c**5 - 37/6*c**3 + 15/4*c**4 + 5*c**2 - 2*c. Factor x(k).
-(k - 1)**2*(3*k - 2)**2/2
Determine o, given that 1/2*o**3 + 5/2*o + 1 + 2*o**2 = 0.
-2, -1
Let i(b) = -b**3 + 7*b**2 - 12*b + 13. Let k be i(5). Solve -2/3*q**k + 1/3*q**4 + 2/3*q - 1/3*q**2 + 0 = 0.
-1, 0, 1, 2
Let l(m) be the second derivative of 4*m**6/15 - m**4/8 - m**3/24 + 15*m. Factor l(x).
x*(2*x - 1)*(4*x + 1)**2/4
Let m = -2 + 2. Suppose -3*z - 13 = -5*x, -3*x + 0*x - z + 5 = m. Factor 0*a**x - 1/2 + 1/2*a**4 - a + a**3.
(a - 1)*(a + 1)**3/2
Let v(m) be the third derivative of -1/6*m**3 - m**2 + 0*m**5 + 0 + 0*m**4 + 0*m**6 + 1/1260*m**7 + 0*m. Let n(a) be the first derivative of v(a). Factor n(k).
2*k**3/3
What is m in 0 - 2/3*m**2 + m**3 - 1/3*m**4 + 0*m = 0?
0, 1, 2
Let c(q) be the first derivative of -6 + 10*q**2 - 8/3*q**3 - 2/3*q**6 - 8*q + 16/5*q**5 - 4*q**4. What is l in c(l) = 0?
-1, 1, 2
Solve 0*n + 0 + 1/6*n**2 - 1/6*n**5 - 1/2*n**3 + 1/2*n**4 = 0.
0, 1
Let d be (1/(-2))/(-4 + (-35)/(-20)). Find m such that 2/9*m**4 - 4/9*m + 0 + 2/3*m**3 - d*m**5 - 2/9*m**2 = 0.
-1, 0, 1, 2
Let m(z) = -z**2 - 5*z + 4. Let c be m(-5). Suppose -5*i + a = -92, c*a + a + 46 = 2*i. Factor 4*s - i*s**3 + 15*s - 4 + 0*s + 14*s**4 - s - 10*s**2.
2*(s - 1)**2*(s + 1)*(7*s - 2)
Let y(o) be the first derivative of -o**7/420 + 7*o**6/720 - o**5/80 + 7*o**3/3 - 6. Let z(b) be the third derivative of y(b). Suppose z(r) = 0. Calculate r.
0, 3/4, 1
Let k(o) = -18*o**2 - 12*o + 2. Let q(j) = 18*j**2 + 12*j - 1. Let t(c) = 3*k(c) + 4*q(c). Factor t(i).
2*(3*i + 1)**2
Determine n so that -4/3*n**2 + 20/3*n - 8 = 0.
2, 3
Suppose 0 = 3*x + 3*k - 6, 4*x = 3*k + 30 - 8. Suppose -2*o - 4 = -x*o. Solve -1/4*g**o - g - 1 = 0 for g.
-2
Let x(k) be the third derivative of 1/100*k**5 + 0 + 4*k**2 + 0*k**3 + 0*k + 0*k**4. Factor x(b).
3*b**2/5
Factor -3/2*s - 3/4 - 3/4*s**2.
-3*(s + 1)**2/4
Determine w so that 2*w**4 + 73*w**2 - w**5 - 43*w**3 + 9*w**4 + 16*w - 72*w + 16 + 0*w**4 = 0.
1, 4
Factor 3*v**3 - 2*v**3 - 2*v**3 + 7 - 3 - 3*v**2.
-(v - 1)*(v + 2)**2
Let b be (-20)/28*(-12)/30. Determine p, given that 0*p + 0 + 4/7*p**2 + b*p**3 = 0.
-2, 0
Suppose -6*m + 20 = -4. Let k(p) be the second derivative of -5/42*p**m - 4/21*p**3 + 0 + 1/7*p**2 - 3*p. Determine l, given that k(l) = 0.
-1, 1/5
Determine n, given that -2*n**4 + 10*n**3 + 18*n - 18*n**2 + 5*n - 4 - 10*n + n = 0.
1, 2
Factor -2/11*i**3 + 2/11*i - 4/11*i**2 + 4/11.
-2*(i - 1)*(i + 1)*(i + 2)/11
Let d(w) be the first derivative of -1/2*w**2 + 1 + 0*w + 1/330*w**5 + 1/132*w**4 - 2/33*w**3. Let f(p) be the second derivative of d(p). Solve f(c) = 0 for c.
-2, 1
Let x(k) = k**3 - 21*k**2 + 21*k - 20. Let c be x(20). Factor 3/4*p + 3/4*p**2 + c.
3*p*(p + 1)/4
Factor p**2 + p**3 - 162 - p**4 - p + 162.
-p*(p - 1)**2*(p + 1)
Factor 18*a + 4*a**2 - 7*a - 15*a.
4*a*(a - 1)
Suppose -2*h - 3*h = -1625. Let x = -967/3 + h. Let -98/3*o**2 - 56/3*o - x = 0. Calculate o.
-2/7
Let i(u) be the second derivative of u**7/42 - u**6/15 - 3*u**5/20 + 2*u**4/3 - 2*u**3/3 - 4*u. Factor i(c).
c*(c - 2)*(c - 1)**2*(c + 2)
Suppose -y + 2*y = 2*o, -3*o + 7 = 2*y. Factor 1/2