- 35*h = 0. What is h?
-2, -1, 1
Find r, given that -172*r**3 + 72*r**3 + 80*r**3 - 12*r**2 + 4*r + 4 - 8*r**4 = 0.
-1, 1/2
Let h(z) be the third derivative of z**7/350 + z**6/40 + 9*z**5/100 + 7*z**4/40 + z**3/5 + 78*z**2. Find o such that h(o) = 0.
-2, -1
Let w = -1039 + 1039. Factor w - 1/5*c**4 - c**2 + 4/5*c**3 + 2/5*c.
-c*(c - 2)*(c - 1)**2/5
Let a(s) be the first derivative of 7*s - 3/5*s**5 - 3 + 0*s**4 + 3/2*s**2 + 3/2*s**3. Let t(m) be the first derivative of a(m). Let t(r) = 0. What is r?
-1/2, 1
Suppose 48*a = 105*a. Factor -1/2*w + 1/2*w**3 + 0 + a*w**2.
w*(w - 1)*(w + 1)/2
Let z(u) be the second derivative of -u**6/30 - 21*u**5/20 - 10*u**4 - 50*u**3/3 + 121*u. Suppose z(c) = 0. Calculate c.
-10, -1, 0
Let z be (8/26)/(-2) - (-28)/13. Factor -3*g**z - g + 2 + 84*g**4 + 2*g - g**3 - 83*g**4.
(g - 2)*(g - 1)*(g + 1)**2
Suppose -1455*v**4 + 2916*v**4 - 96*v**2 - 100*v - 28*v**3 - 34 - 1459*v**4 = 0. Calculate v.
-1, 17
Suppose -5*b - 7 = -107. Factor 0*r**4 - 4*r**4 - 12*r**3 + b*r**3.
-4*r**3*(r - 2)
Let d(t) = 29*t**2 + 44*t - 6. Let m(x) = -4*x**2 + x + 1. Let k(s) = -d(s) - 6*m(s). Factor k(u).
-5*u*(u + 10)
Let o(j) = j**2 + 2*j - 15. Let d be o(-5). Let b(m) be the first derivative of d*m**2 + 0*m + 2/15*m**3 + 1/20*m**4 - 5. Factor b(g).
g**2*(g + 2)/5
Suppose -j - 5*i = -30, i = -1 + 6. Suppose -4*u - j = -13. Determine c so that -4/7*c**u + 0 + 2/7*c**3 + 2/7*c = 0.
0, 1
Let a(b) = -b**3 + 34*b + 14. Let n be a(6). Find x, given that 3/2*x**n + 3/2*x + 0 = 0.
-1, 0
Let i = -6708/5 - -1342. Factor 2/15 + 2/15*z**3 + i*z**2 + 2/5*z.
2*(z + 1)**3/15
Let 18/11*x**4 - 10/11*x**2 + 2/11*x + 0 + 6/11*x**3 = 0. What is x?
-1, 0, 1/3
Let w(p) be the second derivative of -p**4/2 + 55*p**3/3 + 38*p**2 + p - 16. Let w(g) = 0. Calculate g.
-2/3, 19
Let m(c) be the third derivative of 0*c**3 + 46*c**2 + 1/350*c**7 + 1/30*c**4 + 0 + 0*c - 1/120*c**6 - 1/75*c**5. Find p, given that m(p) = 0.
-1, 0, 2/3, 2
Let f be 21/(-4)*8/(-3). Let a = f - 12. Determine u so that -4*u**2 - u**2 + 2*u**2 + u**a = 0.
0
Let l be 10/15*-3*-2. Factor -l*s**4 - 15*s - 21*s**2 - 3*s**5 + s**4 + 9*s - 27*s**3 - 12*s**4.
-3*s*(s + 1)**3*(s + 2)
Let o(h) be the first derivative of 0*h + 0*h**2 + 8 + 0*h**3 - 1/2*h**4. Factor o(d).
-2*d**3
Suppose -5*w - 2 = 5*u - 17, 2*u - 8 = -w. Let j(s) be the first derivative of 0*s + 5 + 1/20*s**u - 1/12*s**3 - 1/16*s**4 + 1/8*s**2. Let j(k) = 0. What is k?
-1, 0, 1
Let c(x) be the second derivative of x**6/90 - 2*x**5/15 + 2*x**4/3 - 2*x**3 - 13*x. Let t(u) be the second derivative of c(u). Find g, given that t(g) = 0.
2
Suppose 4*f - 5 = 7. Factor -9*v**f - 3*v + 4*v + 5*v + 15*v**2.
-3*v*(v - 2)*(3*v + 1)
Find s, given that -261*s + 77 + 32*s**2 + 672*s**3 + 178*s**4 - 445*s**4 - 537*s + 11*s**4 + 21 = 0.
-1, 1/8, 7/4
Let m(c) be the second derivative of -c**6/120 - c**5/40 - 5*c**3/6 - c. Let o(n) be the second derivative of m(n). Suppose o(i) = 0. What is i?
-1, 0
Let c = 29940 + -29937. What is a in 8/7*a**2 + 4/7 - 2/7*a**c - 10/7*a = 0?
1, 2
Let m(c) be the first derivative of c**5/35 - 9*c**4/28 + 8*c**3/7 - 8*c**2/7 + 36. Factor m(y).
y*(y - 4)**2*(y - 1)/7
Let d(f) be the first derivative of -f**4/21 + 2*f**3/7 - 4*f**2/7 + 3*f - 11. Let m(y) be the first derivative of d(y). Factor m(c).
-4*(c - 2)*(c - 1)/7
Suppose 0*j = -9*j + 27. Factor -15*p**2 - 4*p**3 - 3*p**3 - 9*p + 7*p**3 - 3*p**3 + j*p**4.
3*p*(p - 3)*(p + 1)**2
Let w = -72 - -92. Suppose w = -4*u + 20. Determine n so that 2/3*n**3 + 0*n**2 - 2/3*n + u = 0.
-1, 0, 1
Factor -26/5*g + 1/5*g**5 - 8/5 - 29/5*g**2 - 11/5*g**3 + 1/5*g**4.
(g - 4)*(g + 1)**3*(g + 2)/5
Let g(c) be the first derivative of -27/2*c**2 + 3/4*c**4 + 2 - 15*c - 3*c**3. Factor g(f).
3*(f - 5)*(f + 1)**2
Let w(m) be the third derivative of -m**7/15120 - m**6/540 - m**5/45 + m**4/12 - 10*m**2. Let o(x) be the second derivative of w(x). Factor o(h).
-(h + 4)**2/6
Let f(p) be the first derivative of p**6/480 + p**5/120 + p**4/96 + 16*p**3/3 - 34. Let k(s) be the third derivative of f(s). Factor k(l).
(l + 1)*(3*l + 1)/4
Let d = -29 + 30. Suppose -4*s = 5*i + 15, 5*s + 34 = 2*i + 7. Factor -r**2 + d + i - r**2.
-2*(r - 1)*(r + 1)
Factor -2*z**2 - 1071 + 0*z**2 + 535*z + 7*z**2 + 1071.
5*z*(z + 107)
What is f in -6/11*f**3 + 24/11*f + 0 + 32/11*f**2 = 0?
-2/3, 0, 6
Let p(h) be the first derivative of -h**6/18 + 6*h**5/5 - 97*h**4/12 + 16*h**3 - 32*h**2/3 - 14. Find y, given that p(y) = 0.
0, 1, 8
Factor 78*r**2 + 16877*r**3 + 60*r + 14 + 2 + 6*r**4 - 16837*r**3.
2*(r + 1)**2*(r + 4)*(3*r + 2)
Let h(z) be the first derivative of -z**6/240 + z**4/48 + 5*z**2/2 - 3. Let q(v) be the second derivative of h(v). Factor q(b).
-b*(b - 1)*(b + 1)/2
Let s be (-4)/(-5) - 143/195. Let t(u) be the third derivative of -1/15*u**5 + 0*u**4 - s*u**6 + 0*u + 0 - 2/105*u**7 + 0*u**3 - 4*u**2. Factor t(n).
-4*n**2*(n + 1)**2
Let z(b) = -b. Let u(v) = 10*v**2 + 20*v + 4. Suppose 5*f - 5*s = 185, -4*s + 22 = -f + 2*f. Let g = -28 + f. Let c(m) = g*z(m) + u(m). Let c(j) = 0. What is j?
-1, -2/5
Let t(r) = 6*r + 30. Let i be t(-5). Let f(b) = b**3 - b + 2. Let g be f(0). Let -2/3*w**5 + i - 2/9*w**g - 14/9*w**4 + 0*w - 10/9*w**3 = 0. What is w?
-1, -1/3, 0
Let z = 3787 + -26506/7. Let 0 + 18/7*k + z*k**2 = 0. What is k?
-6, 0
Factor -32*v + 1/2*v**2 + 512.
(v - 32)**2/2
Let h(x) be the third derivative of -11*x**5/90 - 7*x**4/72 + x**3/9 + 22*x**2. Suppose h(m) = 0. What is m?
-1/2, 2/11
Let k(n) be the second derivative of -27*n**5/20 + 5*n**4/2 + 17*n**3/2 - 3*n**2 - 40*n. Let k(v) = 0. Calculate v.
-1, 1/9, 2
Let n(c) = 24*c**2 - 25*c**2 + 5*c**5 - 3*c**5 - 3*c**5. Let k(b) = -b**5 - 10*b**3 - 22*b**2 - 15*b - 4. Let u(p) = 3*k(p) - 6*n(p). Factor u(m).
3*(m - 4)*(m + 1)**4
Let z be 0/((36/30)/((-21)/(-35))). Factor -9/5*k**3 - 3/5*k**4 + 3/5*k**2 + z + 9/5*k.
-3*k*(k - 1)*(k + 1)*(k + 3)/5
Let i(b) be the second derivative of b**7/105 + b**6/15 + 3*b**5/25 - b**4/15 - 7*b**3/15 - 3*b**2/5 + 2*b + 39. Factor i(s).
2*(s - 1)*(s + 1)**3*(s + 3)/5
Suppose 177*l = 190*l - 39. Factor 0 - 3/8*b**4 + 3/8*b**2 - 3/8*b + 3/8*b**l.
-3*b*(b - 1)**2*(b + 1)/8
Let c(s) be the second derivative of 2*s**6/15 + 59*s**5/5 - 20*s**4 + 169*s. Solve c(p) = 0.
-60, 0, 1
Let c(n) be the first derivative of n**4/20 - 13*n**3/15 + 23*n**2/10 - 11*n/5 + 289. Find r, given that c(r) = 0.
1, 11
Let l(b) be the second derivative of -5/12*b**4 - 10*b**2 + 25/6*b**3 - 29*b + 0. Factor l(f).
-5*(f - 4)*(f - 1)
Let i = -40 + 42. Suppose k + 3*k = i*q - 12, 5*k = -q - 8. Determine j so that 2/9*j + 4/9*j**q - 4/9 - 2/9*j**3 = 0.
-1, 1, 2
Let a(m) be the second derivative of 2/195*m**6 + 1/39*m**3 + 0 + 0*m**2 - 1/39*m**4 + 4*m + 0*m**5 - 1/273*m**7. Factor a(f).
-2*f*(f - 1)**3*(f + 1)/13
Let b be (-30)/42 + (-4)/14 - -5. Solve -234*l + 37*l - 50*l**3 + 5*l**b - 73*l + 135 + 180*l**2 = 0.
1, 3
Suppose -4/7*n**4 + 26/21*n**3 + 2/21*n**5 - 8/7*n**2 + 0 + 8/21*n = 0. Calculate n.
0, 1, 2
Let h(k) be the first derivative of 28*k**3/3 - 62*k**2 - 80*k + 62. Let h(q) = 0. Calculate q.
-4/7, 5
Solve 0 - 9/5*s - 1/5*s**2 = 0 for s.
-9, 0
Let b be -3*(0 - 4/66). Let f be 4 + (-5 - ((-171)/(-33))/(-3)). Factor -f*i**2 + 0 - 8/11*i**4 - b*i**5 - 2/11*i - 12/11*i**3.
-2*i*(i + 1)**4/11
Let x(t) = -t + 16. Let z be x(18). Let v be (z/(-4))/(6/48). Factor -u**v + 3*u + 6*u**3 - 3*u - 7*u**3.
-u**3*(u + 1)
Let r(u) be the first derivative of 0*u + 2/9*u**3 - 6 - 1/3*u**2. Determine n, given that r(n) = 0.
0, 1
Let w(l) be the third derivative of 1/60*l**6 + 0 + 7/60*l**5 + 0*l**3 + 0*l - 1/30*l**7 + 35*l**2 - 1/12*l**4. Factor w(n).
-n*(n - 1)*(n + 1)*(7*n - 2)
Let p(i) be the second derivative of i**7/42 - 7*i**6/30 - 27*i**5/20 - 29*i**4/12 - 5*i**3/3 + 472*i. Solve p(k) = 0 for k.
-1, 0, 10
Find f, given that -5915 + 3*f**4 - 6*f**3 + 6*f + 5923 - f**4 - 10*f**2 = 0.
-1, 1, 4
Let z be (1008/210)/(18/40*1). Factor z - 16/3*q + 2/3*q**2.
2*(q - 4)**2/3
Let r(m) be the second derivative of m**6/120 - m**5/20 + m**4/8 - m**3/6 + m**2/8 - 124*m. Find p such that r(p) = 0.
1
Let b = -1781 + 8906/5. Find z, given that 1/5*z**3 - 1/5*z**2 - 1/5*z + b = 0.
-1, 1
Factor 4/15*s - 14/15*s**2 + 2/3*s**3 + 0.
2*s*(s - 1)*(5*s - 2)/15
Let y be 49/28*16/14. Factor -3/2