- 1/(-2). Let l = 533/28 + s. Factor 0 - l*b**4 + 2/7*b**3 + 0*b + 0*b**2.
-2*b**3*(b - 1)/7
Let c(s) be the third derivative of s**7/105 - s**6/15 - s**5/6 - s**2. Find n, given that c(n) = 0.
-1, 0, 5
Let q(s) = -s**3 + 5*s**2 - s + 7. Let l be q(5). Solve 13*c + 0*c + 36*c**l - 5*c = 0.
-2/9, 0
Let u(x) = -2*x**2 + 5*x. Let d(r) = -3*r**2 + 6*r + 1. Let g(a) = -3*d(a) + 4*u(a). Factor g(p).
(p - 1)*(p + 3)
Factor -1/2*i**4 + 0*i**2 - i + i**3 + 1/2.
-(i - 1)**3*(i + 1)/2
Let q(x) be the third derivative of x**6/180 + x**5/45 + 11*x**2. What is a in q(a) = 0?
-2, 0
Let d(i) be the second derivative of 1/2*i**2 + 0 + 1/2*i**3 + 1/4*i**4 + 1/20*i**5 - 3*i. Factor d(m).
(m + 1)**3
Let s be (-1)/(-2)*4 - (3 - 3). Let -2*a**2 + s*a + 2/3*a**3 - 2/3 = 0. Calculate a.
1
Suppose 0 = f - 0 - 3. Let q(z) = z**2 + 9*z + 5. Let o(d) = 3*d**2 + 19*d + 11. Let y(k) = f*o(k) - 5*q(k). Determine b so that y(b) = 0.
-2, -1
Let s(d) be the first derivative of d**6/45 + 8*d**5/75 - d**4/15 - 8*d**3/15 + 3*d**2/5 - 6. What is k in s(k) = 0?
-3, 0, 1
Let s(d) = -d - 1. Let v be s(-3). Suppose 0 = -6*o + 5*o + v. Factor 0 + 4/7*b**o + 0*b**3 - 4/7*b**4 + 2/7*b - 2/7*b**5.
-2*b*(b - 1)*(b + 1)**3/7
Let h(y) be the first derivative of 3/4*y**4 - 3/2*y**2 + 0*y - 3 + 0*y**3. Factor h(g).
3*g*(g - 1)*(g + 1)
Suppose 3*o - 14 = -2. Factor 3*x**3 + 7 - 5*x - 1 - o*x.
3*(x - 1)**2*(x + 2)
Factor -1/6*j + 1/6*j**2 + 0.
j*(j - 1)/6
Let r(i) be the third derivative of i**6/1440 + i**5/480 - i**4/48 - i**3/3 + i**2. Let l(z) be the first derivative of r(z). Factor l(k).
(k - 1)*(k + 2)/4
Suppose 0 = g - 5*i + 1, 3 = 2*g - i - 4. Suppose 5*h - 25 = -2*c - c, -28 = -4*h - g*c. Determine a, given that -a**3 - 2*a**h - 8 + 4*a - 16*a - 4*a**2 = 0.
-2
Suppose -4*a + 3 = -3*a. Factor -1 - 3*q**5 + q**a + 0*q**3 + 1 - 2*q**4.
-q**3*(q + 1)*(3*q - 1)
Determine m so that 3*m**4 + 0*m**2 + m**2 - 4*m**4 + m + 2*m**3 - 3*m**3 = 0.
-1, 0, 1
Let f(c) = c**3 - c - 1. Let a(b) = 5*b**3 + 2*b**2 + 2*b**2 - b - 3 + 0*b**3. Let k(h) = h + 1. Let s be k(-4). Let w(d) = s*f(d) + a(d). Solve w(m) = 0 for m.
-1, 0
Suppose 2*t + 1 + 5 = i, i - 4*t = 0. Let g be i/4*(-2)/(-3). Factor -11*h**4 - 3*h**2 + g*h**4 - 7*h**3 - 3*h**5 - 2*h**3.
-3*h**2*(h + 1)**3
Let n = -4 - -6. Let p be n/4 - (-9)/2. Factor p*i**2 - 2*i - 2*i**3 + 2*i**5 - 5*i**4 + i**5 + i**3.
i*(i - 1)**2*(i + 1)*(3*i - 2)
Let b(c) be the first derivative of -5*c**3/12 - 15*c**2/4 - 25*c/4 - 4. What is t in b(t) = 0?
-5, -1
Let x be (12/30)/(1/5). Let u = x - -11. What is o in -2*o**3 - 11*o**2 + u*o**2 + 2*o**5 + 0*o**3 - 2*o**4 = 0?
-1, 0, 1
Suppose 70 = 2*f + 4. What is u in -25*u**3 + 9*u**3 - 5*u**3 - 6*u + 27*u**5 + f*u**4 - 33*u**2 = 0?
-1, -2/9, 0, 1
Let q(k) be the second derivative of -k**5/70 - 2*k**4/21 - 5*k**3/21 - 2*k**2/7 + 45*k. Determine c so that q(c) = 0.
-2, -1
Factor -2*i - 4 - 3*i**2 + 2*i + 4*i**2.
(i - 2)*(i + 2)
Let q be -8*(7/(-2) - -3). Factor 0*h**3 + 3*h**q + 3 - 5*h**2 - h**2 + 0*h**3.
3*(h - 1)**2*(h + 1)**2
Let w(a) be the second derivative of -a**5/10 + 7*a**4/24 - a**3/6 - a**2/4 - 10*a. Determine n so that w(n) = 0.
-1/4, 1
Let y(m) be the second derivative of m**4/4 - 4*m**3 + 27*m. Find c such that y(c) = 0.
0, 8
Let j = 2473/84 + -202/7. Let m(z) be the second derivative of 0*z**2 - j*z**4 + 1/10*z**5 - 1/3*z**3 - z + 7/30*z**6 + 0. Suppose m(g) = 0. What is g?
-1, -2/7, 0, 1
Let p be (1/2*-1)/(-1). Let r = -73/2 + 37. Factor 0 - p*z**2 + r*z.
-z*(z - 1)/2
Let p(x) be the third derivative of x**8/13440 + x**7/5040 + x**4/12 - x**2. Let o(j) be the second derivative of p(j). Solve o(l) = 0.
-1, 0
Factor 0 + 2/5*h + 2/5*h**2.
2*h*(h + 1)/5
Let l = 226 - 221. Factor -1/2*i + 1/4*i**l + 0 + 3/4*i**4 + 1/4*i**3 - 3/4*i**2.
i*(i - 1)*(i + 1)**2*(i + 2)/4
Let v(i) = -i**2 - i + 1. Let q(o) = -6*o**2 - 2*o + 12. Let h(x) = -q(x) + 8*v(x). Factor h(d).
-2*(d + 1)*(d + 2)
Suppose -g + 16*g = 2*g. Factor 0*q + g + 2/5*q**2.
2*q**2/5
Let c = 279 + -276. Factor -7/4*x**3 + c*x**2 + 0 + x.
-x*(x - 2)*(7*x + 2)/4
Let d = 9 - 5. Factor -2*h**2 + 4 - d + h**3.
h**2*(h - 2)
Let u be (2/(-3))/(14/(-21)). What is p in -3 - p**3 - p**3 + 2*p + 3 + p**4 - u = 0?
-1, 1
Factor 0 - 4/3*l**3 - 8/3*l**2 + 0*l.
-4*l**2*(l + 2)/3
Let y(j) = j**5 - 13*j**4 + 44*j**3 - 90*j**2 + 83*j - 25. Let p(o) = -o**5 + 14*o**4 - 43*o**3 + 90*o**2 - 84*o + 24. Let x(t) = -2*p(t) - 3*y(t). Factor x(m).
-(m - 3)**3*(m - 1)**2
Let r be 2/(-6)*(18 - 24). Solve -1/2*x**4 - 3/2*x**3 - 3/2*x**r - 1/2*x + 0 = 0 for x.
-1, 0
Let c = -655 - -4587/7. Solve 10/7*h**3 + 4/7*h**2 + c*h**5 + 8/7*h**4 + 0 + 0*h = 0.
-2, -1, 0
Let l(t) = t - 43. Let u be l(43). Factor 0*w + 0*w**4 + 0 + u*w**2 + 2/7*w**3 - 2/7*w**5.
-2*w**3*(w - 1)*(w + 1)/7
Let l(m) be the third derivative of 1/8*m**4 + 7*m**2 + 1/3*m**3 + 0*m + 1/60*m**5 + 0. Determine w, given that l(w) = 0.
-2, -1
Let q(f) be the first derivative of -f**3/15 - f**2/5 - f/5 + 5. Suppose q(m) = 0. Calculate m.
-1
Let j(o) = -11*o**4 - 11*o**3 + 5*o**2 - 5. Let q(y) = 6*y**4 + 6*y**3 - 3*y**2 + 3. Let a(s) = 3*j(s) + 5*q(s). Let a(m) = 0. What is m?
-1, 0
Let q(w) = 2*w**5 + 4*w**4 + 4*w**3 - 4*w**2 - 2*w + 4. Let g(u) = 2*u**5 + 4*u**4 + 3*u**3 - 4*u**2 - 2*u + 3. Let r(f) = -4*g(f) + 3*q(f). Factor r(k).
-2*k*(k - 1)*(k + 1)**3
Let g(s) be the second derivative of -2*s**6/15 + 4*s**5/5 - s**4 - 5*s. Let g(x) = 0. Calculate x.
0, 1, 3
Let i(f) be the second derivative of -f**5/190 - 5*f**4/114 - 7*f**3/57 - 3*f**2/19 - 32*f. Factor i(k).
-2*(k + 1)**2*(k + 3)/19
Suppose -4*r + r - 3*z + 12 = 0, -2*r + 2*z = 0. Let p be (-2)/6 - (-119)/51. Let 2*g**2 - 2 - 3*g**r + 3*g**p = 0. Calculate g.
-1, 1
Let l(t) be the third derivative of -t**6/40 + t**5/10 + t**4/8 - t**3 - 2*t**2. Solve l(s) = 0 for s.
-1, 1, 2
Let r(k) be the second derivative of k**6/105 + k**5/70 - k**4/14 - 5*k**3/21 - 2*k**2/7 - 22*k. Factor r(s).
2*(s - 2)*(s + 1)**3/7
Factor -2*d**3 + 0 + 4/3*d**2 + 2/3*d**4 + 0*d.
2*d**2*(d - 2)*(d - 1)/3
Let w = 18002 + -89477/5. Let v = -106 + w. Let v*b**3 + 6/5*b**2 - 3/5*b - 6/5 = 0. What is b?
-2, -1, 1
Let r(z) be the second derivative of -7*z**4/24 - 23*z**3/36 - z**2/6 - 7*z. Find l such that r(l) = 0.
-1, -2/21
Suppose g + 4 = 0, 0 = -2*j - 2*g + g + 2. Factor -4/9*h**2 + 2/9*h**j + 0*h + 0.
2*h**2*(h - 2)/9
Let z(c) = 1. Let s(a) = -a**2 + 3*a + 2. Let t(b) = 3*s(b) - 12*z(b). Factor t(m).
-3*(m - 2)*(m - 1)
Let k be 1/4*(-2 - 46/(-7)). Suppose 0 - 2/7*u**3 - 8/7*u - k*u**2 = 0. What is u?
-2, 0
Let y(h) = 0 + 0 - 2*h**2 - h - 3*h**3. Let c be y(-1). Let -4/3*a + 0 - 2/3*a**c - 2*a**5 + 10/3*a**3 + 2/3*a**4 = 0. What is a?
-1, -2/3, 0, 1
Let h(x) = -11*x**2 - 10*x - 13. Let m(o) = 5*o**2 + 5*o + 6. Let b(w) = -6*h(w) - 13*m(w). Determine c so that b(c) = 0.
0, 5
Let l(m) be the first derivative of m**6/6 - 3*m**5/5 + 3*m**4/4 - m**3/3 + 1. Factor l(t).
t**2*(t - 1)**3
Let 12 + f**2 - 87*f**4 + 2*f**3 - 6*f**3 + 16*f + 86*f**4 = 0. What is f?
-3, -2, -1, 2
Let r(g) be the second derivative of -g**7/2520 + g**6/240 - g**5/60 - g**4/6 + g. Let w(f) be the third derivative of r(f). Suppose w(z) = 0. Calculate z.
1, 2
Let r(o) be the first derivative of -8 + 0*o**2 + 0*o**3 + 3/16*o**4 + 0*o. Factor r(s).
3*s**3/4
Let t(j) = 0*j**4 + 1 + 0*j**2 + 2*j - 3 + 3*j**2 - j**4. Let b(f) = -5*f**4 + f**3 + 13*f**2 + 9*f - 9. Let i(g) = 2*b(g) - 9*t(g). Let i(z) = 0. Calculate z.
0, 1
Let o(r) be the first derivative of 2/5*r**2 - 4 - 2/15*r**3 - 2/5*r. Factor o(b).
-2*(b - 1)**2/5
Let t be (6/8)/((-273)/(-112)). Let -2/13*j**3 + t*j**2 - 2/13*j + 0 = 0. Calculate j.
0, 1
Determine l so that -5*l**2 + 5*l + 2 - 3*l**2 + l**2 = 0.
-2/7, 1
Let m(j) be the first derivative of -2*j**5/25 + 4*j**3/15 - 2*j/5 + 2. Suppose m(w) = 0. Calculate w.
-1, 1
Suppose 10 = -2*j, -2*s - j = 3*s - 15. Let 1/2*r**5 - 1/2*r**2 + 0 + 1/2*r**s - 1/2*r**3 + 0*r = 0. What is r?
-1, 0, 1
Let h be (-4)/(-32) + (171/40 - 4). Factor -h*u**2 + 6/5 - 4/5*u.
-2*(u - 1)*(u + 3)/5
Factor -3*k**4 + 514 - 9*k**3 - 6*k**2 - 514.
-3*k**2*(k + 1)*(k + 2)
Let o(i) be the first derivative of 7*i**5/5 - 5*i**4/4 - 16*i**3/3 - 2*i**2 - 1. Suppose o(h) = 0. Calculate h.
-1, -2/7, 0, 2
Let l(s) = -s**2 - 7*s + 2. Let b be l(-7). Factor b*u**2