p?
0, 1
Let w(x) be the second derivative of x**6/10 + 3*x**5/20 - x**4/2 - x. Determine s so that w(s) = 0.
-2, 0, 1
Let o(t) = 8*t**4 - 2*t**2 - 3*t + 3. Let x(d) = 105*d**4 - 25*d**2 - 40*d + 40. Let g(l) = -40*o(l) + 3*x(l). Solve g(u) = 0.
-1, 0, 1
Suppose -7 = -k - 5*p + 6, 0 = -3*k + 4*p + 1. Let -4*r**4 + 4*r**3 + r**k - 3*r**3 + 2*r**4 = 0. Calculate r.
0, 1
Suppose -5*p = -4*x - 7*p, -x + 2*p = 0. Let -2/3*y**3 + 0 + 1/3*y**2 + 1/3*y**4 + x*y = 0. What is y?
0, 1
Suppose 0*g = -2*g + 2. Let v be g + 0 + 6 + -5. Factor 0 + 1/2*q**v + 1/2*q.
q*(q + 1)/2
Solve 16/5*w**2 - 2/5*w - 4/5 - 2*w**3 = 0.
-2/5, 1
Let b(d) = d**3 + d**2 + d + 1. Let n(c) = -3*c**3 + c**2 - 2*c + 5. Let w(y) = 2*b(y) + n(y). Let r(k) be the first derivative of w(k). Factor r(u).
-3*u*(u - 2)
Let b(s) be the first derivative of 15*s**4/4 + 35*s**3/3 + 25*s**2/2 + 5*s + 20. Factor b(f).
5*(f + 1)**2*(3*f + 1)
Let r(y) be the third derivative of -1/20*y**5 + 1/8*y**4 + 5*y**2 + 0 + y**3 + 0*y. Factor r(o).
-3*(o - 2)*(o + 1)
Suppose 0*d - 32 = -4*d. Let -7*j + 11*j + 6*j**4 - d*j**2 - 4*j**5 + 2*j**4 = 0. What is j?
-1, 0, 1
Let r(b) = -b + 4. Let a be r(3). Factor -7 + 10*d + 2 - a - 3*d**2 - d.
-3*(d - 2)*(d - 1)
Let m(g) be the first derivative of -128*g**3/15 + 48*g**2/5 - 18*g/5 + 23. Factor m(p).
-2*(8*p - 3)**2/5
Let c be (-2)/(-12) + 2/6. Let m be (-6)/4 - (0 + 6/(-3)). Let 0*w**2 + w + c - w**3 - m*w**4 = 0. Calculate w.
-1, 1
Let p(w) be the third derivative of w**9/6048 - w**8/3360 - w**7/1680 + w**6/720 - w**3/6 + w**2. Let l(g) be the first derivative of p(g). Factor l(u).
u**2*(u - 1)**2*(u + 1)/2
Let g be (-174)/(-12) + -8 + -5. Let -g*a**4 + 3/2*a**3 + 0 + 0*a**2 + 0*a = 0. What is a?
0, 1
Let w be 24/(-9) - (-4 + 0). Let i(u) be the second derivative of -7/3*u**3 - 2/15*u**6 + 0 + w*u**4 + 1/21*u**7 - u + 2*u**2 - 1/5*u**5. Factor i(v).
2*(v - 1)**4*(v + 2)
Let p = 1307/88 + -162/11. Determine g so that p*g**2 + 1/2*g + 1/2 = 0.
-2
Let f be ((-44)/(-77))/((-10)/(-7)). Let i(j) be the first derivative of -2/5*j - 1/5*j**4 + 3 + 0*j**3 + 2/25*j**5 + f*j**2. Solve i(w) = 0 for w.
-1, 1
Factor -4/5*f**2 + 0 + 4/5*f**3 + 0*f - 4/5*f**5 + 4/5*f**4.
-4*f**2*(f - 1)**2*(f + 1)/5
Let j = -1 - -7. Suppose -5*y - 3*f + j = 0, 3*f = -4*y + 4*f + 15. Find c such that 4/3*c**2 + 2/3*c + 0 + 2/3*c**y = 0.
-1, 0
Let u(l) be the second derivative of l + 1/10*l**3 + 0 - 3/5*l**2 + 1/20*l**4. Determine c, given that u(c) = 0.
-2, 1
Let x = -20 + 21. Let o(f) be the first derivative of -x - 4*f + f**3 - 1/4*f**4 + 0*f**2. Factor o(l).
-(l - 2)**2*(l + 1)
Let m(u) be the first derivative of -u**4/18 + 3*u - 3. Let j(d) be the first derivative of m(d). Factor j(x).
-2*x**2/3
Suppose 8/9*b**2 + 4/9*b**3 - 2/3 - 4/9*b - 2/9*b**4 = 0. What is b?
-1, 1, 3
Suppose 3*y = -3*y - 0*y. Factor 0*u**2 - 2/7*u**5 + y*u - 8/7*u**3 + 0 + 8/7*u**4.
-2*u**3*(u - 2)**2/7
Let u(t) = -11*t**3 - 5*t**2 + 11*t + 11. Let x(k) = -12*k**3 - 5*k**2 + 12*k + 12. Let y(c) = 7*u(c) - 6*x(c). Determine p so that y(p) = 0.
-1, 1
Let c(u) = u + 4. Let h be c(-2). Suppose -6*s**h + 0*s**3 + 4*s**3 - 2*s - 2*s**3 + 6 = 0. What is s?
-1, 1, 3
What is c in 0 + 4/7*c**5 - 68/7*c**2 - 4*c**4 + 68/7*c**3 + 24/7*c = 0?
0, 1, 2, 3
Let y(i) = -i**3 + 2*i**2 + 3*i - 3. Let r be y(2). What is m in -7*m - m**4 + m**2 - m**3 + m**3 + 8*m - m**r = 0?
-1, 0, 1
Let j = 1 - 0. Let n be (j/3)/(5/30). What is d in -9*d**n - 12*d**3 - 4*d**2 + 3*d + 4*d**2 = 0?
-1, 0, 1/4
Let n(m) be the second derivative of -m**7/105 - m**6/30 + m**4/6 + m**3/3 - 3*m**2/2 + 2*m. Let f(j) be the first derivative of n(j). Factor f(s).
-2*(s - 1)*(s + 1)**3
Let v(k) = 71*k**5 + 144*k**4 + 44*k**3 + 8*k + 8. Let o(z) = -24*z**5 - 48*z**4 - 15*z**3 - 3*z - 3. Let t(r) = -8*o(r) - 3*v(r). Factor t(q).
-3*q**3*(q + 2)*(7*q + 2)
Let o = 3 - 3. Let l = 53 + -50. Solve o - 3/4*x**l + 1/2*x - 1/4*x**2 = 0 for x.
-1, 0, 2/3
Factor 0 + 8/5*x**2 - 4/5*x**3 - 4/5*x.
-4*x*(x - 1)**2/5
Let s(g) be the first derivative of 1/30*g**6 + 1/36*g**4 - g + 0*g**2 + 1/12*g**5 - 1/18*g**3 - 1. Let q(v) be the first derivative of s(v). Factor q(u).
u*(u + 1)**2*(3*u - 1)/3
Let z(d) be the third derivative of -d**5/360 + d**4/72 - d**3/36 - 2*d**2. Factor z(a).
-(a - 1)**2/6
Let o(m) be the third derivative of -m**7/140 + 3*m**5/40 - m**4/8 + 2*m**2 - 9*m. Factor o(d).
-3*d*(d - 1)**2*(d + 2)/2
Let l = 8 + -6. Let o**5 + o**4 + 4*o**2 - 3*o**3 - 5*o**l + 2*o**3 + 0*o**3 = 0. What is o?
-1, 0, 1
Let n(u) = u - 3. Let o be n(5). Let y(k) be the first derivative of 0*k - 2/3*k**3 - 2 + 2*k**o. Factor y(j).
-2*j*(j - 2)
Suppose -3*a = -2*z + a + 26, -4*z = 2*a - 2. Find b, given that 6*b + 1 + 15*b**z - 5 - 21*b**2 + 4 = 0.
0, 2/5, 1
Let m be 308/112 - (-2)/(-4). Suppose -3/4*z**3 + 9/4 + 3/4*z - m*z**2 = 0. Calculate z.
-3, -1, 1
Let i(s) be the third derivative of s**6/210 + s**5/210 - 10*s**2. Solve i(r) = 0.
-1/2, 0
Let n = 4/47 - -2389/94. Let m = n - 349/14. Suppose m*s**2 - 2/7 + 2/7*s - 2/7*s**4 + 2/7*s**5 - 4/7*s**3 = 0. What is s?
-1, 1
Suppose -3*w = 4*z - 31, z + 5*w = -3*z + 41. Let r(y) = -6*y**3 + 10*y**2 - 10*y + 2. Let b(n) = n**3 - n + 1. Let i(g) = z*b(g) + r(g). Factor i(s).
-2*(s - 3)*(s - 1)**2
Let w(c) = c**3 - 3*c**2 + 2*c - 4. Let x(v) = v**3 + 9*v**2 + 7*v - 5. Let d be x(-8). Let b be w(d). Factor 8 - 16*z + 2*z**2 + z**2 - 2*z**3 + 7*z**b.
-2*(z - 2)**2*(z - 1)
Let p(v) be the third derivative of v**8/1512 + v**7/1890 + v**3/3 + 2*v**2. Let x(z) be the first derivative of p(z). What is f in x(f) = 0?
-2/5, 0
Let a(m) be the second derivative of -m**4/90 - 7*m**3/45 + 19*m. Factor a(v).
-2*v*(v + 7)/15
Let s(n) be the third derivative of n**6/480 + n**5/240 - n**4/48 - 36*n**2. Find j such that s(j) = 0.
-2, 0, 1
Suppose k - 66 = 18. Let y be -6*(k/(-16) + 3). Factor -33*r**3 - y*r**5 + 0 - 3/2*r - 36*r**4 - 12*r**2.
-3*r*(r + 1)**2*(3*r + 1)**2/2
Let o = -21115/26 - -812. Let i = 28/39 - o. Factor 1/3 + 2/3*u**2 + i*u + 1/6*u**3.
(u + 1)**2*(u + 2)/6
Solve -1 + f**2 + 79*f - 2*f**2 - 77*f = 0.
1
Let t(i) be the first derivative of 0*i**3 + 1/72*i**4 - 3/2*i**2 + 3 + 0*i - 1/180*i**5. Let n(z) be the second derivative of t(z). Let n(m) = 0. What is m?
0, 1
Suppose 0 = 4*j - 23 - 1. Let p(c) be the second derivative of -2/15*c**j - 3/5*c**5 - 1/2*c**2 - c**3 + 0 - 2*c - 13/12*c**4. Factor p(g).
-(g + 1)**2*(2*g + 1)**2
Let j(w) = 35*w**4 - 90*w**3 + 105*w**2 - 35*w. Let d(k) = k**5 + k**2 + k. Let g(h) = 5*d(h) - j(h). Factor g(s).
5*s*(s - 2)**3*(s - 1)
Suppose -4*o = -8, 4*s - 2*o = 9*s - 4. Factor 0*y**3 + s*y + 1/5*y**2 - 1/5*y**4 + 0.
-y**2*(y - 1)*(y + 1)/5
Let j(v) be the second derivative of v**5/50 + v**4/5 + 3*v**3/5 + 16*v. Determine t, given that j(t) = 0.
-3, 0
Let g be 138/322 + (-4)/42. Determine z so that -1/3*z**5 - 1/3*z + 2/3*z**3 - 1/3*z**4 + 2/3*z**2 - g = 0.
-1, 1
Let d(q) be the third derivative of q**5/540 + q**4/216 + 7*q**2. Factor d(m).
m*(m + 1)/9
Let l = -106843/42 - -2544. Let h(d) be the third derivative of -7/12*d**6 + 0 - 23/20*d**5 + 0*d - 2/3*d**3 - l*d**7 - 7/6*d**4 + 3*d**2. Factor h(a).
-(a + 1)**2*(5*a + 2)**2
Let l = -3 + 6. Let w(m) = 2*m**2 - l*m**3 + m + 3 - 5 - 7*m. Let o(f) = 10*f**3 - 5*f**2 + 19*f + 7. Let t(x) = -2*o(x) - 7*w(x). Factor t(u).
u*(u - 2)**2
Let i(f) be the third derivative of f**6/80 - f**5/40 - 5*f**4/16 - 3*f**3/4 + 9*f**2. Factor i(h).
3*(h - 3)*(h + 1)**2/2
What is d in 4/3*d**3 + 2/3*d**5 + 2*d**4 - 4/3*d**2 - 2*d - 2/3 = 0?
-1, 1
Factor 0*q + 2/7*q**4 + 1/7*q**5 + 0 + 0*q**2 + 1/7*q**3.
q**3*(q + 1)**2/7
Let m(j) = -j**2 + 16*j - 26. Let p be m(11). Let r = p + -115/4. Suppose -1/4*y**2 - 1/4*y**3 + 1/4 + r*y = 0. What is y?
-1, 1
Let n(p) = -6*p**2 - 31*p + 31. Let v(z) be the first derivative of 1/3*z**3 - 6*z - 2 + 3*z**2. Let d(x) = 2*n(x) + 11*v(x). Factor d(r).
-(r - 2)**2
Let q(k) be the first derivative of 2 - 1/60*k**4 + 1/10*k**2 + 0*k**3 + k. Let u(a) be the first derivative of q(a). Find j, given that u(j) = 0.
-1, 1
Factor 40/3*u + 200/3 + 2/3*u**2.
2*(u + 10)**2/3
Suppose -4*b + 24 = -16. Factor 235/4*k**3 - 175/4*k**4 - 1 - 145/4*k**2 + b*k + 49/4*k**5.
(k - 1)**3*(7*k - 2)**2/4
Let s(v) = -v + 12. Let u be s(8). Let c = u + 0. Factor 3*i**5 - 3*i - 5*i**2 