- 3*o**5/80 + o**4/24 - 3*o - 3. Let t(k) be the first derivative of i(k). Factor t(g).
-g**2*(g + 1)*(5*g - 2)/4
Let p(f) be the third derivative of f**6/30 - 4*f**5/5 + 8*f**4 - 128*f**3/3 - 28*f**2. Suppose p(z) = 0. What is z?
4
Suppose -264*g = -259*g. Find v such that -1/2*v**3 - v - 3/2*v**2 + g = 0.
-2, -1, 0
Let -18/7*p**2 + 2/7*p**3 + 54/7*p - 54/7 = 0. Calculate p.
3
Suppose 0 = -r - r + 4. Suppose r*p + 1 - 11 = 0. Solve -4 - p + 3*a**2 + 9 + 3*a = 0 for a.
-1, 0
Let r be 0 - (-2 + 1 - 26). Suppose 9*j**4 + 17*j + 6*j**4 - r*j**3 - 15*j**2 - 11*j + 21*j**5 = 0. What is j?
-1, 0, 2/7, 1
Let c(a) = -a**2 - 4*a - 3. Let k(j) = -2*j**2 - 7*j - 5. Let x(z) = -5*c(z) + 3*k(z). Let g be x(-1). Factor -2/3*n**4 + 0*n + g - 2/3*n**2 - 4/3*n**3.
-2*n**2*(n + 1)**2/3
Let c(w) be the first derivative of 2 - 4*w - 2/3*w**3 - 3*w**2. Solve c(m) = 0 for m.
-2, -1
Factor -36*i**5 + 15*i**2 + 33*i**5 + 9*i**3 - 3*i**4 + 6*i + 0*i**2.
-3*i*(i - 2)*(i + 1)**3
Let v be (-4)/(-5)*4/16. Let n(k) be the second derivative of -v*k**2 + 2/15*k**3 - 1/30*k**4 + 0 - k. Factor n(d).
-2*(d - 1)**2/5
Determine i so that -3/2 + 9/4*i**3 + 33/2*i**2 - 9/4*i - 15*i**4 = 0.
-1, -1/4, 2/5, 1
Factor 1/5*n**2 - 3/5*n + 2/5.
(n - 2)*(n - 1)/5
Let d(c) = -c**2 - 3*c - 2. Let y be d(-2). Let h(j) be the third derivative of y*j**3 + j**2 + 0 + 0*j - 1/60*j**4 - 1/150*j**5. Factor h(i).
-2*i*(i + 1)/5
Let m(s) be the first derivative of -2*s**3/15 - 2*s**2/5 - 2*s/5 - 21. Factor m(z).
-2*(z + 1)**2/5
Solve -9/4*z**2 - 5*z - 1 = 0 for z.
-2, -2/9
Let w be (-2)/(-9) - (-4)/(-18). Suppose -q - 4*q = w. Let 2*a**3 + 0 + q + 2*a**4 - 2*a**2 - 2*a = 0. Calculate a.
-1, 0, 1
What is j in -48/5*j**3 + 48/5*j**2 - 16/5*j + 0 + 4*j**4 - 3/5*j**5 = 0?
0, 2/3, 2
Let n(f) be the second derivative of f**6/150 + f**5/20 + 2*f**4/15 + 2*f**3/15 + 19*f. Factor n(j).
j*(j + 1)*(j + 2)**2/5
Let r be (-126)/(-35) - 6/10. Suppose r*i - 20 = -14. Factor 4/9*v**i + 0 + 2/9*v**3 + 2/9*v.
2*v*(v + 1)**2/9
Let u(w) = 3*w**2 - 5. Let l(s) = -2*s**2 + 3. Let d(t) = 7*l(t) + 5*u(t). Factor d(z).
(z - 2)*(z + 2)
Let w(l) be the third derivative of 2*l**5/45 - l**4/36 + 5*l**2. Factor w(h).
2*h*(4*h - 1)/3
Let q(z) = z - 3. Suppose -15 = -2*j - 3. Let g be q(j). Find v, given that 3*v**3 - 2*v + v**2 - v**g + v**2 - 2 + 0*v = 0.
-1, 1
Let x(u) be the second derivative of -u**5/60 + u**4/24 + 3*u**2/2 - 2*u. Let f(l) be the first derivative of x(l). Suppose f(w) = 0. Calculate w.
0, 1
Let x(c) = -c**3 - c**2. Let h(i) = -6*i**3 + 6*i**2 + 27*i - 81. Let w(f) = h(f) - 3*x(f). Let w(l) = 0. Calculate l.
-3, 3
Let r be (187/33 + 4/(-6))/1. Let j be (-8)/42*(-6)/4. Solve -16/7*s**3 + 2/7*s**4 + j + 8/7*s - 4/7*s**2 + 8/7*s**r = 0 for s.
-1, -1/4, 1
Let o be (-1 + 111)*(-492)/72. Let w = 765 + o. What is x in 80/3*x + 10/3*x**4 + w*x**3 + 1/3*x**5 + 32/3 + 80/3*x**2 = 0?
-2
Let u(k) be the first derivative of -4/5*k**5 + 0*k - 2*k**4 + 1 + 0*k**3 + 0*k**2. Factor u(b).
-4*b**3*(b + 2)
Factor 14 + 20*z**3 + 1036*z**4 - 1041*z**4 + 100*z + 112*z**2 + 21 - 22*z**2.
-5*(z - 7)*(z + 1)**3
Let v(f) be the second derivative of -5*f**7/42 + 5*f**6/6 - 5*f**5/2 + 25*f**4/6 - 25*f**3/6 + 5*f**2/2 + 11*f. Factor v(h).
-5*(h - 1)**5
Let i = -1335 + 17361/13. Determine m so that 8/13*m**2 - 4/13*m - i*m**4 + 4/13*m**3 - 2/13 = 0.
-1, -1/3, 1
Let k = -11 - -13. Let l be (1/k)/(11/44). Find a, given that -8/7*a**l - 4/7 + 10/7*a + 2/7*a**3 = 0.
1, 2
Let x(m) be the first derivative of 63*m**4/4 - 20*m**3 + 6*m**2 + 7. Factor x(r).
3*r*(3*r - 2)*(7*r - 2)
Factor -56*j**5 - 7*j**3 + 35*j**4 - 40*j - 111*j**3 + 28*j**3 + 51*j**5 + 100*j**2.
-5*j*(j - 2)**3*(j - 1)
Solve -l - 2/3 - 1/3*l**2 = 0.
-2, -1
Suppose 0 = 31*p - 29*p. Find t, given that -1/3*t**3 + 0*t + p*t**2 + 0 = 0.
0
Let j be 57/(-21) - 4/14. Let n be 0/j*(-4 + 5). Factor 3*f**3 + n*f - 9/4*f**4 - 3/4*f**2 + 0.
-3*f**2*(f - 1)*(3*f - 1)/4
Let v(l) = 5*l - 2. Let o be v(4). Factor -4*q**2 + q**2 - 4 - o*q - 5*q**2.
-2*(q + 2)*(4*q + 1)
Let b be 2 - ((1 - 2) + 1). Factor 6*a**3 - 50*a**b - 4*a + 16*a**4 - 2*a**3 + 2*a**2 + 24*a + 8.
4*(a - 1)**2*(a + 2)*(4*a + 1)
Suppose 0*j + 6 = -3*j. Let n be j + 0 - 15/(-3). Determine s so that 2/3*s**2 - 2/9*s**n - 2/3*s + 2/9 = 0.
1
Let l(q) = 5*q**3 + 3*q**2 - 3*q + 1. Let a(s) = -4*s**3 - 3*s**2 + 3*s - 1. Let i = 22 + -16. Suppose -d = -4 - 1. Let w(v) = d*l(v) + i*a(v). Solve w(x) = 0.
1
Let l(s) = -7*s**2 - 5*s + 17. Let y(j) = -3*j**2 - 3*j + 8. Let w(m) = 2*l(m) - 5*y(m). Find k such that w(k) = 0.
-6, 1
Let v(o) = o**2 - 19*o + 11. Let m be (-2 - -3)/2*14. Let j(b) = -b**2 + 10*b - 5. Let a(l) = m*j(l) + 4*v(l). Let a(z) = 0. Calculate z.
-3, 1
Let f(h) be the first derivative of 3/4*h**4 - 3/5*h**5 - 2 + 0*h**2 + 1/6*h**6 - 1/3*h**3 + 0*h. Factor f(c).
c**2*(c - 1)**3
Let n = -11 - -26. Let h be 21/n - (1 - 0). Factor -h*d**2 + 0 + 2/5*d.
-2*d*(d - 1)/5
Let p(w) be the second derivative of 7*w**6/15 + 9*w**5/10 - 2*w**4 - 4*w**3/3 + 10*w. Let p(h) = 0. What is h?
-2, -2/7, 0, 1
Suppose q - 9 = h, 4*h + 2*q + 17 = 5. Let y(o) = -o**2 - 5*o. Let j be y(h). Factor 0 + j*x - 1/3*x**2.
-x**2/3
Let o = 170 - 1186/7. Let 0 - 2/7*h**3 + 0*h - o*h**2 + 2/7*h**4 = 0. Calculate h.
-1, 0, 2
Let l(u) = u**2 + 7*u + 12. Let y be l(-3). Find z, given that -2/7*z + 2/7*z**3 + 0 + y*z**2 = 0.
-1, 0, 1
Find o such that -2/9*o**4 + 0 + 16/9*o**3 + 4*o - 14/3*o**2 = 0.
0, 2, 3
Let u(r) be the second derivative of -r**7/168 + r**6/40 - 3*r**5/80 + r**4/48 - 2*r + 17. Find o such that u(o) = 0.
0, 1
Solve -12/19 - 6/19*b**2 + 2/19*b**4 - 6/19*b**3 + 22/19*b = 0.
-2, 1, 3
Let l(o) be the second derivative of -1/10*o**6 + 2/3*o**3 + 0 - 2/3*o**4 - 3*o - 11/20*o**5 + 0*o**2. Solve l(x) = 0 for x.
-2, 0, 1/3
Let n(v) be the first derivative of -v**3/18 + v**2/6 - v/6 + 18. What is p in n(p) = 0?
1
Let m be (-4)/8*(-684)/66 - 5. Factor 4/11 - 4/11*g**2 - m*g**3 + 2/11*g.
-2*(g - 1)*(g + 1)*(g + 2)/11
Let u(i) be the third derivative of -3*i**2 - 1/240*i**5 + 0 + 0*i + 0*i**3 - 1/48*i**4. Factor u(p).
-p*(p + 2)/4
Let r(h) be the first derivative of 1/4*h**2 + 0*h + 3 + 1/6*h**3. Factor r(g).
g*(g + 1)/2
Let c = -6 - -8. Let g = 0 + 0. Factor g + 4*x - x**c - 6 + 2 - 8*x.
-(x + 2)**2
Factor -125*w**2 + 64*w**2 + 57*w**2 + 4*w - 4*w**3 + 4*w**4.
4*w*(w - 1)**2*(w + 1)
Let y be ((-90)/(-25) + -4)/(5/(-25)). Find s such that 0*s - 8/5 + 2/5*s**y = 0.
-2, 2
Let i(h) = -2*h**3 + h - 4. Let r(f) = f**2 - f + 1. Let u(v) = -3*i(v) - 15*r(v). Let u(y) = 0. What is y?
1/2, 1
Let m(v) be the first derivative of 0*v**3 + 0*v**4 + 1/50*v**5 - 1 - v + 0*v**2. Let p(y) be the first derivative of m(y). Factor p(h).
2*h**3/5
Let w be -1*(-2 - (-6)/2). Let g(f) = -5*f**3 + 5*f - 6. Let h(t) = -6*t**3 + t - 1 + 2*t**3 + 3*t**3. Let b(r) = w*g(r) + 6*h(r). Suppose b(y) = 0. What is y?
-1, 0, 1
Let s(k) be the third derivative of -k**5/120 + k**4/6 - 4*k**3/3 - 20*k**2. Factor s(p).
-(p - 4)**2/2
Factor 1/3 + 1/3*x**2 - 2/3*x.
(x - 1)**2/3
Let c be 20/(-25)*5/(-2). Factor 2*m**3 + 6*m**c - 6*m**2.
2*m**3
Let x = 166 - 103. Let w be 1 + 2 - x/35. Factor -w*v + 2/5 - 2/5*v**3 + 6/5*v**2.
-2*(v - 1)**3/5
Let c(g) = -g**2 - 7*g - 3. Let z be c(-6). Let a(m) be the third derivative of 3*m**2 - 1/60*m**5 + 1/24*m**4 + 0 + 1/6*m**z - 1/120*m**6 + 0*m. Factor a(w).
-(w - 1)*(w + 1)**2
Let j(b) be the second derivative of b**7/63 + 4*b**6/45 + b**5/10 - 14*b. Solve j(f) = 0.
-3, -1, 0
Let p be (-22)/(-1 - -3)*-1. Let m be ((-4)/12 - -1)*p. Suppose m*q - 32/3*q**2 + 14/3*q**3 - 4/3 = 0. Calculate q.
2/7, 1
Let m be 0/(7/((-21)/6)). Find s such that m*s + 0*s**2 + 0 + 1/4*s**3 = 0.
0
Let k = 65/42 + -22/21. Factor 0 + 1/2*b**2 + k*b.
b*(b + 1)/2
Factor -1/6 + 1/6*a**3 + 1/6*a**2 - 1/6*a.
(a - 1)*(a + 1)**2/6
Let j = 345 - 343. Factor -6/13*b**3 + 0*b + 0 - 4/13*b**j - 2/13*b**4.
-2*b**2*(b + 1)*(b + 2)/13
Let q(g) be the first derivative of 5*g**4/4 - 9. Factor q(d).
5*d**3
Let c = -3 + 1. Let k be 5/((-2)/2 - c). Let -m**2 - m**2 - m**3 + k*m**3 - 2*m**3 = 0. Calculate m.
0, 1
Let a be -4*(-10 + 70/8). Find w, given that 14/3*w**2 - 2/3*w**a - 6*w**3 + 0 + 10/3*w**4 - 4/3*w = 0.
0, 1, 2
Let u(p) = -8*p**3 + 24*p**2 - 16*p. Let i(k) = 7*k**3 - 23*k**2 + 16*k. Let t(y) = 4