vative of -h + 0*h**4 + 0 + 1/42*h**u + 1/6*h**3 + 0*h**6 + 0*h**2 - 1/10*h**5. What is j in g(j) = 0?
-1, 0, 1
Suppose -2*k + 2*u = 4*u + 22, -3*k = -2*u + 13. Let h(l) = l**2 + 6*l - 5. Let d be h(k). Suppose -1 + 2*c**d + 0 - c**2 = 0. What is c?
-1, 1
Let p = -49 - -82. Suppose 3 = -o + r, 4*o + r + 4*r = p. Factor -s**2 + 9*s**o + 4*s - 6*s**2.
2*s*(s + 2)
Let p(c) be the third derivative of -c**5/60 + c**4/8 - c**3/3 - 20*c**2. Find k, given that p(k) = 0.
1, 2
Let p(v) be the third derivative of 0 + 0*v + 0*v**3 - 1/840*v**7 - v**2 - 1/80*v**5 + 1/160*v**6 + 1/96*v**4. Factor p(t).
-t*(t - 1)**3/4
Factor d**4 - 17*d**3 - 6*d**2 - 2*d + 11*d**3 - 3*d**4.
-2*d*(d + 1)**3
Factor 5/4*i**2 + 1/4*i**3 + 1 + 2*i.
(i + 1)*(i + 2)**2/4
Factor -5/3*p**3 + 0*p**2 - 5/3*p**4 + 0 + 0*p.
-5*p**3*(p + 1)/3
Let s(a) be the third derivative of -a**7/105 - a**6/20 - a**5/30 + a**4/4 + 2*a**3/3 + 10*a**2. What is n in s(n) = 0?
-2, -1, 1
Let c be (-2)/(((-10)/3)/5). Suppose 2/7*h**c + 0 - 2/7*h - 2/7*h**2 + 2/7*h**4 = 0. What is h?
-1, 0, 1
Let l(s) = -15*s**3 + 79*s**2 - 135*s + 49. Let k(j) = 5*j**3 - 26*j**2 + 45*j - 16. Let i(p) = -11*k(p) - 4*l(p). Factor i(q).
5*(q - 4)*(q - 1)**2
Suppose 47 + 15 = 2*i. Factor -330*m**4 - 24*m**2 - i*m**3 + 225*m**5 + 92*m**3 + 95*m**3.
3*m**2*(3*m - 2)*(5*m - 2)**2
Let g = -1 + 3. Suppose -3*d - o = g*o + 6, 0 = -2*d - 4*o - 14. Factor -b**d + 1/2*b**4 + b - 1/2 + 0*b**2.
(b - 1)**3*(b + 1)/2
Let n(o) be the first derivative of -3*o**5/50 + 11*o**4/60 - 2*o**3/15 + 2*o**2 - 2. Let s(y) be the second derivative of n(y). Let s(j) = 0. What is j?
2/9, 1
Let u(r) = -4*r**4 + 6*r**3 + 7*r**2 - 6*r - 3. Let l(y) = y**4 - 2*y**3 - 2*y**2 + 2*y + 1. Let t(b) = 14*l(b) + 4*u(b). Find w such that t(w) = 0.
-1, 1
Suppose -3*j = -8*j + 10. Suppose -j*g = -7*g + 5*c - 5, 5*c - 20 = 0. Determine x so that -3*x**5 + x**5 - 6*x**g - 7*x**4 - 2*x**2 + x**4 = 0.
-1, 0
Let t(m) = -8*m**2 - m - 1. Let a(i) = 12*i**2 + 3*i + 2. Let n(r) = -13*r**2 - 3*r - 2. Let d(l) = 2*a(l) + 3*n(l). Let q(y) = 4*d(y) - 7*t(y). Factor q(k).
-(k + 1)*(4*k + 1)
Let m(q) be the second derivative of 0 - 1/16*q**4 + 9/80*q**5 + 0*q**2 - 5*q - 1/4*q**3. Determine r, given that m(r) = 0.
-2/3, 0, 1
Let l(z) = -9*z**2 + 222*z + 1473. Let p(t) = -2*t**2 + 56*t + 368. Let v(u) = 5*l(u) - 21*p(u). Factor v(j).
-3*(j + 11)**2
What is o in -o + 5*o + 35 - 29 + 3*o**2 + 5*o = 0?
-2, -1
Factor 0 + 3/2*y**2 + 0*y + 3/2*y**3.
3*y**2*(y + 1)/2
Let y = -146 + 148. Factor 4/3*k + 5/3*k**3 + 8/3*k**y + 0 + 1/3*k**4.
k*(k + 1)*(k + 2)**2/3
Let p(z) = -44*z**2 - 112*z. Let x(l) = 14*l**2 + 37*l. Let w(c) = -5*p(c) - 16*x(c). Factor w(r).
-4*r*(r + 8)
Let i = 65 + -60. Let u be (-4)/(-16) + 2 + -2. Factor 1/4*d + u*d**i + 1/4*d**4 - 1/2*d**2 - 1/2*d**3 + 1/4.
(d - 1)**2*(d + 1)**3/4
Factor -8/7*l - 8/7 - 2/7*l**2.
-2*(l + 2)**2/7
Suppose -5*k + k + j = -24, -2*j = 8. Let c(h) be the first derivative of 0*h**3 - 1/25*h**k + 0*h - 1/20*h**4 + 1 + 0*h**2. Factor c(r).
-r**3*(r + 1)/5
Let r be (-7)/(-6)*6/21. Factor 1/3 + 2*m**2 - 4/3*m**3 + r*m**4 - 4/3*m.
(m - 1)**4/3
Let v(o) = o**3. Let y(l) = l**5 - 3*l**4 + 6*l**3 + 11*l**2 - 12*l + 4. Let h(p) = 35*v(p) - 5*y(p). Determine a so that h(a) = 0.
-2, 1, 2
Factor -2/5*s**2 + 8/5*s**4 + 0 + 0*s - 6/5*s**3.
2*s**2*(s - 1)*(4*s + 1)/5
Let c = -250 + 1005/4. Factor -c*p + 1/2 + 1/2*p**2.
(p - 2)*(2*p - 1)/4
Let o(q) = q**2 + 0*q**3 + q**3 + 2*q**2. Let v be o(-3). Solve c**2 + 0*c**2 - 2 + c + v = 0 for c.
-2, 1
Factor -18*r + 97/2*r**2 + 2 - 36*r**3 + 8*r**4.
(r - 2)**2*(4*r - 1)**2/2
Let b = 3 - 0. Suppose -2*d - 4*d**2 + 6*d - d**b + 2*d**3 + 0*d = 0. Calculate d.
0, 2
Suppose -2*r = -3*r - 11. Let h be 10/4*r/(-55). Factor 0*z**2 + h*z**3 + 1/2*z**5 + 0 + z**4 + 0*z.
z**3*(z + 1)**2/2
Suppose 0 = 5*i - 2*i - 15. Let p(l) = i - l**2 + 2 + 0*l**2 - l. Let m(f) = 2. Let u(y) = -7*m(y) + 2*p(y). Factor u(d).
-2*d*(d + 1)
Find s such that -s**2 + 2*s**2 - 12*s - 4*s**2 + 16 - s**2 = 0.
-4, 1
Let d(a) = a + 1. Let j be d(1). Factor -6*s**j + 3*s**3 - 2*s + s + 4*s**2.
s*(s - 1)*(3*s + 1)
Let f = -1 + 6. Suppose 19 - 59 = -f*s. Factor -4*p**3 - s*p**3 - 3*p**2 + 2*p - 2*p**2.
-p*(3*p + 2)*(4*p - 1)
Let d(o) = 6*o**2 + 6*o + 8. Let q(p) = 11*p**2 + 12*p + 15. Let l(w) = -7*d(w) + 4*q(w). Factor l(f).
2*(f + 1)*(f + 2)
Let q(j) be the first derivative of -j**6/12 + j**4/4 - j**2/4 - 3. Factor q(x).
-x*(x - 1)**2*(x + 1)**2/2
Let t(w) be the first derivative of 0*w**3 - 7/2*w**6 + 3/2*w**4 - 3*w**5 + 0*w**2 + 0*w - 2. Factor t(v).
-3*v**3*(v + 1)*(7*v - 2)
Let b = 16 + -8. Suppose b = -3*i + 7*i + 4*r, 0 = 2*r. Determine p, given that 1/2*p - 1/2 - 1/2*p**3 + 1/2*p**i = 0.
-1, 1
Suppose 0 = 2*g - g, 4*b + 3*g - 20 = 0. Suppose n = b - 3. Factor -n*l**3 + 2*l**2 + 0*l**2 + 3*l**3.
l**2*(l + 2)
Let h be (24/20)/(2/5). Factor 13 - 12*d**2 - 13 + 3*d**h + 12*d.
3*d*(d - 2)**2
Let o = 27 + -53/2. Let i(q) be the first derivative of 2/3*q**3 - 1/3*q**6 - 2 + o*q**4 + 0*q**2 + 0*q - 2/5*q**5. Let i(m) = 0. Calculate m.
-1, 0, 1
Let p(o) = 6*o**5 + 2*o**4 - 2*o**3 + 2*o**2 - 2*o - 2. Let z(d) = -31*d**5 - 9*d**4 + 11*d**3 - 11*d**2 + 11*d + 11. Let a(v) = 11*p(v) + 2*z(v). Factor a(t).
4*t**4*(t + 1)
Let -9/2*h + 3/2*h**2 + 0 = 0. What is h?
0, 3
Let f(s) be the third derivative of 0*s + 1/16*s**4 + 1/20*s**5 + 0 - 7*s**2 + 1/80*s**6 + 0*s**3. Factor f(d).
3*d*(d + 1)**2/2
Let c(a) be the second derivative of 4*a + 1/15*a**6 - 1/3*a**4 + 0*a**3 + 0*a**2 + 1/10*a**5 + 0. Solve c(n) = 0.
-2, 0, 1
Let m(u) be the third derivative of 1/3*u**5 + 0 + 0*u**3 + 1/6*u**4 + u**2 + 0*u + 5/24*u**6. Solve m(r) = 0 for r.
-2/5, 0
Find y such that -56/17*y**2 + 288/17*y**3 - 18/17*y - 128/17*y**4 + 4/17 = 0.
-1/4, 1/4, 2
Let v(p) be the third derivative of 8*p**2 + 0*p**3 + 1/672*p**8 + 1/20*p**6 + 0*p**4 - 1/15*p**5 + 0 - 1/70*p**7 + 0*p. Let v(q) = 0. Calculate q.
0, 2
Let w(o) = 2*o**2 - 54*o - 114. Let m be w(-2). Factor 4/7*p + 2/7 + 2/7*p**m.
2*(p + 1)**2/7
Let s(c) be the first derivative of -2*c**5/5 + 4*c**3 + 8*c**2 + 6*c + 20. Suppose s(h) = 0. What is h?
-1, 3
Let f(t) = -t**2 - 8*t + 7. Let k be f(-9). Let p be (14/6 - 0) + k. Factor 0*h - 1/3*h**3 + 0 + p*h**2.
-h**2*(h - 1)/3
Suppose -14 = -a - k + 5, 0 = 3*a - 2*k - 37. Let d(f) = f - 15. Let h be d(a). Let h*s + 0 + 2/3*s**2 = 0. Calculate s.
0
Let -4/17*c**4 + 0*c - 6/17*c**3 - 2/17*c**2 + 0 = 0. What is c?
-1, -1/2, 0
Let h(q) = q**3 + q**2 + 5. Let a be h(0). Let z = a - 1. Find g, given that 0*g**z + 2/9*g**5 + 2/9*g + 0 + 0*g**2 - 4/9*g**3 = 0.
-1, 0, 1
Let d be (-10)/16*-6*(-4)/(-180). Let m(a) be the first derivative of d*a**6 + 1/2*a**5 + 1/2*a**2 + 9/8*a**4 + 7/6*a**3 + 2 + 0*a. Factor m(h).
h*(h + 1)**3*(h + 2)/2
Let j(g) = -4*g**3 - 8*g**5 - 2*g**4 - 10 - 18*g + 10*g - 8*g**4. Let p(b) = b**5 + b**4 + b + 1. Let r(h) = -j(h) - 10*p(h). Find t such that r(t) = 0.
-1, 0, 1
Let s(v) = 6*v**4 - 12*v**2 + 6*v. Let u(x) = 31*x**4 - 60*x**2 + 29*x. Let t(r) = 11*s(r) - 2*u(r). Factor t(d).
4*d*(d - 1)**2*(d + 2)
Let z = 9/20 + -1/4. Find a such that 1/5*a**4 - 1/5*a + 1/5*a**3 - z*a**2 + 0 = 0.
-1, 0, 1
Let b(c) be the second derivative of -c**4 + 3*c + 0 + 2/5*c**6 + 0*c**2 + 4/3*c**3 - 2/5*c**5. Factor b(p).
4*p*(p - 1)*(p + 1)*(3*p - 2)
Let r(p) = 4*p**2 + 4*p - 4. Let t(c) = -8*c**2 - 9*c + 8. Let d(y) = -9*r(y) - 4*t(y). Find q, given that d(q) = 0.
-1, 1
Let c(r) = -3*r - 18. Let p be c(-7). Factor -12*z**2 - 31*z + 0*z**p - 5 - 4*z**3 + 1 + 19*z.
-4*(z + 1)**3
Let l(g) be the second derivative of -2*g**6/135 - 10*g. Let l(v) = 0. What is v?
0
Let x(l) = l**2 - 2*l + 4. Let v be x(3). Let -4*j - 21*j**3 - 2 - 1 + 6*j + 3*j**2 + v*j + 12*j**5 = 0. Calculate j.
-1, 1/2, 1
Suppose 5*j = 2*o - 55, j - 5*j + 180 = 4*o. Let t = -159/4 + o. What is a in -1/4*a**3 + 0 + t*a**4 + 0*a + 0*a**2 = 0?
0, 1
Suppose -3*m + 4 = -4*p, 0 = -m + 4*p - 5*p - 1. Factor u**5 - 1/4*u**2 + m*u + 0 + 1/2*u**3 + 7/4*u**4.
u**2*(u + 1)**2*(4*u - 1)/4
Let f(j) be the second derivative of 1/24*j**4 + 5*j - 1/6*j**3 + 1/4*j**2 + 0. Factor f(h).
(h - 1)**2/2
Let q(g) be the third derivative of g**8/3360 - g**7/315 + g**6/72 - g**5/30 - g**4/24 + 2*g**2. Let b(n) be the second derivative of q(n). Factor b(j