3*y - 6 = 3. Let o = -3 + y. Factor o*l**3 + 0*l - 1/5 - 1/5*l**4 + 2/5*l**2.
-(l - 1)**2*(l + 1)**2/5
Let w(f) be the first derivative of -f**4/14 - 8*f**3/21 + 5. Factor w(t).
-2*t**2*(t + 4)/7
Let 39/2*g**3 + 9 + 48*g**2 + 75/2*g = 0. What is g?
-1, -6/13
Let m(d) be the second derivative of d**4/21 - 26*d**3/21 - 20*d + 2. Suppose m(s) = 0. Calculate s.
0, 13
Factor 6*z**2 + 8*z + 12 + 4*z**2 - 9*z**2.
(z + 2)*(z + 6)
Suppose -g + 0*x = 3*x - 6, 0 = -4*g - 4*x + 16. Let j = 31 + -27. Factor 5 - o + o**j + g*o**2 + 11 - 3*o**3 - 16.
o*(o - 1)**3
Let c(p) = -2*p**2 - p + 210. Let k be c(10). Suppose 1/3*u**2 + k - 2/3*u = 0. What is u?
0, 2
Let h(j) = j**3 - j**2. Let a(w) = -12*w**4 + 56*w**3 + 16*w**2. Let b(y) = a(y) - 16*h(y). Determine p so that b(p) = 0.
-2/3, 0, 4
Let d = 278 - 275. Suppose -16/7*y + 0 - 2*y**4 - 40/7*y**2 + 52/7*y**d = 0. Calculate y.
-2/7, 0, 2
Let y(v) be the second derivative of -1/30*v**4 + 0*v**2 + 3*v + 0 - 3/100*v**5 + 1/70*v**7 + 1/75*v**6 + 0*v**3. Find i, given that y(i) = 0.
-1, -2/3, 0, 1
Let m(n) be the first derivative of 2*n**5/45 - n**4/6 + 2*n**3/9 - n**2/9 + 237. Suppose m(d) = 0. What is d?
0, 1
Let x(b) be the first derivative of b**2 - 13/3*b**3 - 1 - b**5 + 4*b**4 + 0*b. Suppose x(v) = 0. Calculate v.
0, 1/5, 1, 2
Suppose -38*q + 105 = -85. Determine d, given that -2*d**3 + 1/2*d**q + 1 - d**2 + 3/2*d + 0*d**4 = 0.
-1, 1, 2
Let b be (-33)/9 + 2/(-6). Let w be (8/2)/(b - -14). Factor 24/5*h - 6/5*h**3 - 16/5 + w*h**4 - 4/5*h**2.
2*(h - 2)**2*(h - 1)*(h + 2)/5
Let a be 2/4*1*0. Factor a*u + 9*u**2 + 3*u**3 - 8*u + 17*u + 3.
3*(u + 1)**3
Let a be (-544)/(-900) - (6 - (-135)/(-25)). Let z(j) be the second derivative of 0 + 4*j + a*j**6 + 1/50*j**5 + 1/45*j**4 + 0*j**3 + 0*j**2. Factor z(t).
2*t**2*(t + 1)*(t + 2)/15
Let 138*g**3 + 35*g + 138*g**3 - 275*g**3 - 12*g**2 = 0. Calculate g.
0, 5, 7
Let j(z) be the first derivative of 16*z**3/7 + 36*z**2/7 + 27*z/7 - 9. Solve j(k) = 0.
-3/4
Suppose 0 = 3*l - 15*l - 228. Let q = 19 + l. Factor -2/11*o**5 + 2/11*o**3 + 0 + 0*o**2 + 0*o**4 + q*o.
-2*o**3*(o - 1)*(o + 1)/11
Let d(w) = -4*w + 15. Let g be d(5). Let r be -2 + (16 + g - 6). Factor y**2 + 7/3*y**4 + 2/3*y + 0 - 4*y**r.
y*(y - 1)**2*(7*y + 2)/3
Let p be 2288/18 - (11 + -9). Let j = p + -124. Let 14/9*q - 2/3 - j*q**2 + 2/9*q**3 = 0. Calculate q.
1, 3
Let q be (-148)/32 + 3/1. Let k = -1/8 - q. Solve -3/4*m**4 + 9/4*m**3 - 3/4*m**5 + 0 - k*m + 3/4*m**2 = 0 for m.
-2, -1, 0, 1
Suppose 5*j - 3*b - 155 = -b, -3*b - 15 = 0. Let u = -26 + j. Factor 4/7*x**u + 0 - 4/7*x + 4/7*x**2 - 4/7*x**4.
-4*x*(x - 1)**2*(x + 1)/7
Let l(s) be the first derivative of s**7/245 + 3*s**6/280 - s**4/56 + 4*s**2 - 3. Let i(r) be the second derivative of l(r). Factor i(m).
3*m*(m + 1)**2*(2*m - 1)/7
Let h(q) be the third derivative of 0 + 0*q + 1/6*q**4 - 1/168*q**8 - 1/105*q**7 + 1/6*q**5 - 12*q**2 + 1/20*q**6 + 0*q**3. Factor h(m).
-2*m*(m - 2)*(m + 1)**3
Let j be (-9)/90 - (-21)/35. Suppose 3*k = -2*k. Factor 1/4*o**5 + 1/2 + k*o**4 - o**3 - j*o**2 + 3/4*o.
(o - 2)*(o - 1)*(o + 1)**3/4
Suppose 3*l = 16 + 5. Let p = 60 + -58. Factor -3*u**2 + l*u**3 + 0*u**3 + p*u**3.
3*u**2*(3*u - 1)
Let h = -496/29 + 6506/377. Factor 2/13*g**2 + 2/13*g - 2/13*g**3 - h.
-2*(g - 1)**2*(g + 1)/13
Let t + 2802*t**2 + 2*t**4 - 2814*t**2 - 6*t**3 + 15*t = 0. What is t?
-2, 0, 1, 4
Let z(t) be the second derivative of -t**6/540 + t**5/180 + t**4/18 + t**3/6 + 7*t. Let p(v) be the second derivative of z(v). What is r in p(r) = 0?
-1, 2
Let c be 47/15 - (-62)/(-465). Let t(x) be the third derivative of 0 - 1/3*x**c + 2*x**2 + 0*x + 1/18*x**4 - 1/270*x**5. Solve t(y) = 0.
3
Let y = 138 - 136. Factor -18*a**2 + 19*a**2 + y + 5*a - 2.
a*(a + 5)
What is t in -3/2*t**2 - 1/2*t**3 - 1/2 - 3/2*t = 0?
-1
Let f(w) be the first derivative of 2*w**5/5 - 2*w**4 + 10*w**3/3 - 2*w**2 - 72. Factor f(i).
2*i*(i - 2)*(i - 1)**2
Let x(p) be the second derivative of 0*p**2 - 1/15*p**3 + 1/105*p**7 + 3*p - 1/15*p**4 + 0 + 2/75*p**6 + 0*p**5. Factor x(d).
2*d*(d - 1)*(d + 1)**3/5
Factor -40/17*j**4 - 126/17*j**2 - 46/17*j - 2/17 - 122/17*j**3.
-2*(j + 1)**3*(20*j + 1)/17
Factor -96/5*b**2 - 102/5*b - 6/5.
-6*(b + 1)*(16*b + 1)/5
Let k be (-3 + 282/(-70))*(-10)/28. Let x = k + -1/98. Factor -x*b**2 - 1/4*b**5 - 1/4 - 5/2*b**3 - 5/4*b**4 - 5/4*b.
-(b + 1)**5/4
Let q(j) be the first derivative of -2*j**3/7 - 17*j**2/7 + 12*j/7 + 91. Solve q(w) = 0 for w.
-6, 1/3
Let t = -34 - -40. Let v(a) = 100*a**3 - 145*a**2 - 55*a. Let l(g) = 11*g**3 - 16*g**2 - 6*g. Let z(o) = t*v(o) - 55*l(o). Factor z(b).
-5*b**2*(b - 2)
Let t(h) be the third derivative of -h**8/10080 - h**7/420 - h**6/72 - h**5/4 - 26*h**2. Let z(s) be the third derivative of t(s). Suppose z(d) = 0. What is d?
-5, -1
Let l(x) be the second derivative of x**5/150 - x**3/45 + 4*x - 17. Factor l(i).
2*i*(i - 1)*(i + 1)/15
Solve -6/7*t**2 - 18/7*t + 0 = 0 for t.
-3, 0
Let t(l) be the second derivative of l**6/360 - l**5/40 + l**4/12 + 5*l**3/6 + 21*l. Let r(j) be the second derivative of t(j). Factor r(z).
(z - 2)*(z - 1)
Let t(c) = -c**2 + 60*c - 116. Let z(s) = -s**2 + 60*s - 116. Let i(o) = -4*t(o) + 3*z(o). Factor i(y).
(y - 58)*(y - 2)
Suppose 3*k = -0*k + 6. Suppose 9 = 2*g - 5*j, k*g = g - 5*j - 3. Let 7*p**2 - 9*p**4 + 0*p**g + 5*p**2 + 0*p**2 + 3*p**5 = 0. Calculate p.
-1, 0, 2
Factor -z**2 + 448 - 2*z**2 - 2*z**3 - 12*z - 448 + 17*z**2.
-2*z*(z - 6)*(z - 1)
Suppose 21*a - 12 = 17*a. Factor -5*w**2 + 5*w**4 - 7*w**3 + 31*w + 2*w**a - 26*w.
5*w*(w - 1)**2*(w + 1)
Let 2080*t - 7*t**2 - 11*t**2 - 216320 - 8*t**2 + 21*t**2 = 0. What is t?
208
Let r = 471/380 - -1/95. Factor 0*c + 15/4*c**2 - r*c**3 - 5.
-5*(c - 2)**2*(c + 1)/4
Let c(s) be the third derivative of s**5/120 - 41*s**4/48 - 43*s**3/6 + 87*s**2 + 3*s. Factor c(p).
(p - 43)*(p + 2)/2
Let o(r) be the second derivative of -r**5/4 - 5*r**4/12 - 39*r - 2. Determine x so that o(x) = 0.
-1, 0
Let h(a) be the second derivative of -2/5*a**4 - 1/5*a**2 - 17/100*a**5 + 20*a - 13/30*a**3 + 0 - 2/75*a**6. Solve h(w) = 0.
-2, -1, -1/4
Determine b, given that -b**4 + 3*b**4 + 7*b + 5*b**3 + 0*b**4 - 3*b**4 - 2 - 9*b**2 = 0.
1, 2
Let l(r) = 6*r - 33. Let m be l(7). Let u be (-1)/(-3)*(m + 0) - 0. Suppose 5/4*g**2 - 2*g - 1/4*g**u + 1 = 0. What is g?
1, 2
Let c(d) be the third derivative of d**7/105 - 11*d**6/60 + 19*d**5/15 - 13*d**4/3 + 8*d**3 + 44*d**2 - 3. Determine k so that c(k) = 0.
1, 2, 6
Let j(k) = 19*k + 7. Let o be j(-7). Let q be (-6)/o*-3*-14. Solve 0 - 2/7*x**3 - 2/7*x + 4/7*x**q = 0.
0, 1
Suppose 0 = 3*l - 16 - 2. Suppose 3*f + 3*m - 3 = 0, -f - 6 = -l*f - 4*m. Solve 4 + 2*t**f - t - 3*t - 2*t + 0*t = 0 for t.
1, 2
Let p(c) be the third derivative of c**9/22680 - c**8/10080 - c**7/7560 - c**5/3 - 8*c**2. Let s(j) be the third derivative of p(j). Factor s(n).
2*n*(n - 1)*(4*n + 1)/3
Let v(m) be the first derivative of 5*m**6/2 + 36*m**5/5 + 3*m**4 - 101. Factor v(r).
3*r**3*(r + 2)*(5*r + 2)
Let x = 30 + -26. Factor 7*i**4 - 6*i**3 + 6*i**3 - 3*i**4 + x*i**3.
4*i**3*(i + 1)
Let m(j) = 6*j**2 - j. Let h be m(1). Suppose h*o - 16 = o. Find r, given that o*r - r**2 + r - 6*r + 0*r = 0.
-1, 0
Suppose -2*z = -2, 5*z + 15 = 2*k + 3*k. Suppose k*i - 15 = i. Find m, given that 0 - 3 + 3 + m**4 - m**i = 0.
0, 1
Let t = 34/9 + -28/9. Let k(c) be the first derivative of 1/6*c**6 - 1/2*c**4 - 2 - c + 1/2*c**2 - 1/5*c**5 + t*c**3. Suppose k(g) = 0. Calculate g.
-1, 1
Suppose 7*d = -c - 47, 4*d - 2 + 24 = -3*c. Find u such that -7/3*u**3 - 4/3*u - 29/6*u**c + 7/6*u**4 + 2/3*u**5 + 2/3 = 0.
-2, -1, 1/4, 2
Let t be (-11)/(-28) - (-11)/(-77). Let s(y) be the second derivative of 9/20*y**5 + t*y**4 + 0 - 1/2*y**6 + 1/7*y**7 + 0*y**2 - 1/2*y**3 - 6*y. Factor s(k).
3*k*(k - 1)**3*(2*k + 1)
Let l(y) be the second derivative of -4/9*y**3 + 0 + 1/10*y**5 + 46*y - 5/18*y**4 + 4/3*y**2. Factor l(r).
2*(r - 2)*(r + 1)*(3*r - 2)/3
Let f be ((-2140)/(-4815))/(-2*(-1)/3). Factor f*y**2 + 8 + 16/3*y.
2*(y + 2)*(y + 6)/3
Suppose a + 6*a = 0. Factor 2*w**3 - 4*w + a*w + w + w**3.
3*w*(w - 1)*(w + 1)
Let y(a) be the second derivative of a**8/13440 - a**7/2520 + a**6/1440 + 3*a**4 - 10*a. Let i(o) be the third derivative of y(o). Factor i(h).
h*(h - 1)**2/2
Let o(x) be the third d