11*b**2 - n*b.
-2*(b - 1)*(b + 3)/11
Let l(n) = -15*n**3 - 770*n**2 - 4880*n - 7020. Let q(i) = -2*i**3 - 110*i**2 - 697*i - 1003. Let p(a) = 3*l(a) - 20*q(a). Suppose p(r) = 0. What is r?
-10, -2
Let y(z) be the first derivative of -4*z**5/25 + 2*z**4/5 + 16*z**3/15 - 4*z**2/5 - 12*z/5 + 91. Find p, given that y(p) = 0.
-1, 1, 3
Let q(g) = -20*g - 24. Let r be q(-3). Factor -63*m**4 + 31*m**4 + 4*m**5 - 8*m**3 + r*m**4.
4*m**3*(m - 1)*(m + 2)
Let p(l) be the first derivative of -l**6/21 - 18*l**5/35 - 15*l**4/7 - 92*l**3/21 - 33*l**2/7 - 18*l/7 + 48. Suppose p(n) = 0. Calculate n.
-3, -1
Let j(b) = -6*b**3 + 103*b**2 - 384*b + 7. Let f(w) = -2*w**3 + 34*w**2 - 128*w + 2. Let u(a) = 14*f(a) - 4*j(a). Solve u(s) = 0.
0, 8
Factor -1 - 6*h + 7 + 2*h**2 - h - h.
2*(h - 3)*(h - 1)
Suppose -3*r = -h - 14, 5*r - 3*r = h + 8. Suppose 25*g - 22*g - r = 0. Find z such that 6/5*z**3 - 3/5*z**4 - 6/5*z + 0*z**g + 3/5 = 0.
-1, 1
Let n(r) be the first derivative of -r**6/66 - 12*r**5/55 - 37*r**4/44 - 14*r**3/11 - 8*r**2/11 - 52. Determine v so that n(v) = 0.
-8, -2, -1, 0
Let k(d) be the second derivative of d**5/15 - d**4/3 - 16*d**3/3 + 24*d**2 - 20*d. Let x(j) be the first derivative of k(j). Let x(l) = 0. Calculate l.
-2, 4
Factor -3/5*o**2 + 1/5*o**4 - 32/5*o - 4 + 2*o**3.
(o - 2)*(o + 1)**2*(o + 10)/5
Let b(d) be the second derivative of -d**8/2240 + d**7/420 - d**6/240 + 5*d**4/4 - 19*d. Let q(t) be the third derivative of b(t). Solve q(n) = 0 for n.
0, 1
Let l(k) = 3*k**5 - k**4 - 17*k**3 - 21*k**2 + 8*k + 4. Let t(w) = w**4 + w**3 - 2*w. Let h(v) = -l(v) - 6*t(v). What is y in h(y) = 0?
-2, -1, 1/3, 2
Let r = 17 + 2. Suppose -33 = -5*i - 3*s - 4, i - r = -5*s. Find u such that -17 + 10*u - 22*u**4 - i*u**3 + 27*u**2 - u**2 - 8*u**5 + 13 + 2*u**3 = 0.
-2, -1, 1/4, 1
Let t(m) = -m**2 + 4*m. Let d be t(2). Let r = -4/173 + 704/519. Suppose 0 + 4/3*u**d - r*u**2 + 4/3*u - u**3 - 1/3*u**5 = 0. What is u?
-1, 0, 1, 2
Let s(j) = j**3 - 9*j. Let m(x) = x. Let c(t) = 18*m(t) + 2*s(t). Let i(d) = -d**4 + 3*d**3. Let y(b) = 6*c(b) - 3*i(b). Find n, given that y(n) = 0.
-1, 0
Let b(r) be the second derivative of 2/15*r**6 - 4/5*r**5 + 0 + 5/3*r**4 - 4/3*r**3 + 8*r + 0*r**2. Determine h, given that b(h) = 0.
0, 1, 2
Let w(o) be the second derivative of -o**7/84 + o**6/15 - 5*o**4/12 + o**3/12 + 3*o**2/2 - 5*o - 1. Let w(k) = 0. What is k?
-1, 1, 2, 3
Let f be (4 - 2)/2 - (6 + -5). Suppose f = 6*r - 39 + 21. Let 0 + 2/9*w + 8/9*w**5 + 4/3*w**2 + 8/3*w**4 + 26/9*w**r = 0. What is w?
-1, -1/2, 0
Let b be 3/(-14) - ((-275)/630)/1. Suppose -8/9*l - 16/9 + 10/9*l**3 + b*l**4 + 4/3*l**2 = 0. Calculate l.
-2, 1
Factor -2 - 20*v + 15*v**2 + 175*v**3 + 9*v**2 - 4*v**2 + 2.
5*v*(5*v + 2)*(7*v - 2)
Suppose 736 - 4*w - 368 + 7*w**3 - 3*w**3 - 368 = 0. What is w?
-1, 0, 1
Suppose -291 = u - 296. Factor 900 - 4*j**4 - 900 + 4*j**u.
4*j**4*(j - 1)
Let v = 373 + -373. Let n(w) be the third derivative of 0*w + 0*w**5 - 1/20*w**6 + 1/4*w**4 + 1/70*w**7 + v - 1/2*w**3 - 6*w**2. Factor n(i).
3*(i - 1)**3*(i + 1)
Let i(n) = 10*n**4 - 22*n**3 + 12*n**2. Let r(f) = f**4 - f**3. Let m(k) = -i(k) + 12*r(k). Let m(s) = 0. Calculate s.
-6, 0, 1
Let v(j) = 3*j**3 + 12*j**2 - 13*j + 1. Let m be v(1). Factor -2/11*h + 2/11*h**m - 2/11*h**4 + 2/11*h**2 + 0.
-2*h*(h - 1)**2*(h + 1)/11
Let p(q) = q**4 + q**3 - q - 1. Let d(z) = 7*z - 1 + 3*z**2 - 2*z + 3 - 2*z**4 + 3 - 11*z**3. Let s(i) = -d(i) - 5*p(i). Find k, given that s(k) = 0.
0, 1
Let i(q) = -155*q + 622. Let b be i(4). Factor 3/5*l**b + 0*l - 3/5*l**3 + 0.
-3*l**2*(l - 1)/5
Let y be ((2 - 5) + 2)/((-3)/24). Suppose -3*t + 8 = q, -y = q - 8*t + 3*t. Factor 0 - 1/4*i**3 - 3/4*i**q - 1/2*i.
-i*(i + 1)*(i + 2)/4
Suppose 88*s**4 + 48*s**3 - 48*s + 140*s**2 + 53*s**4 - 144 - 137*s**4 = 0. Calculate s.
-6, -1, 1
Let i = 101/84 + -29/28. Factor 0*z**2 + 1/6*z**5 + 0*z**4 + i*z - 1/3*z**3 + 0.
z*(z - 1)**2*(z + 1)**2/6
Factor -17*t**2 - 208*t**3 - 1458*t + 206*t**3 - 91*t**2.
-2*t*(t + 27)**2
Let a = -144 - -67. Let k be 22/a + 2/7. Factor -1/2*g**2 - 1/2*g**4 + k*g + 0 + g**3.
-g**2*(g - 1)**2/2
Suppose 3*n - 9 = 0, j + 2*j - n = 6. Let -84 - 3*p**2 + 84 - 4*p**j + p = 0. Calculate p.
-1, 0, 1/4
Let x = 158/77 + -21/11. Let s(g) be the first derivative of 4/21*g**3 + 1/21*g**6 - x*g**2 - 4/35*g**5 + 0*g + 6 + 0*g**4. Determine o, given that s(o) = 0.
-1, 0, 1
Factor -53*u - 1120*u**2 - 9*u - 64 + 1122*u**2.
2*(u - 32)*(u + 1)
Let f(n) = -11*n**2 + 69*n + 98. Let a(t) = -t**2 - t + 3. Let q(h) = -6*a(h) + f(h). Factor q(c).
-5*(c - 16)*(c + 1)
Let b(o) be the first derivative of -35*o**6/6 - 33*o**5 - 40*o**4 + 20*o**3 - 101. Let b(w) = 0. What is w?
-3, -2, 0, 2/7
Let k(q) be the third derivative of 1/360*q**6 + 1/12*q**4 - 1/3*q**3 + 1/40*q**5 + 0*q + 6*q**2 + 0. Let y(t) be the first derivative of k(t). Factor y(v).
(v + 1)*(v + 2)
Let x(t) be the first derivative of t**4/26 + 70*t**3/39 + 67*t**2/13 + 66*t/13 - 51. Factor x(a).
2*(a + 1)**2*(a + 33)/13
Let n(v) be the third derivative of 8*v**2 - 1/18*v**3 + 0*v + 0 - 1/180*v**5 + 1/36*v**4. Find r, given that n(r) = 0.
1
Let s(v) be the first derivative of v**5/10 - v**4/12 - 7*v**2/2 - 46. Let m(n) be the second derivative of s(n). Find u such that m(u) = 0.
0, 1/3
Let y be 1*6 + -5 + 1. Factor 2*m**y - 6*m**4 - 3*m**4 + 7*m**4.
-2*m**2*(m - 1)*(m + 1)
Let u(o) = o**2 - 8*o - 4. Let p be u(9). Let d(w) = -w**3 + p + 6 + w - 12. Let b(j) = j**3 + 3*j**2 - 2*j + 2. Let m(v) = -b(v) - 2*d(v). Factor m(l).
l**2*(l - 3)
Let y(u) be the first derivative of 5*u**6/2 + 23*u**5 + 225*u**4/4 + 125*u**3/3 - 249. Determine b, given that y(b) = 0.
-5, -5/3, -1, 0
Suppose -2*b - 10 - 558 = 0. Let y = b + 287. Factor 0 + 1/3*p**y + 0*p**2 - 1/3*p**4 + 0*p.
-p**3*(p - 1)/3
Suppose 20664*h - 46 + 28*h**2 - 20292*h + 150 = 0. What is h?
-13, -2/7
Factor -758*p**2 - 1200 - 726*p - 1314*p - 471*p**3 + 307*p**2 - 27*p**4 - 776*p**2 + 165*p**3.
-3*(p + 4)**2*(3*p + 5)**2
Let q(l) = -l**3 + 25*l**2 - 22*l - 26. Let o be q(24). Let m be (-8)/22*(-11)/o. Factor -m*a**2 - 8/11 + 8/11*a.
-2*(a - 2)**2/11
Let z(d) be the second derivative of -d**5/120 - 5*d**4/36 + 23*d**3/36 - d**2 - 59*d + 2. Find r such that z(r) = 0.
-12, 1
Suppose 88*u**3 - 42/5*u**4 + 32/5 - 192/5*u + 32*u**2 - 98/5*u**5 = 0. What is u?
-2, -1, 2/7, 2
Let x be (-3 - (-18)/(-4))*4/(-6). Factor 25*y + 20*y**3 - 20 + x*y**4 + 18*y**2 - 15*y**3 - 3*y**2 - 30*y**3.
5*(y - 4)*(y - 1)**2*(y + 1)
What is q in -3820*q**2 + 0*q + 5*q**3 + 20*q + 1927*q**2 + 1918*q**2 = 0?
-4, -1, 0
Let g(a) be the third derivative of -a**6/120 - 3*a**5/40 - a**4/4 + 7*a**3/6 - 9*a**2. Let j(c) be the first derivative of g(c). Factor j(q).
-3*(q + 1)*(q + 2)
Let w(b) = 5*b**2 - 40*b + 3. Let t be w(8). Suppose -3*j - 2*j = 0. Suppose -2/5*m + j - 4/5*m**2 + 6/5*m**t = 0. Calculate m.
-1/3, 0, 1
Let w = -151/23 - -1717/230. Factor w*r**2 + 2/5 + 6/5*r.
(3*r + 2)**2/10
Let c(x) be the third derivative of -16*x**7/105 + 43*x**6/30 + 11*x**5/5 - 3*x**4 - 25*x**2 + 2. Find n, given that c(n) = 0.
-1, 0, 3/8, 6
Let t(z) be the first derivative of -z**4/10 - 3*z**3/5 + 2*z**2 + 12*z/5 - 15. Factor t(d).
-(d - 2)*(d + 6)*(2*d + 1)/5
Let c(d) be the first derivative of 3*d**4/4 + 20*d**3 - 129*d**2/2 + 66*d + 97. Factor c(l).
3*(l - 1)**2*(l + 22)
Suppose -21*w + 189 = 84. Let p(d) be the third derivative of -4/21*d**3 + 0 + 0*d - 1/210*d**w - 5*d**2 + 1/21*d**4. Factor p(h).
-2*(h - 2)**2/7
Suppose -16*h - 364 + 364 = 0. Let -1/4*a**3 + h - 1/2*a**2 + 0*a = 0. What is a?
-2, 0
Let d(w) be the second derivative of 1/90*w**6 + 0*w**2 + 0 + 1/9*w**3 - 1/12*w**4 + 31*w + 0*w**5. Factor d(i).
i*(i - 1)**2*(i + 2)/3
Determine p so that 20 + 18*p + 56 + 3*p**2 + 12*p - 4 = 0.
-6, -4
Let s(n) be the second derivative of n**4/8 + 11*n**3/4 - 63*n**2/2 - 180*n. Factor s(i).
3*(i - 3)*(i + 14)/2
Let i(w) be the third derivative of w**9/141120 + w**8/1960 + 3*w**7/245 + w**5/12 + w**3/6 - w**2. Let d(r) be the third derivative of i(r). Factor d(f).
3*f*(f + 12)**2/7
Let r(y) be the second derivative of y**4/18 + 19*y**3/3 - 58*y**2/3 + 391*y. Factor r(l).
2*(l - 1)*(l + 58)/3
Factor -58*c + 574*c**2 - 576*c**2 + 11 - 67.
-2*(c + 1)*(c + 28)
Suppose -60*w - 2395*w**3 + 670*w**2 + 0 + 48